Citations to Robert Fullér’s works, H-index: 31 (July 15, 2016)
Journal papers
[A4] Robert Fullér, József Mezei and Péter Várlaki, An improved index of interactivity for fuzzy numbers, FUZZY
SETS AND SYSTEMS, 165(2011) 56-66. doi 10.1016/j.fss.2010.06.001
in journals
A4-c7 Sadegh Niroomand, Ali Mahmoodirad, Ahmad Heydari, Fatemeh Kardani, Abdollah Hadi-Vencheh, An
extension principle based solution approach for shortest path problem with fuzzy arc lengths, INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH (to appear). 2016
http://dx.doi.org/10.1007/s12351-016-0230-4
In this section, some initial concepts of fuzzy set theory are presented which are used while dealing
with problems with fuzzy parameters (Zadeh 1987; Zimmermann 1996; Fullér et al. 2011; HadiVencheh and Mokhtarian 2011; Kumar and Kaur 2012).
A4-c6 Lucian Coroianu, Necessary and sufficient conditions for the equality of the interactive and non-interactive
sums of two fuzzy numbers, FUZZY SETS AND SYSTEMS, 283(2016), pp. 40-55. 2016
http://dx.doi.org/10.1016/j.fss.2014.10.026
A4-c5 Dug Hun Hong, Jae Duck Kim, The Lower Limit for Possibilistic Correlation Coefficient, APPLIED
MATHEMATICAL SCIENCES, 9(2015), number 121, pp. 6041-6047. 2015
http://dx.doi.org/10.12988/ams.2015.58520
Recently, Fullér et al. [Fuzzy Sets and Systems, 2011] introduced a new f -weighted index of
interactivity, ρf (A, B), between marginal possibility distributions A and B of a joint possibility
distribution C for any weighting function f . They also left two open questions in connection with
the lower limit for f -weighted possibilistic correlation coefficient related to the improved index of
interactivity. In this paper, we obtain a more general result than the suggested open problem, and
hence completely prove this open question. (page 6041)
Fullér and Majlender [A7] defined a measure of possibilistic correlation between marginal possibility distributions of a joint possibility distribution as the f -weighted average of probabilistic
covariances between marginal probability distributions whose joint probability distribution is defined to be uniform on the γ-level sets of their joint possibility distribution. Carlsson and Fullér
[A6] defined the same measure as their possibilistic covariance divided by the square root of the
product of their possibilistic variances. There is a drawback to the measure of possibilistic correlation introduced in [A6]: it does not necessarily take its values from [−1, 1] if some level sets of the
joint possibility distribution are not convex. A new normalization technique is needed. Recently,
Fullér et al. [A4] introduced a new index of interactivity between marginal distributions of a joint
possibility distribution; the index is defined for a whole family of joint possibility distributions.
At the end of their paper, they proposed two open questions as follows:
1. Can we define a joint possibility distribution C with the non-symmetrical but identical marginal
distributions A(x) = B(x) = (1 − x) or all x ∈ (0, 1] and a weighting function f for which
ρf (A, B) could go below the value of -3/5?
2. What is the lower limit for f-weighted possibilistic correlation coefficient ρf (A, B) between
non-symmetrical marginal possibility distributions with the same membership function A = B?
Recently, Harmati [4] proved the open question. In this paper, we obtained a more general results
that the suggested open question. In this regard, we consider the open questions and prove them.
(page 6042)
1
Fullér et al. [A4] guessed that for the non-symmetrical, but identical marginal distributions,
A(x) = B(x) = (1 − x), for all x ∈ [0, 1], one cannot define any joint possibility distribution and any f for which ρf (A, B) could go below the value of -3/5. They also left the lower limit
for f-weighted possibilistic correlation co-efficient between non-symmetrical marginal possibility
distributions with the same membership function as an open question. In the following section, we
prove that inf C sup0<γ≤1 ρ(Xγ , Yγ ) = −1 for non-symmetrical marginal possibility distributions
with the same membership function, A(x) = B(x) = (1 − x), for all x ∈ [0, 1]. This immediately
proves these open questions suggested by Fullér et al. [A4] (page 6043)
A4-c4 Arnold F Shapiro, Fuzzy post-retirement financial concepts: an exploratory study, METRON, 71(2013),
issue 3, pp 261-278. 2013
http://dx.doi.org/10.1007/s40300-013-0028-6
A4-c3 Zhang Xili, Zhang Weiguo, Xiao Weilin, Multi-period portfolio optimization under possibility measures,
Economic Modelling 35(2013), pp. 401-408.
http://dx.doi.org/10.1016/j.econmod.2013.07.023
A4-c2 István Á. Harmati, A note on f-weighted possibilistic correlation for identical marginal possibility distributions, FUZZY SETS AND SYSTEMS, 165(2011) 106-110. 2011
http://dx.doi.org/10.1016/j.fss.2010.11.005
Fullér, Mezei and Várlaki defined the f -weighted possibilistic correlation coefficient as a new
measure of interactivity of fuzzy numbers, which can be determined from the joint possibility
distribution. At the end of their paper they formulated problems in connection with the lower limit
of the f-weighted possibilistic correlation coefficient, if we know only the marginal distributions.
In this paper we will discuss these problems. (page 106)
in proceedings and edited volumes
A4-c1 Arnold F Shapiro, Fuzzy Post-Retirement Solvency Concepts: Some Preliminary Observations, 45th
Actuarial Research Conference, July 26-28, 2010, Simon Fraser University, Burnaby, Canada, pp. 1-9.
2010
http://www.soa.org/library/proceedings/arch/2011/arch-2011-iss1-shapiro.pdf
The interested reader will find an overview of FRVs, from an actuarial perspective, in Shapiro
(2009), and discussions of such topics as the expected value, variance, covariance and correlation
of FRVs in Kwakernaak (1978, 1979), Kruse and Meyer (1987), Puri and Ralescu (1986), Körner
(1997), Watanabe and Imaizumi (1999), Feng et al. (2001), Näther (2001), Couso and Dubois
(2009) and Fullér et al (2010). (page 3)
[A5] Christer Carlsson, Robert Fullér, Markku Heikkilä and Péter Majlender, A fuzzy approach to R&D project
portfolio selection, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 44(2007) 93-105.
[MR2295331] doi 10.1016/j.ijar.2006.07.003
in journals
2016
A5-c135 V Mohagheghi, S M Mousavi, B Vahdani, M R Shahriari, R&D project evaluation and project portfolio selection by a new interval type-2 fuzzy optimization approach, NEURAL COMPUTING & APPLICATIONS (to appear). 2016
http://dx.doi.org/10.1007/s00521-016-2262-3
Wang and Hwang [62] used a fuzzy zero-one integer programming model that considered uncertain and flexible parameters to achieve optimal project portfolio. The fuzzy nature of uncertain
elements was not fully addressed in this model. Carlsson et al. [A5] applied trapezoidal fuzzy
numbers to predict future cash flow and developed a fuzzy mixed integer programming model.
Since this model was based on classical fuzzy sets, it could not be effective under highly uncertain
environments.
2
A5-c134 Ming-Gao Dong, Shou-Yia Li, Project investment decision making with fuzzy information: A literature review of methodologies based on taxonomy, JOURNAL OF INTELLIGENT & FUZZY SYSTEMS,
30: (6) pp. 3239-3252. 2016
http://dx.doi.org/10.3233/IFS-152068
A5-c133 Andreas Lundell, Kaj-Mikael Björk, Global optimisation of a portfolio adjustment problem under
credibility measures, INTERNATIONAL JOURNAL OF OPERATIONAL RESEARCH, Volume 25, Issue
4, 2016, Pages 464-474. 2016
http://dx.doi.org/10.1504/IJOR.2016.075292
A5-c132 Fatemeh Hossein Ali Parvaneh Sameh Monir El-Sayegh, Project selection using the combined approach of AHP and LP, JOURNAL OF FINANCIAL MANAGEMENT OF PROPERTY AND CONSTRUCTION, 21: (1), pp. 39-53. 2016
http://www.emeraldinsight.com/doi/abs/10.1108/JFMPC-09-2015-0034
A5-c131 Renard Yung Jhien Siew, Integrating sustainability into construction project portfolio management,
KSCE JOURNAL OF CIVIL ENGINEERING, 20(2016), issue 1, pp. 101-108. 2016
http://dx.doi.org/10.1007/s12205-015-0520-z
A review of the literature reveals that much of the discussion in this area has taken a narrow focus
on company’s financial objectives (Meskendahl, 2010), resource constraints (Gutjahr et al., 2008;
Gutjahr et al., 2010; Stummer et al., 2009) and refinement of portfolio analysis methods (see
Doerner et al., 2006; Carlsson et al., 2007; Hu et al., 2008; Carazo et al., 2010) with little or no
consideration for sustainability issues. There are myriad of definitions available for sustainability
or sustainable development. (page 101)
2015
A5-c130 S. Samantha Bastiani, Laura Cruz-Reyes, Eduardo Fernandez, Claudia Gomez, Portfolio Optimization From a Set of Preference Ordered Projects Using an Ant Colony Based Multi-objective Approach,
International Journal of Computational Intelligence Systems, Volume 8, Supplement 2, pp. 41-53. 2015
http://dx.doi.org/10.1080/18756891.2015.1129590
A5-c129 Wei-dong Zhu, Fang Liu, Yu-wang Chen, Jian-bo Yang, Dong-ling Xu, Dong-peng Wang, Research
project evaluation and selection: an evidential reasoning rule-based method for aggregating peer review
information with reliabilities, SCIENTOMETRICS, 105(2015), number 3, pp. 1469-1490. 2015
http://dx.doi.org/10.1007/s11192-015-1770-8
Many methods and techniques have been presented to deal with research project evaluation and
selection, which tend to be either qualitative or quantitative. According to Henriksen and Traynor
(1999), project evaluation and selection methods can be categorized into unstructured peer review, scoring, mathematical programming, economic models, decision analysis, interactive methods, artificial intelligence, portfolio optimization, etc. An organizational decision support system
(ODSS) architecture has been proposed to support R&D project selection from organizational
decision-making perspective, which focuses on the whole life cycle of the selection process (Tian
et al. 2005). Data envelopment analysis (DEA) has been illustrated to be a useful method for
dividing projects into different groups, and it does not require variables to have the same scale or
conversion weight. It is an ideal solution for the comparison of research projects that potentially
have many different non-cost and non-numeric variables (Linton et al. 2002). Huang et al. (2008)
employs fuzzy numbers to represent subjective expert judgments, and the fuzzy analytic hierarchy process method is utilized to identify the most important evaluation criteria. For selecting an
appropriate portfolio of research projects, a fuzzy mixed integer programming model for valuing
options on R&D projects is developed, and future cash flows are considered to be trapezoidal
fuzzy numbers (Carlsson et al. 2007). (page 1471)
A5-c128 Hall NG, Long DZ, Qi J, Sim M, Managing underperformance risk in project portfolio selection,
OPERATIONS RESEARCH, 63(2015), number 3, pp. 660-675. 2015
http://dx.doi.org/10.1287/opre.2015.1382
3
A5-c127 Farshad Faezy Razi, Abbas Toloie Eshlaghy, Jamshid Nazemi, Mahmood Alborzi, Alireza Poorebrahimi, A hybrid grey-based fuzzy C-means and multiple objective genetic algorithms for project portfolio selection, International Journal of Industrial & Systems Engineering, 21(2015), number 2, pp. 154-179.
2015
http://dx.doi.org/10.1504/IJISE.2015.071503
A5-c126 Vahid Mohagheghi S Meysam Mousavi, Behnam Vahdani, A New Optimization Model for Project
Portfolio Selection Under Interval-Valued Fuzzy Environment, ARABIAN JOURNAL FOR SCIENCE
AND ENGINEERING, Volume 40, Issue 11, 1 November 2015, Pages 3351-3361. 2015
http://dx.doi.org/10.1007/s13369-015-1779-6
A5-c125 Don Jyh-Fu Jeng, Kuo-Hsin Huang, Strategic project portfolio selection for national research institutes,
JOURNAL OF BUSINESS RESEARCH, 68(2015), pp. 2305-2311. 2015
http://dx.doi.org/10.1016/j.jbusres.2015.06.016
A5-c124 Rupak Bhattacharyya, A Grey Theory Based Multiple Attribute Approach for R&D Project Portfolio
Selection, FUZZY INFORMATION AND ENGINEERING, 7(2015), number 2, pp. 211-225. 2015
http://dx.doi.org/10.1016/j.fiae.2015.05.006
A5-c123 Fátima Pérez, Rafael Caballero, Ana F Carazo, Trinidad Gómez, Vicente Liern, A multiobjective
fuzzy model for selecting and planning a project portfolio in a public organisation, International Journal of
Engineering Management and Economics, 5(2015), issue 1-2, pp. 48-58. 2015
http://dx.doi.org/10.1504/IJEME.2015.069893
A5-c122 Olga Kokshagina, Pascal Le Masson, Benoit Weil, Patrick Cogez, Portfolio Management in Double
Unknown Situations: Technological Platforms and the Role of Cross-Application Managers, CREATIVITY
AND INNOVATION MANAGEMENT, 25: (2) pp. 270-291. 2015
http://dx.doi.org/10.1111/caim.12121
A5-c121 Irem Ucal Sari, Cengiz Kahraman, Interval Type-2 Fuzzy Capital Budgeting, INTERNATIONAL
JOURNAL OF FUZZY SYSTEMS, 17: (4) pp. 635-646. 2015
http://dx.doi.org/10.1007/s40815-015-0040-5
A5-c120 Giovanna Lo Nigro, Azzurra Morreale, Lorenzo Abbate, An Open Innovation Decision Support System to Select a Biopharmaceutical R&D Portfolio, MANAGERIAL AND DECISION ECONOMICS: THE
INTERNATIONAL JOURNAL OF RESEARCH AND PROGRESS IN MANAGEMENT ECONOMICS
(to appear). 2015
http://dx.doi.org/10.1002/mde.2727
A5-c119 Kayvan Salehi, A hybrid fuzzy MCDM approach for project selection problem, Decision Science
Letters, 4(2015), pp. 109-116. 2015
http://dx.doi.org/10.5267/j.dsl.2014.8.003
A5-c118 Majid Shakhsi-Niaei, Morteza Shiripour, Hamed Shakouri G, Seyed Hossein Iranmanesh, Application
of Genetic and Differential Evolution Algorithms on selecting portfolios of projects with consideration of
interactions and budgetary segmentation, International Journal of Operational Research, 22(2015), number
1, pp. 106-128. 2015
Gabriel et al. (2006) proposed a unique multi-objective project selection model with probability
distributions to describe costs and incorporating Monte Carlo simulation and AHP. Carlsson et al.
(2007) presented a fuzzy mixed-integer programming model for R&D portfolio selection problem.
Huang (2007) incorporated random fuzzy uncertainty into project selection by integrating genetic
algorithm with random fuzzy simulation.
A5-c117 Ching-Torng Lin, Yuan-Shan Yang, A Linguistic Approach to Measuring the Attractiveness of New
Products in Portfolio Selection, Group Decision and Negotiation, 24(2015), issue 1, pp. 145-169. 2015
http://dx.doi.org/10.1007/s10726-014-9384-8
To balance risk and revenue, align projects with strategy, and estimate the value of R&D project
options, Carlsson and Fuller (2007) incorporated future cash flow estimates into their portfolio
4
selection model. Wang and Hwang (2007) considered each stage of a new product project similar
to purchasing an option on a future investment, and developed a fuzzy real-options valuation
model, combined with fuzzy integer linear programming, t o conduct portfolio selection. (page
148)
NPD is a complex process and a business risk. NPD requires substantial monetary and nonmonetary commitments, but the costs of the consequences of failure are even greater. The CEO of BIT
has mandated that all new product proposals must be thoroughly analyzed and evaluated before
undergoing full-scale development. BIT seeks to develop an attractive and integrated portfolio
containing high-value projects, with an appropriate balance in the type and number of projects.
As suggested by previous studies (Dickinson et al. 2001; Lin and Hsieh 2004; Carlsson and Fuller
2007; Killen et al. 2012; Ho et al. 2013), BIT established a framework for new product portfolio
selection, revised most recently in 2013, as shown in Fig. 2. (page 153)
This study provides potential value to companies by offering a rational structure to reflect on
imprecise or ambiguous phenomena commonly present in many business environments, and accounting for the uncertainty of each factor to assure a reasonably realistic and sharp evaluation.
This study is potentially valuable to researchers in its demonstration of still another application of
fuzzy logic. Furthermore, compared with existing studies (Lin and Hsieh 2004; Chen et al. 2006,
2007; Carlsson and Fuller 2007; Wang and Hwang 2007; Lin et al. 2010; Wei and Chang 2011),
the proposed approach offers the following distinct features: (page 166)
2014
A5-c116 Gaston S Milanesi, Diego Broz, Fernando Tohme, Daniel Rossit, Strategic Analysis Of Forest Investments Using Real Option: The Fuzzy Pay-Off Model (Fpom), Fuzzy Economic Review, XIX(2014), issue
1, pp. 33-44. 2014
A5-c115 C C Popescu, A Fuzzy Optimization Model, ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, 48(2014), number 2, pp. 201-213. 2014
WOS: 000338090100012
A5-c114 Aimin Heng, Qian Chen, Yingshuang Tan, Fuzzy Optimization of Option Pricing Model and Its Application in Land Expropriation, JOURNAL OF APPLIED MATHEMATICS 2014(2014), Paper 635898.
2014
http://dx.doi.org/10.1155/2014/635898
The B-S pricing formula usually uses the random probability to represent the uncertain factors, but
in practical problems it often contains fuzziness and the fuzzy theory is a powerful tool to deal with
them. With the precondition of considering the fuzziness of pricing parameters, many scholars
have improved the classical theory of real option pricing. Carlsson et al. [1, 2] introduced the
fuzzy concept to the traditional Black-Scholes model (B-S model), publishing a series of research
results on fuzzy real option; for example, Yoshida [3] established the fuzzy real option model and
of traditional B-S model, it used trapezoidal fuzzy number to estimate the net present value of
expected cash flows and introduced the concepts of mean value and variance of probability. (page
1)
A5-c113 Hassanzadeh Farhad, Modarres Mohammad, Nemati Hamid R, Amoako-Gyampah Kwasi, A Robust
R&D Project Portfolio Optimization Model for Pharmaceutical Contract Research Organizations, International Journal of Production Economics (to appear). 2014
http://dx.doi.org/http://dx.doi.org/10.1016/j.ijpe.2014.07.001
Our formulated model allows for reinvestment of revenues generated from successfully delivered
R&D projects as an alternative to borrowing from a financial institution. Third, R&D projects
usually have long life cycles and are very imprecise and uncertain in terms of cash flow estimates
compared to non-R&D projects (Carlsson et al. 2007).
A5-c112 Hassanzadeh F, Nemati H, Sun M, Robust optimization for interactive multiobjective programming
with imprecise information applied to R&D project portfolio selection, European Journal of Operational
Research, 238: (1) pp. 41-53. 2014
http://dx.doi.org/10.1016/j.ejor.2014.03.023
5
R&D is often an original endeavor with long lead time and unclear life time expenditure, resource
usage and market outcome. These unique characteristics imply that much of the information required in making R&D decisions is very imprecise and impossible to accurately estimate. To
address uncertainties, probabilistic and fuzzy approaches have been proposed to capture the imprecision of data by considering reasonable distributions to describe possible values of imprecise
coefficients in optimization models. One drawback of such approaches is, however, that they cannot handle the situation where there is a possible range for each of these coefficients, but the most
probable or plausible value within the range cannot be estimated (Carlsson, Fullér, Heikkilä, &
Majlender, 2007). This calls for novel approaches which can more adequately capture the realworld situation of R&D project portfolio selection. (page 41)
A5-c111 Hassanzadeh Farhad, Nemati Hamid, Sun Minghe, Imprecise Information Applied to R&D Project
Portfolio Selection, European Journal of Operational Research (to appear). 2014
http://dx.doi.org/http://dx.doi.org/10.1016/j.ejor.2014.03.023
A5-c110 F Perez, T Gomez, Multiobjective project portfolio selection with fuzzy constraints, Annals of Operations Research (to appear). 2014
http://dx.doi.org/10.1007/s10479-014-1556-z
A5-c109 Laura Cruz, Eduardo Fernandez, Claudia Gomez, Gilberto Rivera, Fatima Perez, Many-Objective Portfolio Optimization of Interdependent Projects with ’a priori’ Incorporation of Decision-Maker Preferences,
Applied Mathematics & Information Sciences, 8(2014), No. 4, pp. 1517-1531. 2014
http://dx.doi.org/10.12785/amis/080405
A5-c108 Abbassi Mohammad, Ashrafi Maryam, Sharifi Tashnizi Ebrahim, Selecting balanced portfolios of
R&D projects with interdependencies: A Cross-Entropy based methodology, Technovation, 34(2014), number 1, pp. 54-63. 2014
http://dx.doi.org/10.1016/j.technovation.2013.09.001
Fang et al. (2008) proposed a scenario generation approach for the mixed single-stage R&D
projects and multi-stage securities portfolio selection problem. Huang et al. (2008) presented
a fuzzy analytic hierarchy process method for R&D project selection. R&D portfolio selection
problem as a fuzzy zeröone integer programming model which could handle both uncertain and
flexible parameters was formulated by Wang and Hwang (2007) and Carlsson et al. (2007). (page
55)
A5-c107 Rafiee Majid, Kianfar Farhad, Farhadkhani Mehdi, A multistage stochastic programming approach
in project selection and scheduling, The International Journal of Advanced Manufacturing Technology,
Volume 70, Issue 9-12, February 2014, Pages 2125-2137. 2014
http://dx.doi.org/10.1007/s00170-013-5362-6
The project portfolio selection models can be presented based on linear [9, 15], non-linear [10,
11], integer [10, A5], dynamic [17, 18], goal [10, 19], fuzzy [A5, 20], and stochastic mathematical
programming [21]. Methods such as decision-tree approach [22], game-theoretical approach [23],
simulation models [17, 24] and heuristic methods [18, 25] have been utilized for solving these
problems as well [7]. (page 2126)
2013
A5-c106 Huei-Wen Lin, Huei-Fu Lu, Evaluating the BOT project of sport facility: an application of fuzzy net
present value method, Journal of Industrial and Production Engineering, 30(2013), issue 4, 220-229. 2013
http://dx.doi.org/10.1080/21681015.2013.818067
A5-c105 Sadoullah Ebrahimnejad, Mohammad Hossein Hosseinpour, Ali Mohammadi Nasrabadi, A fuzzy biobjective mathematical model for optimum portfolio selection by considering inflation rate effects, The
International Journal of Advanced Manufacturing Technology, 69(2013), number 1-4, pp. 595-616. 2013
http://dx.doi.org/10.1007/s00170-013-5052-4
6
A5-c104 Collan M, Fedrizzi M, Luukka P, A multi-expert system for ranking patents: An approach based on
fuzzy pay-off distributions and a TOPSIS-AHP framework, Expert Systems with Applications, 40(2013),
number 12, pp. 4749-4759. 2013
http://dx.doi.org/10.1016/j.eswa.2013.02.012
Possibilistic skewness in this context can be interpreted as a measure of potential. The more
the triangular fuzzy number (the value of the patent) is skewed towards the right (high values)
the better. Skewness has, in other words, a relationship with the real option value, a measure
of potential also used in the analysis of patents and Rand D projects (see e.g., Carlsson, Fuller,
Heikkilä, and Majlender, 2007; Hassanzadeh et al., 2012; Mathews & Salmon, 2007). (page 4573)
A5-c103 Lilian Noronha Nassif, Joao Carlos Santiago Filho, Jose Marcos Nogueira, Project Portfolio Selection
in Public Administration Using Fuzzy Logic, Procedia - Social and Behavioral Sciences, 74(2013), pp.
322-331. 2013
http://dx.doi.org/10.1016/j.sbspro.2013.03.036
The literature presents new methods of project selection using fuzzy logic. Carlsson et al. (2007)
use fuzzy logic to select projects of research and development (R & D) with the objective of
avoiding inaccuracies of return. (page 323)
A5-c102 Nitin T Patil, S M Sawant, SHOP MANAGEMENT COMPRISING OF RESEARCH PROJECT PROTOTYPE AT RESEARCH & DEVELOPMENT WORKSHOP, International Journal of Advanced Engineering Research and Studies,2(2013), issue 4, pp. 11-13. 2013
Christer Carlsson et al. (1) said that innovations are unpredictable, and thus involve large uncertainties with respect to both the development of opportunities in existing product market and those
in production processes. R&D projects possess the following properties: (i) long life cycles (taking into account their possible impacts on other investments), (ii) uncertain (i.e. vague), sometimes
overly optimistic or pessimistic future cash flow estimates,(iii) uncertain (i.e. biased), sometimes
questionable profitability estimates, (iv) imprecise assessments of future effects on productivity,
market positions, competitive advantages and shareholder value, and v) the ability to generate
series of further investments
2012
A5-c101 Bhattacharyya Rupak, Kumar Pankaj, Kar Samarjit, Mondal Seema Sarkar, Portfolio Selection of
Interdependent R&D Projects, INDIAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS,
3(2012), number 1, pp. 62-73. 2012
http://www.indianjournals.com/ijor.aspx?target=ijor:ijiam&volume=3
&issue=1s&article=005
A5-c100 Wu Y, Qiu W-H, Zhou P, Real option model under fuzzy group decision making, Kongzhi yu Juece/Control
and Decision, 27(2012), number 12, pp. 1828-1832+1838. 2012
Scopus: 84872239869
A5-c99 Yingshuang Tan and Yong Long, Option-Game Approach to Analyze Technology Innovation Investment under Fuzzy Environment, JOURNAL OF APPLIED MATHEMATICS, Volume 2012, Article ID
830850. 2012
http://dx.doi.org/10.1155/2012/830850
A5-c98 Hassanzadeh F, Collan M, Modarres M, A practical approach to R&D portfolio selection using the
fuzzy pay-off method, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 20(2012), number 4, pp. 615622. Paper 6109284. 2012
http://dx.doi.org/10.1109/TFUZZ.2011.2180380
A5-c97 Danmei Zhu, Xingtong Wang, A Petroleum R&D Project Portfolio Investment Selection Model with
Project Interactions under Uncertainty, JOURNAL OF PETROLEUM SCIENCE RESEARCH, 1(2012),
number 3, pp. 44-50. 2012
7
http://www.jpsr.org/paperInfo.aspx?ID=3675
However, there are still two problems. First, these selection models obtain optimal solutions by
exact mathematical relationships between the objectives and constraints in model. But the R&D
project portfolio decision deals with future events and opportunities, much of the information
required making portfolio decisions is at best uncertain and at worst very unreliable. Second, the
problem of project interactions has long been recognized but has received relatively little attention
in the R&D project selection literatures [A5-6].
A5-c96 Mohammad Abbassi, Maryam Ashrafi, Variable Neighborhood Search for R&D Project Portfolio Selection with Interdependencies, INTERNATIONAL JOURNAL OF MODERN SCIENCE AND TECHNOLOGY 2012(2012), 1-14. 2012
A5-c95 Chen L-H, Yin W-L, Fang Y, Chen C, Scenario generation model for single stage R&D projects and
securities portfolio optimization, Xitong Gongcheng Lilun yu Shijian/System Engineering Theory and Practice, 32(2012), number 8, pp. 1639-1646. 2012
Scopus: 84867420390
A5-c94 Wang Y-S, Liang C-Y, Ju Y-Z, Multi-phase rolling optimization model of project portfolio selection
under uncertainty, Xitong Gongcheng Lilun yu Shijian/System Engineering Theory and Practice, 32(2012),
number 6, pp. 1290-1297. 2012
Scopus: 84865303210
A5-c93 Von Ahsen A, Heesen M, Prozessbegleitende Innovationsbewertung - Entscheidungssituationen und
Auswirkungen auf die Anwendbarkeit d es Realoptionsansatzes,Betriebswirtschaftliche Forschung und
Praxis, 64(2012), number 4, pp. 444-463. 2012
Scopus: 84865112782
A5-c92 Babak Amiri, A Multi-Objective Hybrid Optimization Algorithm for Project Selection Problem, JOURNAL OF BASIC AND APPLIED SCIENTIFIC RESEARCH, 2(2012), number 7, pp. 6995-7002. 2012
Carlsson, Fullér, Heikkilä, and Majlender [A5] presented a fuzzy mixed-integer programming
model for R&D portfolio selection problem. Huang [12] incorporated random fuzzy uncertainty
into project selection by integrating genetic algorithm with random fuzzy simulation. (page 6995)
A5-c91 Frederic J Villeneuve, Dimitri N Mavris, Aircraft technology portfolio optimization using ant colony
optimization, ENGINEERING OPTIMIZATION, Volume 44, Issue 11, 1 November 2012, Pages 13691387. 2012
http://dx.doi.org/10.1080/0305215X.2011.649747
A5-c90 Doraid Dalalah, Mohammad Al-Tahat, Khaled Bataineh, Mutually dependent multi-criteria decision
making, FUZZY INFORMATION AND ENGINEERING, 4(2012), number 2, pp. 195-216. 2012
http://dx.doi.org/10.1007/s12543-012-0111-3
A5-c89 Kamran Shahanaghi, Armin Jabbarzadeh, Mohammadreza Hamidi, Mohammadreza Ghodoosi, Selecting the Most Economic Project under Uncertainty Using Bootstrap Technique and Fuzzy Simulation,
Iranian Journal of Management Studies, 5(2012), number 1, pp. 9-24. 2012
http://www.ijms.ir/pg/06/IJMS05101.pdf
Investment risks embedded in many realistic issues such as research and development (R&D) and
developing new products (DNP), would result in a decision to survive or die. Under uncertainty
and risk, the reality of lack of reliable information can’t be hidden or ignored (Carlsson et al.,
2007).
A5-c88 H Khademizare, T Aliheidari Bioki, Finding a Probabilistic Approach to Develop a Fuzzy Expert System for the Assessment of Research Projects using ANP Approach, INTERNATIONAL JOURNAL OF
INDUSTRIAL ENGINEERING & PRODUCTION RESEARCH, 23(2012), number 2, pp. 143-153. 2012
ijiepr.iust.ac.ir/files/site1/user_files/admin-A-10-1-138-f069807.pdf
8
A5-c87 Adrian I Ban, Lucian Coroianu, Nearest interval, triangular and trapezoidal approximation of a fuzzy
number preserving ambiguity, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 53(2012),
number 5, pp. 805-836. 2012
http://dx.doi.org/10.1016/j.ijar.2012.02.001
A5-c86 Madjid Tavana, Faramak Zandi, Applying fuzzy bi-dimensional scenario-based model to the assessment
of Mars mission architecture scenarios, ADVANCES IN SPACE RESEARCH, 49(2012), issue 4, pp. 629647. 2012
http://dx.doi.org/10.1016/j.asr.2011.11.019
Next, we use the approach proposed by Carlsson et al. (2007) to determine the following expected
value of the total benefits, total costs and real option values for each non-dominated mission
scenario; (page 638)
A5-c85 F. Hassanzadeh, M. Collan, M. Modarres, A practical R&D selection model using fuzzy pay-off method,
INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY, 58(2012), numbers 1-4, pp. 227-236. 2012
http://dx.doi.org/10.1007/s00170-011-3364-9
The FROV is used by several authors, e.g., Carlsson et al. [A5] who considered a situation where
each candidate project either absorbs its budget and starts immediately or is postponed to a future
time period at a particular cost. They used FROV reasoning to compute the deferral flexibility of
each project and then developed a fuzzy zeröone integer programming model to determine projects
that must immediately start in order to maximize aggregate possibilistic deferral flexibility subject
to budget availability. (page 229)
The model presented in [A5] is a version of the Black-Scholes option valuation formula that uses
fuzzy inputs; the model assumes that there is a geometric Brownian motion compatible underlying
process that determines the asset value and the resulting probability distribution and hence is a
hybrid of fuzzy inputs (possibility theory) and probability theory. Datar and Mathews [21] do
not assume that there is a singular underlying process behind asset value, but uses scenarios as
an input into a Monte-Carlo simulation which eventually generates a probability distribution and
hence relies on probability theory. The method used in this paper, the payoff method, is based on
possibility theory – the distribution of expected present value is created from fuzzy cash-flows and
is a fuzzy number (possibility distribution). From this fuzzy number, the real option value can be
calculated by using the pay-off method. (page 229)
2011
A5-c84 Faramak Zandi, Madjid Tavana, A Fuzzy Goal Programming Model for Strategic Information Technology Investment Assessment, BENCHMARKING: AN INTERNATIONAL JOURNAL, 18(2011), issue 2,
pp. 1-34. 2011
http://www.emeraldinsight.com/journals.htm?articleid=1905896&show=abstract
A5-c83 P. J. Trotter, A new modified total front end framework for innovation: New insights from health related
industries, INTERNATIONAL JOURNAL OF INNOVATION MANAGEMENT, 15(2011), number 5, pp.
1013-1041. 2011
http://dx.doi.org/10.1142/S1363919611003519
A5-c82 Qun Zhang, Xiaoxia Huang, Leming Tang, Optimal multinational capital budgeting under uncertainty,
COMPUTERS AND MATHEMATICS WITH APPLICATIONS, 62(2011), number 12, pp. 4557-4567.
2011
http://dx.doi.org/10.1016/j.camwa.2011.10.035
Monte Carlo simulation was used [15] to evaluate the expected return and the risk of a project,
and an evolutionary method was proposed to handle multiple stochastic objectives for the project
selection problem [16]. When parameters were treated as fuzzy numbers, Carlsson et al. [A5]
proposed a fuzzy mixed integer programming selection model for R & D projects. Wei et al. [18]
used fuzzy set theory to resolve the ambiguities involved in assessing supply chain management
alternatives and aggregating the linguistic evaluations. (page 4558)
9
ThusfA14-c1 the uncertainty of parameters is of subjective uncertainty rather than randomness.
Many scholars argued that in this situation we should find another way to describe the project
uncertainty, and some of them have tried using fuzzy set theory or credibility theory to solve the
different domestic capital budgeting problems in this situation, e.g., Carlsson et al. [A5], Huang
[22], and Bas and Kahraman [19] etc. However, with the deeper research on the problem, we find
that paradoxes will appear if we use fuzzy variable to describe the subjective estimation of project
parameters. (page 4558)
A5-c81 ZHANG Weiguo, MEI Qin, CHEN Chiwen, Optimization Method on Multi-Project Portfolio with
Fuzzy Returns CHINESE JOURNAL OF MANAGEMENT, 8(2011), number 6, pp. 938-942 (in Chinese).
2011
www.glxb.ac.cn/CN/article/downloadArticleFile.do?attachType=PDF&id=9697
A5-c80 Rupak Bhattacharyya; Pankaj Kumar; Samarjit Kar, Fuzzy R&D portfolio selection of interdependent
projects, COMPUTERS AND MATHEMATICS WITH APPLICATIONS, 62(2011), number 10, pp. 38573870. 2011
http://dx.doi.org/10.1016/j.camwa.2011.09.036
The R&D portfolio selection problem is formulated as a zeröone integer programming model
that can handle both uncertain and flexible parameters to determine the optimal project portfolio. Carlsson et al. [A5] consider a methodology for valuing options on R&D projects. They
estimate the future cash flows by trapezoidal fuzzy numbers. They also develop a fuzzy mixed
integer programming model for the R&D optimal portfolio selection problem and discuss how
the methodology can be used to build decision support tools for optimal R&D project selection in
corporate environment. (page 3858)
A5-c79 Wei-Guo Zhang, Qin Mei, Qian Lu, Wei-Lin Xiao, Evaluating methods of investment project and optimizing models of portfolio selection in fuzzy uncertainty, COMPUTERS & INDUSTRIAL ENGINEERING, 61(2011), number 3, pp. 721-728. 2011
http://dx.doi.org/10.1016/j.cie.2011.05.003
They also stated that the proposed framework presented in that paper can facilitate the complex
SCM selection process and consolidate efforts to enhance group decision-making process. Carlsson, Fullér, Heikkila, and Majlender (2007) used trapezoidal fuzzy numbers to estimate future
cash flows and presented a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem. (page 721)
A5-c78 Shiu-Hwei Ho, Shu-Hsien Liao, A fuzzy real option approach for investment project valuation, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), issue 12, pp. 15296-15302. 2011
http://dx.doi.org/10.1016/j.eswa.2011.06.010
Carlsson, Fuller, Heikkila, and Majlender (2007) also developed a methodology for valuing options on R&D projects, in which future cash flows were estimated by trapezoidal fuzzy numbers.
In particular, they presented a fuzzy mixed integer programming model for the R&D optimal
portfolio selection problem. (page 15297)
A5-c77 Adiel Teixeira de Almeida, Marina D. O. Duarte, A MULTI-CRITERIA DECISION MODEL FOR
SELECTING PROJECT PORTFOLIO WITH CONSIDERATION BEING GIVEN TO A NEW CONCEPT
FOR SYNERGIES, Pesquisa Operacional, 31(2011), number 2, pp. 301-316. 2011
http://dx.doi.org/10.1590/S0101-74382011000200006
A5-c76 Manish Arora, M Syamala Devi, A Fuzzy-AHP Approach to Solve Multi Criteria Budget Allocation
Problem, INTERNATIONAL JOURNAL OF COMPUTER SCIENCE ENGINEERING AND TECHNOLOGY, 1(2011), number 6, pp. 284-289. 2011
http://www.ijcset.net/docs/Volumes/volume1issue6/ijcset2011010605.pdf
NPV and other discounted cash flow methods are inappropriate in research and development
project selection as they favor short-term projects not longterm projects where market is uncertain
[A5]. Problem arises when non-economic benefits are considered. The Operational Research uses
10
mathematical programming techniques to optimize selection of alternatives, provided constraints
and other resources are available. (page 284)
A5-c75 Majid Rafiee, Farhad Kianfar, A scenario tree approach to multi-period project selection problem using real-option valuation method, INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING
TECHNOLOGY 56(2011), number 1-4, pp. 411-420. 2011
http://dx.doi.org/10.1007/s00170-011-3177-x
Mavrotas, Diakoulaki, and Kourentzis [30] proposed a two-phase method. First, projects were
ranked by a multi-criteria approach. Second, the pre-order of projects was applied in an integer
programming model to derive the final selection. Carlsson et al. [A5] presented a fuzzy mixedinteger programming model for R&D portfolio selection problem. Huang [22] incorporated random fuzzy uncertainty into project selection by integrating genetic algorithm with random fuzzy
simulation. (page 412)
A5-c74 Faramak Zandi, Madjid Tavana, A fuzzy group quality function deployment model for e-CRM framework assessment in agile manufacturing, COMPUTERS & INDUSTRIAL ENGINEERING, 61(2011), issue 1, pp. 1-19. 2011
http://dx.doi.org/10.1016/j.cie.2011.02.004
A5-c73 Faramak Zandi; Madjid Tavana; David Martin, A fuzzy group Electre method for electronic supply
chain management framework selection, INTERNATIONAL JOURNAL OF LOGISTICS: RESEARCH
AND APPLICATIONS, 14(2011), number 1, pp. 35-60. 2011
http://dx.doi.org/10.1080/13675567.2010.550872
Next, we use the approach proposed by Carlsson et al. (2007) to determine the expected value and
the variance of the non-dominated e-SCM frameworks as follows: (page 48)
2010
A5-c72 Xue Deng, Rongjun Li, A portfolio selection model based on possibility theory using fuzzy two-stage
algorithm, JOURNAL OF CONVERGENCE INFORMATION TECHNOLOGY 5(2010), number 6, pp.
138-145. 2010
http://www.aicit.org/jcit/ppl/14.%20JCIT_vol5num6.pdf
Carlsson and Fullér and Heikkilä and Majlender [A5] developed a methodology for valuing options on Research and Development (R&D) projects, when future cash flows are estimated by
trapezoidal fuzzy numbers. (page 139)
A5-c71 Bo Wang, Shuming Wang, Junzo Watada, Real Options Analysis Based on Fuzzy Random Variables,
INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING, INFORMATION AND CONTROL,
6(2010), number 4, pp. 1689-1698. 2010
http://www.ijicic.org/08-1132-1.pdf
A5-c70 Faramak Zandi; Madjid Tavana, A hybrid fuzzy real option analysis and group ordinal approach for
knowledge management strategy assessment, KNOWLEDGE MANAGEMENT RESEARCH & PRACTICE, 8(2010), pp. 216-228. 2010
http://dx.doi.org/10.1057/kmrp.2010.12
A5-c69 Mehdi Ravanshadnia; Hossein Rajaie; Hamid R. Abbasian, Hybrid fuzzy MADM project-selection
model for diversified construction companies, CANADIAN JOURNAL OF CIVIL ENGINEERING, 37(2010),
issue 8, pp. 1082-1093. 2010
http://dx.doi.org/10.1139/L10-048
A5-c68 Ricardo Colomo-Palacios, Angel Garcia-Crespo, Pedro Soto-Acosta, Marcos Ruano-Mayoral, Diego
Jimenez-Lopez, A case analysis of semantic technologies for R&D intermediation information management, INTERNATIONAL JOURNAL OF INFORMATION MANAGEMENT, 30(2010), pp. 465-469.
2010
http://dx.doi.org/10.1016/j.ijinfomgt.2010.05.012
11
Firstly, it will be necessary to develop learning mechanisms so that the tool can take advantage
of the feedback generated during its operation. This characteristic will allow the elimination of
recurrent errors in partner selection, so allowing the continuous improvement in its results. Secondly, the addition of fuzzy mechanisms for consortium construction using approximate reasoning
is suggested as proposed by Carlsson, Fullér, Heikkilä, and Majlender (2007). Thirdly, the scope
of project portfolio selection is intended to be broadened. In the current scenario it is supposed
that all of the companies can participate in the analyzed projects and that they present a similar
interest in developing them. (page 469)
A5-c67 Chiara Verbano; Anna Nosella, Addressing R&D investment decisions: A cross analysis of R&D project
selection methods, EUROPEAN JOURNAL OF INNOVATION MANAGEMENT, 13(2010), number 3, pp.
355-379. 2010
http://dx.doi.org/10.1108/14601061011060166
A5-c66 Ali Pahlavani, A New Fuzzy MADM Approach and its Application to Project Selection Problem, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 3(2010), issue 1, pp.
103-114. 2010
http://dx.doi.org/10.2991/ijcis.2010.3.1.10
A5-c65 Shu-Hsien Liao, Shiu-Hwei Ho, Investment project valuation based on a fuzzy binomial approach,
INFORMATION SCIENCES, 180(2010), issue 11, pp. 2124-2133. 2010
http://dx.doi.org/10.1016/j.ins.2010.02.012
Carlsson et al. [A5] also developed a methodology for valuing options on R&D projects, in which
future cash flows were estimated by trapezoidal fuzzy numbers. In particular, they presented a
fuzzy mixed integer programming model for the R&D optimal portfolio selection problem. (page
2125)
A5-c64 Hervé Corvelleca and Nikos Macheridis, The moral responsibility of project selectors, INTERNATIONAL JOURNAL OF PROJECT MANAGEMENT, 28(2010), Issue 3, pp. 212-219. 2010
http://dx.doi.org/10.1016/j.ijproman.2009.05.004
A5-c63 M. Rabbani; M. Aramoon Bajestani; G. Baharian Khoshkhou, A multi-objective particle swarm optimization for project selection problem, EXPERT SYSTEMS WITH APPLICATIONS, 37(2010), pp. 315321. 2010
http://dx.doi.org/10.1016/j.eswa.2009.05.056
The pre-order of projects is used in an integer programming model to derive the final selection.
Carlsson, Fullér, Heikkilä, and Majlender (2007) presented a fuzzy mixed-integer programming
model for R& D portfolio selection problem. Huang (2007) incorporated random fuzzy uncertainty into project selection by integrating genetic algorithm with random fuzzy simulation. According to the literature review, meta-heuristic approaches in solving project selection problems
have a diminutive role in attracting researchers’ attention. In this study, our contribution is to propose a multi-objective particle swarm optimization with a creative approach to identify and keep
the best global and personal solutions to distinguish Pareto front. (page 316)
2009
A5-c62 M. Tkáč, Š. Lyócsa, On the evaluation of Six Sigma projects, QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, 26(2009), issue 1, pp. 115-124. 2009
http://dx.doi.org/10.1002/qre.1062
Real options theory represents a huge amount of theoretical and practical work. For this reason, we
will limit our review only to the basic principles necessary for one to understand the employment
of real options theory in the evaluation of Six Sigma projects. Six Sigma projects may be perceived
as a specific form of investment. An investment [23] is the act of incurring an immediate cost with
the expectation of future rewards. Similarly, as in R &D projects, the information required for the
valuation is revealed gradually as we progress through the individual stages of the project [25, 26].
However, the decision maker at the time of the decision does not have this useful information, as
12
Carlsson et al. [A5] describes ’this management position can be described as if the management
had some information hidden or in shadow, and it had to make a decision about consuming some
resources in order to uncover the information’. (page 117)
A5-c61 Mohammad Modarres; Farhad Hassanzadeh, A Robust Optimization Approach to R&D Project Selection, WORLD APPLIED SCIENCES JOURNAL, 7(2009), No. 5, pp. 582-592. 2009
http://idosi.org/wasj/wasj7%285%29/4.pdf
A5-c60 Jin Wang, Yujie Xu, Zhun Li, Research on project selection system of pre-evaluation of engineering
design project bidding, INTERNATIONAL JOURNAL OF PROJECT MANAGEMENT, 27(2009) 584599. 2009
http://dx.doi.org/10.1016/j.ijproman.2008.10.003
A5-c59 Y.-Q. Xia, J.-F. Chen, Fuzzy optimization of real options valuation for multi-phase R&D project, Shanghai Jiaotong Daxue Xuebao/Journal of Shanghai Jiaotong University, 43(2009), pp. 583-586. 2009
A5-c58 Hsin-Yun Lee, Ren-Jye Dzeng, A hybrid system for planning the development level of resort, EXPERT
SYSTEMS WITH APPLICATIONS, 36(2009), pp. 6266-6275. 2009
http://dx.doi.org/10.1016/j.eswa.2008.07.056
Several decision models or problem-solving techniques for the project portfolio selection and plan
optimization have been developed. Examples are the applied linear and integer programming (e.g.
Gori, 1996), CAPM (e.g. Sandsmark & Vennemo, 2007), and, more recently, real options analysis
(e.g. Carlsson, Fullér, Heikkila, & Majlender, 2007). Most of these techniques, however, still rely
on a series of assumptions that limit the complexity of the model (Better & Glover, 2006). Besides,
these models are unsuitable for resort development projects because they cannot simultaneously
deal with selection, ordering, and planning the level and schedule of feasible investment items. The
purpose of this paper is to present a decision support system, by integrating simulation and genetic
algorithms (GAs), so as to optimize the level of the amenities of resort development projects. (page
6266)
A5-c57 Mohsen Pirdashti, Arezou Ghadi, Mehrdad Mohammadi, Gholamreza Shojatalab, Multi-Criteria Decision-Making Selection Model with Application to Chemical Engineering Management Decisions, INTERNATIONAL JOURNAL OF BUSINESS, ECONOMICS, FINANCE AND MANAGEMENT SCIENCES,
1(2009), number 3, pp.228-233. 2009
http://www.waset.ac.nz/journals/ijbefms/v1/v1-3-30.pdf
R&D management has several common features with strategic management. It actively aims
at utilizing possibilities supplied by new technologies and innovations in business operations.
Similarly to strategic management, R&D management also has to define objectives for the R&D
operations [A5]. (page 228)
A5-c56 Dan-mei Zhu, Tie Zhang, Xing-tong Wang, Dong-ling Chen, Developing an R&D projects portfolio
selection decision system based on fuzzy logic, INTERNATIONAL JOURNAL OF MODELLING, IDENTIFICATION AND CONTROL, 8(2009), No. 3, pp. 205-212. 2009
http://dx.doi.org/10.1504/IJMIC.2009.029265
2008
A5-c55 Zhu, D.-M., Zhang, T., Chen, D.-L., Gao, H.-X., New fuzzy pricing approach to real option, Dongbei
Daxue Xuebao/Journal of Northeastern University, 29(2008), pp. 1544-1547. 2008
Scopus: 56849088713
A5-c54 A.C. Tolga, Fuzzy multicriteria R&D project selection with a real options valuation model, JOURNAL
OF INTELLIGENT AND FUZZY SYSTEMS, 19(2008), pp. 359-371. 2008
A5-c53 A.C. Tolga and C. Kahraman, Fuzzy multiattribute evaluation of R&D projects using a real options
valuation model, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 23(2008), pp. 11531176. 2008
http://dx.doi.org/10.1002/int.20312
13
The fuzzy mixed integer programming model for R&D project selection problem with FROV is
developed by Carlsson et al. [A5] They discussed how their methodology could be used to build
decision support tools for optimal R&D project selection in a corporate environment. Our study
integrates the fuzzy multiattribute evaluation of R&D projects with a fuzzy real options valuation
model. The fuzzy analytic hierarchy process is selected as the multiattribute evaluation model.
..
.
The fuzzy ROV model used in this paper takes Wang and Hwang’s [19] valuation model into consideration. Contrary to Carlsson’s the mono phase model, Wang and Hwang’s [19] used multiple
phases because of the nature of R&D projects. Therefore, the compound options valuation model
that involves options whose value is contingent on the value of other options is more suitable to
evaluate an R&D project [19]. (pages 1155-1156)
A5-c52 Xiaoxia Huang, Mean-variance model for fuzzy capital budgeting, COMPUTERS & INDUSTRIAL
ENGINEERING, 55 (2008), pp. 34-47. 2008
http://dx.doi.org/10.1016/j.cie.2007.11.015
Kuchta (2001), Carlsson, Fullér, Heikkilä, and Majlender (2007) and Wang and Hwang (2007)
proposed different fuzzy models for selecting R&D projects in different situations. (page 35)
A5-c51 Tahir Conka, Ozalp Vayvay, Bahar Sennaroglu, A combined decision model for R&D project portfolio
selection, INTERNATIONAL JOURNAL OF BUSINESS INNOVATION AND RESEARCH, 2(2008) pp.
190-202. 2008
A5-c50 LIU Jingjian, Study on the coupling measurement and evaluation between R&D project portfolio and
enterprise business strategy, SCIENCE AND TECHNOLOGY MANAGEMENT RESEARCH, 28(2008),
number 12, pp. 106-109 (in Chinese). 2008
http://d.wanfangdata.com.cn/Periodical_kjglyj200812037.aspx
in proceedings and edited volumes
2015
A5-c34 Michael E Cholette, Lin Ma, Lawrence Buckingham, Lutfiye Allahmanli, Andrew Bannister, Gang
Xie, A Decision Support Framework for Prioritization of Engineering Asset Management Activities Under
Uncertainty, In: 9th WCEAM Research Papers, Lecture Notes in Mechanical Engineering, Springer Verlag,
[ISBN 978-3-319-15535-7], pp. 49-60. 2015
http://dx.doi.org/10.1007/978-3-319-15536-4_5
2014
A5-c33 Louis A Cox, R&D Planning and Risk Management, In: Wiley StatsRef: Statistics Reference Online,
John Wiley & Sons, 2014, [ISBN 9781118445112], Paper stat03772. 2014
http://dx.doi.org/10.1002/9781118445112.stat03772
A5-c32 Qin, Quande; Li, Jinpeng; Li, Li, A Fuzzy Two-stage Project Portfolio Selection Model Addressing
Financial and Non-financial Factors, The 26th Chinese Control and Decision Conference (2014 CCDC),
[ISBN 978-1-4799-3707-3], pp. 1349-1352. 2014
http://dx.doi.org/10.1109/CCDC.2014.6852376
Researchers have realized that they could use the fuzzy set theory to investigate project portfolio
selection problems under uncertain environment. Carlsson et al. presented a fuzzy mixed integer
programming model using trapezoidal fuzzy numbers to estimate future cash flows [6]. (page
1349)
2013
14
A5-c31 Laura Cruz, Eduardo R Fernandez, Claudia G Gomez, Gilberto Rivera, Multicriteria optimization of
interdependent project portfolios with ’a priori’ incorporation of decision maker preferences, Proceedings
of Eureka-2013. Atlantis Press, Advances in Intelligent Systems Research, [ISBN 978-90-78677-86-4], pp.
169-178.
http://www.atlantis-press.com/php/download_paper.php?id=9635
A5-c30 Mira Cleber, Feijao Pedro, Souza Maria Angelica, Moura Arnaldo, Meidanis Joao, Lima Gabriel,
Bossolan Renato P, Freitas Italo T, A project portfolio selection decision support system, Proceedings of
the 10th International Conference on Service Systems and Service Management, pp. 725-730. 2013
http://dx.doi.org/10.1109/ICSSSM.2013.6602536
Decision makers are usually confronted with the problem of constructing a project portfolio by
selecting and scheduling projects over a period of time. This is known as the project portfolio
selection (PPS) problem. There are several formulations for the PPS problem and various methods
for solving PPS variants have been proposed in the literature [1], [2], [A5]. A PPS problem can
be summarized as follows: given a set of projects, with the corresponding resource requirements
and limitations to be executed over a predetermined time horizon, find an instance of a project
portfolio, that is, a selection and a schedule of projects, that maximizes a given objective function
over all viable portfolios. (page 725)
2012
A5-c29 Mira Cleber, Feijao Pedro, Souza Maria Angelica, Moura Arnaldo, Meidanis Joao, Lima Gabriel,
Schmitz Rafael, Bossolan Renato P, Freitas Italo T, A GRASP-based Heuristic for the Project Portfolio
Selection Problem, 2012 IEEE 15th International Conference on Computational Science and Engineering
(CSE), December 5-7, 2012, Paphos, Cyprus, pp. 36-41. 2012
http://dx.doi.org/10.1109/ICCSE.2012.102
A5-c28 Maryam Ashrafi, Hamid Davoudpour, Mohammad Abbassi, Developing a decision support system
for R&D project portfolio selection with interdependencies, PROCEEDINGS OF THE SIXTH GLOBAL
CONFERENCE ON POWER CONTROL AND OPTIMIZATION, August 6-8, 2012, Las Vegas, pp. 370378. 2012
http://dx.doi.org/10.1063/1.4769016
2011
A5-c27 Justin CY, Briceno SI, Mavris DN, Villeneuve F, A competitive market approach to gas turbine technology portfolio selection, ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition, GT2011,
June 6-10, 2011, Vancouver, BC, Canada, [ISBN 9780791854631], pp. 653-663. 2011
Scopus: 84865501223
A5-c26 Chuan-Sheng Wang, Wei Chen, A Fuzzy Model for R&D Project Portfolio Selection, International
Conference on Information Management, Innovation Management and Industrial Engineering, November
26-27, 2011, Shenzhen, China, [ISBN: 978-0-7695-4523-3], pp. 100-104. 2011
http://dx.doi.org/10.1109/ICIII.2011.30
A5-c25 Tanatch Tangsajanaphakul, Junzo Watada, Fuzzy Game-Based Real Option Analysis in Competitive
Investment Situation, Fifth International Conference on Genetic and Evolutionary Computing (ICGEC),
August 29-September 1, 2011, Kitakyushu, Japan, [ISBN: 978-1-4577-0817-6], pp. 381-384. 2011
http://dx.doi.org/10.1109/ICGEC.2011.102
2010
A5-c24 Kurtay Ogunc, Decisive risk management for corporate governance, in: Güler Aras, David Crowther
eds., A Handbook of Corporate Governance and Social Responsibility, Gower Publishing Company, [ISBN
978-0-566-08817-9], 2010. pp. 249-264. 2010
http://www.gowerpublishing.com/isbn/9780566088179
15
A5-c23 Shu-Hsien Liao, Shiu-Hwei Ho, Investment Appraisal under Uncertainty - A Fuzzy Real Options Approach, Neural Information Processing. Models and Applications 17th International Conference, ICONIP
2010. Sydney, Australia, November 22-25, 2010, LNCS 6444/2010, Springer, [ISBN 978-3-642-17533-6],
pp. 716-726. 2010
http://dx.doi.org/10.1007/978-3-642-17534-3_88
A5-c22 Shao-Wei Yu, A Pricing Approach to Real Option Based on Normal Cloud Model, International Conference on Engineering and Business Management, March 25-27, 2010, Chengdu, China, pp. 4205-4208.
2010
ISI:000276079501442
A5-c21 Dang Luo; Lijun Xu, The grey B-S model of R&D project evaluation, 2010 International Conference on
Artificial Intelligence and Education (ICAIE), 29-30 October 2010, Hangzhou, China, [ISBN 978-1-42446935-2], pp. 414-417. 2010
http://dx.doi.org/10.1109/ICAIE.2010.5641153
Currently, there exists a lot of research on using real option approach to evaluate R&D project
[2, 3]. As the present value of expected cash flow is forecast and it is impractical to assume it as
an exact number in R&D project evaluation, existing literatures describe it with triangular fuzzy
number [A5,5], trapezoidal fuzzy number or normal fuzzy number, and then use the B-S pricing
formula for fuzzy value assessment. (page 414)
A5-c20 Shu-Hsien Liao, Shiu-Hwei Ho, Investment Project Valuation Based on the Fuzzy Real Options Approach, 2010 International Conference on Technologies and Applications of Artificial Intelligence, November 18-20, 2010, Hsinchu City, Taiwan, [ISBN 978-0-7695-4253-9], pp. 94-101. 2010
http://dx.doi.org/10.1109/TAAI.2010.26
Carlsson et al. [18] also developed a methodology for valuing options on R&D projects, in which
future cash flows were estimated by trapezoidal fuzzy numbers. In particular, they presented a
fuzzy mixed integer programming model for the R&D optimal portfolio selection problem. (page
95)
A5-c19 Shu-Hsien Liao, Shiu-Hwei Ho, A fuzzy real options approach for investment project valuation, Proceedings of the 5th WSEAS International Conference on Economy and Management Transformation, October 24-26, 2010, Timisoara, Romania, vol. I, pp. 86-91. 2010
http://www.wseas.us/e-library/conferences/2010/TimisoaraW/EMT/EMT1-12.pdf
Carlsson et al. [5] also developed a methodology for valuing options on R&D projects, in which
future cash flows were estimated by trapezoidal fuzzy numbers. (page 87)
A5-c18 Shu-Hsien Liao, Shiu-Hwei Ho, Investment project valuation using a fuzzy real options approach,
Proceedings of the 10th WSEAS international conference on Systems theory and scientific computation, N.
E. Mastorakis, V. Mladenov, and Z. Bojkovic eds., Mathematics And Computers In Science Engineering,
August 20-22, 2010, Taipei, Taiwan, World Scientific and Engineering Academy and Society (WSEAS),
[ISBN 978-960-474-218-9], pp. 172-177. 2010
A5-c17 Zhu Danmei, Wang Xingtong, Ren Rongrong, A heuristics R&D projects portfolio selection decision system based on data mining and fuzzy logic, International Conference on Intelligent Computation
Technology and Automation, May 11-12, 2010, Changsha, Hunan, China, [ISBN 978-0-7695-4077-1], pp.
118-121. 2010
http://doi.ieeecomputersociety.org/10.1109/ICICTA.2010.257
A5-c16 Z Wang, S Zhang, J Kuang, A dynamic MAUT decision model for R&D project selection, 1st International Conference on Computing Control and Industrial Engineering, CCIE 2010, June 5-6, 2010, Wuhan,
China, [ISBN 978-076954026-9], pp. 423-427. 2010
http://dx.doi.org/10.1109/CCIE.2010.112
With the increasingly fierce competition and globalization, innovation is one of the important key
strategies for technologically based firms. Therefore, research and development (R&D) plays a
16
very important role in the successful performance for these firms. However, economical and technological resources are limited, whereas candidate projects abound. In addition, R&D project
selection is always considered as a classical example of decision-making under large uncertainties, because innovations are unpredictable and involve risk and uncertainty, which make decision
making more complex than usual [A5-2]. So how to scientifically select the best candidate project
that can make optimal use of limited resources to improve the firm’s competitive advantage has
increasingly become a difficulty question. (page 424)
2009
A5-c15 H. Chen, X. Wang, T. Gu, The research on technical M&A pricing based on real option method, 6th
International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2009, Tianjin, China, 14 -16
August 2009, Volume 2, [ISBN 978-076953735-1], Article number 5359478, pp. 400-404 . 2009
http://dx.doi.org/10.1109/FSKD.2009.458
A5-c14 WM Ma; XJ Ma, A Fuzzy Real Option Model for Information Technology Investment Evaluation, 11th
International Conference on Informatics and Semiotics in Organisations, APR 11-12, 2009, Beijing, China,
AUSSINO ACAD PUBL HOUSE, [ISBN 978-0-9806057-2-3], pp. 485-491. 2009
ISI:000268388300064
A5-c13 C. Verbano; A. Nosella; K. Venturini; F. Turra, Addressing R&D Investment Decisions: a Critical Review and Comparison of R&D Project Selection Methods, 4th European Conference on Entrepreneurship
and Innovation, The University of Antwerp, Belgium, 10-11 September 2009, ACADEMIC CONFERENCES LTD, [ISBN 978-1-906638-41-2], pp. 537-548. 2009
A5-c12 Bo Wang; Shu-Ming Wang; J. Watada, Improved real option analysis based on fuzzy random variables,
2009 International Conference on Machine Learning and Cybernetics, Volume 2, Issue , 12-15 July 2009,
pp. 694-699. 2009
http://dx.doi.org/10.1109/ICMLC.2009.5212448
Carlsson, et al. [A5] developed a methodology for valuing option on R&D projects, which future
cash flows are estimated by trapezoidal fuzzy numbers. Wang, et al. [10] also developed a fuzzy
R&D portfolio selection model to hedge against the uncertainty, they introduced fuzzy set theory
and obtained a fine result. Compared with traditional theories (such as the DCF method), the real
options analysis can better solve one project’s future uncertainty [11]. Therefore, describing the
future cash flow under uncertainty is quite important for real options analysis. Nevertheless, with
the development of information diversification, nowadays market environment become more and
more complicated. It is hard to determine the cash flow of each invest phase with crisp value, even
fuzzy number used by pre-researchers cannot play the role well. To solve this problem, we are
required to handle hybrid uncertainty of randomness and vagueness. The fuzzy random variable
[12, 13, 14, 15, 16] was introduced to depict such phenomena in which vagueness and randomness
appear at the same time, which serves as a basic tool to construct a framework of decision making
models under fuzzy and random environment. Making use of fuzzy random variable, this paper
aims to build a more effect real options analysis model, which characterizes the cash flow under
hybrid uncertainty. (page 694)
A5-c11 Zhu Weidong, Guan Shiping, Intelligent Decision Support System and its Application in Science Research Project Selection, First International Workshop on Education Technology and Computer Science,
March 07-March 08, 2009, Wuhan, Hubei, China, vol. 1, pp. 858-862. 2009.
http://doi.ieeecomputersociety.org/10.1109/ETCS.2009.194
The key step in the processes is how to aggregate the expert’s evaluation. Methods have been
proposed to aggregate reviewer’s evaluation, such as fuzzy linguistic assessment [A5], DEA [11],
D-S evidence theory [12] and so on. Different method has different advantages. (page 858)
2008
17
A5-c11 Dzeng R J, Pan N F, Lee H Y, A development planner for Resort Investment, Proceedings of the 6th
International Conference on Engineering Computational Technology, Athens, Greece, September 2-5, 2008,
[ISBN 978-190508824-9], pp. 1-13. 2008
Scopus: 84858379403
A5-c10 Louis A Cox, R&D Planning and Risk Management, in: Brian S Everitt, Edward L Melnick eds.,
Encyclopedia of Quantitative Risk Analysis and Assessment, John Wiley and Sons, [ISBN 978-0-47003549-8], pp. 1785-1861. 2008
http://dx.doi.org/10.1002/9780470061596.risk0686
A5-c9 A.C. Tolga, C. Kahraman, Fuzzy multi-criteria evaluation of R&D projects and a fuzzy trinomial lattice
approach for real options, in: Proceedings of the 3rd International Conference on Intelligent System and
Knowledge Engineering, ISKE 2008, November 17-19, 2008, Xiamen, China, Article number 4730966,
pp. 418-423. 2008
http://dx.doi.org/10.1109/ISKE.2008.4730966
Wang and Hwang [5] used fuzzy zero-one integer programming to determine the optimal R&D
portfolio selection. Fuzzy mixed integer programming model for R&D project selection problem
with FROV is developed by Carlsson et al. [A5]. Pricing of grid/distributed computing resources
as a problem of real option pricing is investigated by Allenotor and Thulasiram [7]. (page 418)
A5-c8 C.Yi; Y. Ning; Q. Jin, A decision-making approach to R&D project in a fuzzy environment, Proceedings
of the ISECS International Colloquium on Computing, Communication, Control, and Management, CCCM
2008, vol. 2, art. no. 4609648, pp. 90-94. 2008
http://dx.doi.org/10.1109/CCCM.2008.268
New production technologies are developed infrequently in real world, and they often evolve in uneven pace. Innovations are unpredictable, and thus involve large uncertainties with respect to both
the development of opportunities in existing product markets and those in production processes.
Firm’s R&D management, supporting the maximal use of innovations and new technologies, always tries to keep the company up with the pace of technological development [A5]. In order to
get good performance from R&D activity, the efficient and effective management of R&D project
is important for these firms. (page 90)
A5-c7 Z. Danmei, Z. Tie, W. Xingtong, C. Dongling, A novel R&D project portfolio selection decision approach
based on fuzzy logic and heuristics scheduling, Chinese Control and Decision Conference, 2008, CCDC
2008 2008, Article number 4597287, Pages 144-147. 2008
http://dx.doi.org/10.1109/CCDC.2008.4597287
A5-c6 M. Matos, A. Dimitrovski, Case studies using fuzzy equivalent annual worth analysis, in: Fuzzy Engineering Economics with Applications, Studies in Fuzziness and Soft Computing, vol. 233/2008, [ISBN
9783540708094], Springer, pp. 83-95. 2008
http://dx.doi.org/10.1007/978-3-540-70810-0_5
A5-c5 A. Dimitrovski, M. Matos, Fuzzy present worth analysis with correlated and uncorrelated cash flows,
in: Fuzzy Engineering Economics with Applications, Studies in Fuzziness and Soft Computing, vol. 233,
[ISBN 9783540708094], Springer, pp. 11-41. 2008
http://dx.doi.org/10.1007/978-3-540-70810-0_2
A5-c4 Mait Rungi, Visual Representation of Interdependencies Between Projects, in: M. H. Elwany, A. B.
Eltawil eds., Proceedings of the 37th International Conference on Computers and Industrial Engineering,
October 20-23, 2007, Alexandria, Egypt, pp. 1061-1072. 2007
in books
A5-c3 Adrian I Ban, Lucian Coroianu, Przemyslaw Grzegorzewski, FUZZY NUMBERS: APPROXIMATIONS,
RANKING AND APPLICATIONS, Institute of Computer Science, Polish Academy of Sciences, 2015.
Information technologies: research and their interdisciplinary applications, vol. 9, (ISBN 978-83-6315921-4). 2015
18
A5-c2 Sipp Caroline M, Carayannis Elias G, Real Options and Strategic Technology Venturing: A New Paradigm
in Decision Making, Springer, SpringerBriefs in Business, vol. 31, [ISBN 978-1-4614-5813-5]. 2012
A5-c1 Daniel Küpper, Die Erfolgswirkung von Effectuation im Kontext von F&E-Projekten. Eine empirische
Analyse, [ISBN 978-3-8349-2411-7], Gabler Verlag, 2010.
www.gabler.de/Buch/978-3-8349-2411-7/Die-Erfolgswirkung-von-Effectuation-im-Kontext-von-F-E-Projekten.html
in Ph.D. dissertations
• Kari Korpela, Value of Information Logistics Integration in Digital Business Ecosystem, Lappeenranta University of Technology, Lappeenranta, Finland, [ISBN 978-952-265-735-0]. 2014
http://urn.fi/URN:ISBN:978-952-265-736-7
Our contribution to these issues is, in particular, to form a method to analyse investment options on
the DBE level. Real option valuation is used to assess network values with real options. This paper
shows how ROV (cf. Carlsson et al., 2005; Collan, 2004) can be used to analyse DBE investment
options. By using the collected data, we are able to show the overall investment potential for B2B
integration. The results support our assumption that real option valuation can be applied to deal
with ecosystem complexity in a coherent and financially sound way. (page 106)
• John Nicholas, An investigation into the practices and underlying factors during the fuzzy front end of radical
innovation, University of Limerick, Limerick, Ireland. 2014
Due to their proactive nature, R&D projects can be difficult to evaluate. The information required
for evaluation is typically revealed gradually during the development of the project. Consequently
when the opportunity is first identified there are no cash flow estimates available or similar information available that would either justify or invalidate the decision to proceed with the project
(Carlsson et al. 2007). (page 209)
• Nassim DEHOUCHE, MANAGEMENT DE PORTEFEUILLES DE PROJETS: MODELES MULTICRITERES
D’EVALUATION, DE SELECTION ET D’ARGUMENTATION, Universite Paris-Dauphine. 2014
https://polynum.dauphine.fr/public-document/10560/
• Steven Pudney, Asset renewal decision modeling with application to the water utility industry, School of Engineering Systems, Faculty of Built Environment and Engineering, Queensland University of Technology,
Australia. 2010
http://eprints.qut.edu.au/40933/
• Pertti Aaltonen, Co-Selection in R&D Project Portfolio Management: Theory and Evidence, Faculty of Information and Natural Sciences, Aalto University School of Science and Technology, Helsinki, Finland, ISBN
978-952-60-3033-3. 2010
http://lib.tkk.fi/Diss/2010/isbn9789526030333/
[A6] Christer Carlsson, Robert Fullér and Péter Majlender, On possibilistic correlation, FUZZY SETS AND SYSTEMS, 155(2005) 425-445. [MR2181000]. doi 10.1016/j.fss.2005.04.014
in journals
2016
A6-c37 Lucian Coroianu, Necessary and sufficient conditions for the equality of the interactive and noninteractive sums of two fuzzy numbers, FUZZY SETS AND SYSTEMS, 283(2016), pp. 40-55. 2016
http://dx.doi.org/10.1016/j.fss.2014.10.026
A6-c36 S Rezvani, Cardinal, Median Value, Variance and Covariance of Exponential Fuzzy Numbers with
Shape Function and its Applications in Ranking Fuzzy Numbers, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 9: (1) pp. 10-24. 2016
http://dx.doi.org/10.1080/18756891.2016.1144150
2015
19
A6-c35 Yanyan He, Mahsa Mirzargar, Sophia Hudson, Mike Kirby, Ross Whitaker, An Uncertainty Visualization Technique Using Possibility Theory: Possibilistic Marching Cubes, INTERNATIONAL JOURNAL
FOR UNCERTAINTY QUANTIFICATION, 5(2015), number 5, pp. 433-451. 2015
http://dx.doi.org/10.1615/Int.J.UncertaintyQuantification.2015013730
Although there have been a few attempts in the literature to discover the correlation between
uncertain variables represented by possibility distributions [A6], it is still an open problem to
construct joint distribution for correlated variables in applications. Therefore, we assume the
independent relation among variables in the current work and leave the dependent scenario for
future research. (page 437)
A6-c34 Dug Hun Hong, Jae Duck Kim, The Lower Limit for Possibilistic Correlation Coefficient, APPLIED
MATHEMATICAL SCIENCES, 9(2015), number 121, pp. 6041-6047. 2015
http://dx.doi.org/10.12988/ams.2015.58520
A6-c33 Bahram Sadeghpour Gildeh, Niloufar Shafiee, X-MR control chart for autocorrelated fuzzy data using
D p,q -distance The International Journal of Advanced Manufacturing Technology, 81(2015), number 5-8,
pp. 1047-1054. 2015
http://dx.doi.org/10.1007/s00170-015-7199-7
In many applications, the correlation between fuzzy numbers is of interest. Several authors have
proposed different measures of correlation between membership functions, intuitionistic fuzzy sets
and correlation. It is usually formulated using defuzzification methods or α-cut sets, and resulted
as a crisp number or a fuzzy number, (for more information, see [3], [A6], and [13]). (page 1050)
A6-c32 V M Cabral, L C Barros, Fuzzy differential equation with completely correlated parameters, FUZZY
SETS AND SYSTEMS, 265(2015), pp. 86-98. 2015
http://dx.doi.org/10.1016/j.fss.2014.08.007
2014
A6-c31 Adel Azar, Hossein Sayyadi Tooranloo, Ali Rajabzadeh, Laya Olfat, A Model for Assessing Agility
Drivers with Possibility Theory, Applied mathematics in Engineering, Management and Technology, June
2014: (1119) p. 1134. 2014
http://amiemt.megig.ir/test/sp2/136.pdf
2013
A6-c30 M Ahmadi Anvigh, On linguistic approximation of uncertainty quantities based on signal-noise ratio
Communications on Advanced Computational Science with Applications, 2013(2013). Article id: cacsa00008. 2013
http://dx.doi.org/10.5899/2013/cacsa-00008
A6-c29 R Saneifard, Nader Hassasi, Parametric correlation coefficient of fuzzy numbers African Journal of
Business Management 7: (35) 3410-3415 (2013)
http://dx.doi.org/10.5897/AJBM11.1588
Several authors have proposed different measures of correlation between membership functions,
intuitionistic fuzzy sets and correlation [Carlsson et al., 2005; Bustince and Burillo, 1995]. (page
3413)
A6-c28 Zhang Xili, Zhang Weiguo, Xiao Weilin, Multi-period portfolio optimization under possibility measures, Economic Modelling 35(2013), pp. 401-408. 2013
http://dx.doi.org/10.1016/j.econmod.2013.07.023
Hence, the measure of the expected value and variance of an integrable function on C are defined
in Carlsson et al. (2005) by using the measure of central value and dispersion. (page 403)
2012
20
A6-c27 I. Georgescu, Expected utility operators and possibilistic risk aversion, SOFT COMPUTING, Volume
16, Issue 10, September 2012, Pages 1671-1680. 2012
http://dx.doi.org/10.1007/s00500-012-0851-3
A6-c26 R Saneifard, S Khodaei, A Method for Defuzzification Based on General Translation Research Journal
of Applied Sciences, Engineering and Technology, 4(2012), number 13, pp. 1850-1856. 2012
http://maxwellsci.com/print/rjaset/v4-1850-1856.pdf
An alternative crisp interval, B(A), for representing a given fuzzy interval A was introduced by
(Carlsson et al., 2005) and further investigated by Yager (2004). (page 1853)
A6-c25 Rahim Saneifard, Rasoul Saneifard, Correlation Coefficient Between Fuzzy Numbers Based On Central
Interval, Journal of Fuzzy Set Valued Analysis 2012(2012), pp. 1-9. Paper jfsva-00108. 2012
http://dx.doi.org/10.5899/2012/jfsva-00108
A6-c24 Rahim Saneifard, Modelling And Initiating Knowledge Management Program Using Correlation Coefficient Between Fuzzy Numbers, INTERNATIONAL JOURNAL OF NATURAL AND ENGINEERING
SCIENCES, 6(2012), number 1, pp. 25-30. 2012
http://nobel.gen.tr/Makaleler/IJNES-Issue
%201-396cb2fc4e604a70ab7db0a25cde61b5.pdf
2011
A6-c23 R Saneifard, E Noori, A Novel Approach for Defuzzification Based on Ambiguity- Preserving, INTERNATIONAL JOURNAL OF NATURAL AND ENGINEERING SCIENCES, 5(2011), number 3, pp.
21-26. 2011
http://www.nobel.gen.tr/Makaleler/IJNES-Issue%203-93-2012.pdf
A6-c22 Irina Georgescu; Jani Kinnunen, Multidimensional possibilistic risk aversion, MATHEMATICAL AND
COMPUTER MODELLING, 54(2011), issues 1-2, pp. 689-696. 2011
http://dx.doi.org/10.1016/j.mcm.2011.03.011
A6-c21 Irina Georgescu, A possibilistic approach to risk aversion, SOFT COMPUTING, 15(2011), pp. 795801. 2011
http://dx.doi.org/10.1007/s00500-010-0634-7
A6-c20 Zhang Qiansheng, Jiang Shengyi, Probabilistic interval-valued fuzzy sets and its application in pattern
recognition APPLIED MATHEMATICS, 26(2011), number 1, pp. 111-120. 2011
http://www.math.zju.edu.cn/amjcu/A/201101/111-120.pdf
2010
A6-c19 V. S. Vaidyanathan, Correlation of Triangular Fuzzy Variables Using Credibility Theory, INTERNATIONAL JOURNAL OF COMPUTATIONAL COGNITION, 8(2010), number 1, pp. 21-23. 2010
http://www.yangsky.com/ijcc/pdf/ijcc814.pdf
The correlation coefficient between any two variables is an important measure because it helps
in identifying the strength and degree of relationship between them. Though much work has
been done in developing different correlation measures, most of these are suitable only for crisp
numbers. However, when the observations are fuzzy in nature, these correlation measures cannot
be applied. Therefore, developing a measure to find the correlation coefficient between a set of
fuzzy numbers is of interest because much of data in practical situations can be expected to be
of fuzzy in nature. For example, the body temperature of a person may be expressed in fuzzy
terms like low, moderate, high and the performance of a student may be expressed as poor, good,
excellent etc. Gerstenkorn and Manko [3], Yu [8], Bustince and Burillo [1], Hung and Wu [4] and
Carlsson, Fuller and Majlender [A6] have proposed different measures of correlation coefficient
between fuzzy numbers. Recently Saeidifar and Pasha [6] have proposed a weighted possibilistic
21
measure to find the correlation coefficient between fuzzy numbers. All these measures are based
on the α-cut values of the membership functions of the fuzzy numbers. In this paper, a new
measure to find the correlation coefficient between triangular fuzzy variables is proposed using
the concepts of Credibility Theory. (page 21)
A6-c18 Zhang Qian-Sheng; Jiang Sheng-Yi, On Weighted Possibilistic Mean, Variance and Correlation of
Interval-valued Fuzzy Numbers, COMMUNICATIONS IN MATHEMATICAL RESEARCH, 26(2010),
number 2, pp. 105-118. 2010
http://www.cqvip.com/qk/96600A/201002/34084956.html
2009
A6-c17 Dug Hun Hong, A Note on Possibilistic Correlation, INTERNATIONAL JOURNAL OF FUZZY
LOGIC AND INTELLIGENT SYSTEMS, 9(2009), pp. 1-3. 2009
http://www.dbpia.co.kr/view/ar_view.asp?arid=1196795#
A6-c16 Irina Georgescu, Possibilistic risk aversion, FUZZY SETS AND SYSTEMS, 160(2009), pp. 26082619. 2009
http://dx.doi.org/10.1016/j.fss.2008.12.007
A6-c15 A. Saeidifar, E. Pasha, The possibilistic moments of fuzzy numbers and their applications, JOURNAL
OF COMPUTATIONAL AND APPLIED MATHEMATICS, 223 (2009), pp. 1028-1042. 2009
http://dx.doi.org/10.1016/j.cam.2008.03.045
2008
A6-c14 Chi-Chi Chen, Hui-Chin Tang, Degenerate Correlation and Information Energy of Interval-Valued
Fuzzy Numbers, INTERNATIONAL JOURNAL OF INFORMATION AND MANAGEMENT SCIENCES,
19(2008) pp. 119-130. 2008
http://jims.ms.tku.edu.tw/PDF/M19N18.pdf
2007
A6-c13 B. Bede, T.G. Bhaskar, V. Lakshmikantham, Perspectives of fuzzy initial value problems, COMMUNICATIONS IN APPLIED ANALYSIS, 11 (3-4), pp. 339-358. 2007
Scopus: 37349131979
A6-c12 Hong, D.H., Kim, K.T., A maximal variance problem, APPLIED MATHEMATICS LETTERS, 20 (10),
pp. 1088-1093. 2007
http://dx.doi.org/10.1016/j.aml.2006.12.008
In this work, we provide a direct proof concerning a special type of concave density function on a
bounded closed interval with minimal variance. This proof involves elementary methods, without
using any advanced theories such as Weierstrass’s Approximation Theorem, from which the technical core result of the paper [C. Carlsson, R. Fullér, P. Majlender, On possibilistic correlation,
Fuzzy Sets and Systems 155 (2005) 425-445] comes. (page 1088)
Recently, Carlsson, Fullér and Majlender [A6] presented the concept of a possibilistic correlation
representing an average degree of interaction between the marginal distribution of a joint possibility distribution as compared to the respective dispersions. They also formulated the weak and
strong forms of the possibilistic Cauchy-Schwarz inequality. (page 1088)
The strong forms of the possibilistic Cauchy-Schwarz inequality of the paper [A6] are based on
the following theorem.
Theorem 1 ([A6]). Let C be a joint possibility distribution with marginal possibility distribution
A = πx (C) ∈ F, B = πy (C) ∈ F, and let γ ∈ [0, 1]. If [C]γ is convex then
R[C]γ (πx , πy ) ≤ R[A]γ (id, id).
(page 1090)
22
A6-c11 Mizukoshi, M.T., Barros, L.C., Chalco-Cano, Y., Roman-Flores, H., Bassanezi, R.C., Fuzzy differential
equations and the extension principle, INFORMATION SCIENCES, 177 (17), pp. 3627-3635. 2007
http://dx.doi.org/10.1016/j.ins.2007.02.039
In this section we will discuss the fuzzy differential equations obtained from a deterministic differential equation introducing an uncertainty coefficient and fuzzy initial condition. For this, we
will consider that parameter w and initial condition x0 are uncorrelated [A6]. (page 3632)
2006
A6-c10 Matia F, Jimenez A, Al-Hadithi BM, et al. The fuzzy Kalman filter: State estimation using possibilistic
techniques, FUZZY SETS AND SYSTEMS, 157 (16): 2145-2170 AUG 16 2006
http://dx.doi.org/10.1016/j.fss.2006.05.003
in proceedings and edited volumes
A6-c8 Mahsa Mirzargar, Yanyan He, Robert M Kirby, Application of Uncertainty Modeling Frameworks to Uncertain Isosurface Extraction, In: Van-Nam Huynh, Masahiro Inuiguchi, Thierry Denoeux eds., Integrated
Uncertainty in Knowledge Modelling and Decision Making, Lecture Notes in Computer Science, vol. 9376,
Springer, 2015. (ISBN 978-3-319-25134-9) pp. 336-349. 2015
http://dx.doi.org/10.1007/978-3-319-25135-6_32
Although there have been a few attempts to discover the correlation between uncertain variables
in possibility theory [A6], it is still an open problem to construct joint distribution for dependent
variables from ensembles.
A6-c7 Alessandro Ferrero, Marco Prioli, Simona Salicone, Barbara Vantaggi, 2D Probability-Possibility Transformations, Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol. 190/2013, Springer, [ISBN 978-3-642-33042-1], pp. 63-72. 2013
http://dx.doi.org/10.1007/978-3-642-33042-1_8
A6-c6 Irina Georgescu, Combining probabilistic and possibilistic aspects of background risk, 2012 IEEE 13th
International Symposium on Computational Intelligence and Informatics (CINTI), 20-22 Nov. 2012, Budapest, [ISBN 978-1-4673-5205-5], pp. 225,229. 2012
http://dx.doi.org/10.1109/CINTI.2012.6496765
A6-c5 I Georgescu, J Kinnunen, A Generalized 3-Component Portfolio Selection Model, 11th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (AIKED ’12),
February 22-24, 2012, Cambridge, England, [ISBN: 978-1-61804-068-8], pp. 142-147. 2012
http://www.wseas.us/e-library/conferences/2012/CambridgeUK/AIKED/AIKED-22.pdf
A6-c4 Tatari, F.; Akbarzadeh-T, M.-R.; Mazouchi, M.; Javid, G. Agent-based centralized fuzzy Kalman filtering for uncertain stochastic estimation, Fifth International Conference on Soft Computing, Computing
with Words and Perceptions in System Analysis, Decision and Control, ICSCCW 2009, 2-4 Sept. 2009,
Famagusta, North Cyprus, pp.1-4. 2009
http://dx.doi.org/10.1109/ICSCCW.2009.5379483
A6-c3 Jan M Baeten, Bernard De Baets, Incorporating Fuzziness in Spatial Susceptible-Infected Epidemic
Models, in: J. P. Carvalho, D. Dubois, U. Kaymak and J. M. C. Sousa eds., Proceedings of the Joint 2009
International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and
Technology Conference, Lisbon, Portugal, July 20-24, 2009, [ISBN: 978-989-95079-6-8], pp. 201-206.
2009
http://www.eusflat.org/publications/proceedings/IFSA-EUSFLAT_2009/
pdf/tema_0201.pdf
23
A6-c2 D Degrauwe, G De Roeck, G Lombaert, Fuzzy frequency response function calculation with interactive fuzzy numbers, Leuven Symposium on Applied Mechanics in Engineering, March 31-April 2, 2008,
Leuven, Belgium, [ISBN: 978-90-73802-85-8 ], pp. 659-670. 2008
ISI:000259733800046
https://lirias.kuleuven.be/handle/123456789/212966
in books
A6-c2 Adrian I Ban, Lucian Coroianu, Przemyslaw Grzegorzewski, FUZZY NUMBERS: APPROXIMATIONS,
RANKING AND APPLICATIONS, Institute of Computer Science, Polish Academy of Sciences, 2015.
Information technologies: research and their interdisciplinary applications, vol. 9, (ISBN 978-83-6315921-4). 2015
A6-c1 Dominik Ocker, Unscharfe Risikoanalyse strategischer Ereignisrisiken, Peter Lang Internationaler Verlag
der Wissenschaften, 2010, Schriften zur Unternehmensplanung, vol. 83, [ISBN 978-3-631-59752-1]. 2010
in Ph.D. dissertations
• József Mezei, A quantitative view on fuzzy numbers, Department of Information Technologies (TUCS), Åbo
Akademi University, Åbo, Finland, [ISBN 978-952-12-2670-0]. 2011
http://www.doria.fi/handle/10024/72548
• Daan Degrauwe, Uncertainty propagation in structural analysis by fuzzy numbers, Department of Civil Engineering, K.U.Leuven, Belgium. 2007
http://www.kuleuven.be/bwm/papers/phd-daan-07a.pdf
Interactive fuzzy numbers are mentioned by numerous authors as a generalization of non-interactive
fuzzy numbers [32, 103], but most researchers investigate theoretical properties and actual applications are rare until present: Carlsson et al. [A6] define fuzzy equivalents of mean value, variance
and covariance, and Fullér et al. [W16] investigate analogies between multivariate probability
theory and multivariate possibility theory. (page 24)
[A7] Robert Fullér and Péter Majlender, On interactive fuzzy numbers, FUZZY SETS AND SYSTEMS 143(2004)
355-369. [MR2052672]. doi 10.1016/S0165-0114(03)00180-5
in journals
2016
A7-c41 Guixiang Wang, Peng Shi, Ramesh K c Agarwal, Yan Shi, On fuzzy ellipsoid numbers and membership
functions, JOURNAL OF INTELLIGENT & FUZZY SYSTEMS (to appear). 2016
http://dx.doi.org/10.3233/IFS-162152
A7-c40 S Rezvani, Cardinal, Median Value, Variance and Covariance of Exponential Fuzzy Numbers with
Shape Function and its Applications in Ranking Fuzzy Numbers, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 9: (1) pp. 10-24. 2016
http://dx.doi.org/10.1080/18756891.2016.1144150
A7-c39 Lucian Coroianu, Necessary and sufficient conditions for the equality of the interactive and noninteractive sums of two fuzzy numbers, FUZZY SETS AND SYSTEMS, 283(2016), pp. 40-55. 2016
http://dx.doi.org/10.1016/j.fss.2014.10.026
Fuzzy numbers can be perceived as possibility distributions, which inspired Fullér and Majlender
(see [A7]) to introduce the so-called joint possibility distribution. (page 43)
2015
24
A7-c38 Andrzej Piegat, Marcin Plucinski, Fuzzy number addition with the application of horizontal membership
functions, THE SCIENTIFIC WORLD JOURNAL, 2015(2015). Article ID 367214. 2015
http://dx.doi.org/10.1155/2015/367214
A7-c37 Dug Hun Hong, Jae Duck Kim, The Lower Limit for Possibilistic Correlation Coefficient, APPLIED
MATHEMATICAL SCIENCES, 9(2015), number 121, pp. 6041-6047. 2015
http://dx.doi.org/10.12988/ams.2015.58520
A7-c36 Ellen Simoen, Guido De Roeck, Geert Lombaert, Dealing with uncertainty in model updating for damage assessment: A review, Mechanical Systems and Signal Processing, 56-57(2015), pp. 123-149.2015
http://dx.doi.org/10.1016/j.ymssp.2014.11.001
This means that fuzzy modeling always yields the maximal (worst case) range on the output variables at each α-level, as it is implicitly assumed that any combination of input variable values is
equally plausible. In other words, solving e.g. the problem in (44) produces the extreme values
of the objective function, regardless of the (known) feasibility of the input variable set. In FE
model updating, for instance, an optimum may be found for a data set that includes very large
differences between neighboring mode shape displacements, which is physically highly unlikely.
One possible approach to overcome this problem is to make use of so-called interactive fuzzy
numbers [188, A7,234], where dependency between variables is taken into account by modifying
the joint membership function to exclude physically infeasible or unlikely input combinations at
each α-level. (page 142)
A7-c35 Soheil Sadi-Nezhad, Kaveh Khalili-Damghani, Ameneh Norouzi, A new fuzzy clustering algorithm
based on multi-objective mathematical programming, TOP, 23(2015), issue 1, pp. 168-197. 2015
http://dx.doi.org/10.1007/s11750-014-0333-0
2014
A7-c34 Ondřej Pavlačka, On various approaches to normalization of interval and fuzzy weights, FUZZY SETS
AND SYSTEMS, Volume 243, 16 May 2014, Pages 110-130. 2014
http://dx.doi.org/10.1016/j.fss.2013.07.026
A7-c33 Zhang Wei-Guo, Liu Yong-Jun, Xu Wei-Jun, A new fuzzy programming approach for multi-period
portfolio optimization with return demand and risk control, FUZZY SETS AND SYSTEMS, 246(2014) pp.
107-126 . 2014
http://dx.doi.org/10.1016/j.fss.2013.09.002
2013
A7-c32 Zhang Xili, Zhang Weiguo, Xiao Weilin, Multi-period portfolio optimization under possibility measures, Economic Modelling, 35(2013), pp. 401-408. 2013
http://dx.doi.org/10.1016/j.econmod.2013.07.023
The aim of this paper is to develop a multiperiod mean-variance portfolio selection model with
fuzzy returns based on possibility theory. By using the central value operator introduced by Fullér
and Majlender (2004) and Fullér et al. (2010a,b, 2011), we formulate the possibilistic expected
value and possibilistic variance for the terminal wealth after T periods. A class of multi-period
possibilistic mean-variance models is formulated originally. Moreover, an efficient solution is
achieved for this class of fuzzy multi-period portfolio selection formulation, which makes the
derived investment strategy an easy implementation task. (page 402)
The relationships of central value, expected value and variance of possibility distributions and the
corresponding probabilistic values have been explained in Carlsson et al. (2005) and Fullér and
Majlender (2004). As pointed out in Fullér and Majlender (2004), if all γ-level sets of C are
symmetrical, then the covariance between its marginal distributions A and B becomes zero for
any weighting function f , that is,
Covf (A, B) 6= 0,
even though A and B may be interactive. (page 403)
25
A7-c31 Irina Georgescu, Possibilistic risk aversion and coinsurance problem, FUZY INFORMATION AND
ENGINEERING, Volume 5, Issue 2, pp 221-233. 2013
http://dx.doi.org/10.1007/s12543-013-0136-2
2012
A7-c30 Sai Anjani Kumar KVN, Mohapatra PKJ, Fuzzy control charts for correlated multi-attribute quality
characteristics, INTERNATIONAL JOURNAL OF PERFORMABILITY ENGINEERING, Volume 8, Issue 6, 2012, Pages 645-652. 2012
Scopus: 84873050428
A7-c29 K Scheerlinck, H Vernieuwe, B De Baets, Zadeh’s extension principle for continuous functions of noninteractive variables: a parallel optimization approach, IEEE TRANSACTIONS ON FUZZY SYSTEMS,
20(2012), issue 1, pp. 96-108. 2012
http://dx.doi.org/10.1109/TFUZZ.2011.2168406
One way to model interactivity is to replace the minimum operator in the joint membership function by another triangular norm, which can be chosen based on mathematical or physical properties
[27][A7]. Another way to construct the joint membership function is by applying a possibilistic
clustering algorithm to a joint measurement of the relevant variables, based on physical or artificially generated data [30]. (page 97)
2011
A7-c28 Ondřej Pavlačka, Modeling uncertain variables of the weighted average operation by fuzzy vectors,
INFORMATION SCIENCES, 181(2011), number 22, pp. 4969-4992. 2011
http://dx.doi.org/10.1016/j.ins.2011.06.022
If an output fuzzy number is obtained as the result of the fuzzy extension of some real-valued
function, we can apply for finding the scalar representation the concept of the central value and
the expected value of a possibility distribution that was introduced in [A7]. (page 4975)
A7-c27 Irina Georgescu; Jani Kinnunen, Multidimensional possibilistic risk aversion, MATHEMATICAL AND
COMPUTER MODELLING, 54(2011), issues 1-2, pp. 689-696. 2011
http://dx.doi.org/10.1016/j.mcm.2011.03.011
2010
A7-c26 Ondřej Pavlačka, Jana Talasova, Fuzzy vectors as a tool for modeling uncertain multidimensional quantities, FUZZY SETS AND SYSTEMS, 161(2010, issue 11, pp. 1585-1603. 2010
http://dx.doi.org/10.1016/j.fss.2009.12.008
2009
A7-c25 ML Koc, Risk assessment of a vertical breakwater using possibility and evidence theories, OCEAN
ENGINEERING, 36(2009), issue 14, pp. 1060-1066. 2009
http://dx.doi.org/10.1016/j.oceaneng.2009.07.002
A7-c24 Dug Hun Hong, A Note on Possibilistic Correlation, INTERNATIONAL JOURNAL OF FUZZY
LOGIC AND INTELLIGENT SYSTEMS, 9(2009), pp. 1-3. 2009
http://www.dbpia.co.kr/view/ar_view.asp?arid=1196795#
2007
A7-c23 D.H. Hong, K.T. Kim, A maximal variance problem, APPLIED MATHEMATICS LETTERS, 20(10),
pp. 1088-1093. 2007
http://dx.doi.org/10.1016/j.aml.2006.12.008
26
Fullér and Majlender [A7] presented the idea of interaction between a marginal distribution of a
joint possibility distribution. They introduced the notion of covariance between fuzzy numbers
via their joint possibility distribution to measure the degree to which the fuzzy numbers interact.
(page 1088)
A7-c22 Jian-li ZHAO, Zhi-gang JIA, Ying LI, Weighted Ranking and Simple Operation Approaches of Fuzzynumber Based on Four-dimensional Representations, FUZZY SYSTEMS AND MATHEMATICS, 2007,
Vol.21 No.2 pp. 97-101. 2007
2006
A7-c21 B. Bede and J. Fodor, Product Type Operations between Fuzzy Numbers and their Applications in
Geology, ACTA POLYTECHNICA HUNGARICA, Vol. 3, No. 1, pp. 123-139. 2006
http://www.bmf.hu/journal/Bede_Fodor_5.pdf
2005
A7-c20 Przemysław Grzegorzewski and Edyta Mrówka, Trapezoidal approximations of fuzzy numbers, FUZZY
SETS AND SYSTEMS 153(1): 115-135 JUL 1 2005
http://dx.doi.org/10.1016/j.fss.2004.02.015
in proceedings and edited volumes
2016
A7-c11 Andrea Sgarro, Laura Franzoi, (Ir)relevant T-norm Joint Distributions in the Arithmetic of Fuzzy Quantities: 16th International Conference, IPMU 2016, Eindhoven, The Netherlands, June 20 - 24, 2016, Proceedings, Part II In: Joao Paulo Carvalho, Marie-Jeanne Lesot, Uzay Kaymak, Susana Vieira, Bernadette
Bouchon-Meunier, Ronald R Yager eds., Information Processing and Management of Uncertainty in KnowledgeBased Systems, Communications in Computer and Information Science, vol. 611, Springer, 2016. (ISBN
978-3-319-40580-3) pp. 3-11. 2016
http://dx.doi.org/10.1007/978-3-319-40581-0 1
2015
A7-c10 Estevao Esmi, Gustavo Barroso, Laecio C Barros, Peter Sussner, A Family of Joint Possibility Distributions for Adding Interactive Fuzzy Numbers Inspired by Biomathematical Models, In: Proceedings of the
16th World Congress of the International Fuzzy Systems Association (IFSA) and the 9th Conference of the
European Society for Fuzzy Logic and Technology (EUSFLAT), Atlantis Press, (ISBN 978-94-62520-776), pp. 1318-1323. 2015
http://dx.doi.org/10.2991/ifsa-eusflat-15.2015.186
For the case where f : Rn → R, Fuller and Majlender [10, 11] employed the notion of a joint
possibility distribution to propose a method that deals with an n-tuple of fuzzy numbers and that
can be viewed as a generalization of Zadeh?s extension principle. (page 1319)
Fuller and Majlender?s definition of completely correlated fuzzy numbers can only be applied to
a subset of the pairs of fuzzy numbers in which a joint possibility distribution can be generated
in terms a characteristic function of a line. In contrast, our approach as well as the t-norm-based
approach can be applied to establish an interactivity relation between any pair of fuzzy numbers.
(page 1323)
A7-c9 Irina Georgescu, Jani Kinnunen, Ana Maria Lucia-Casademunt, Possibilistic Models of Risk Management, In: Intelligent Techniques in Engineering Management, Intelligent Systems Reference Library, vol.
87/2015, Springer, (ISBN 978-3-319-17905-6) pp. 21-44. 2015
http://dx.doi.org/10.1007/978-3-319-17906-3_2
27
2012
A7-c8 Irina Georgescu, Combining probabilistic and possibilistic aspects of background risk, 2012 IEEE 13th
International Symposium on Computational Intelligence and Informatics (CINTI), 20-22 Nov. 2012, Budapest, [ISBN 978-1-4673-5205-5], pp. 225,229. 2012
http://dx.doi.org/10.1109/CINTI.2012.6496765
A7-c7 Wim Verhaeghe, Wim Desmet, Dirk Vandepitte, Isaac Elishakoff, David Moens, Bounding the dependence measures for spatial uncertainties, 5th International Conference on Reliable Engineering Computing,
June 13-15, 2012, Brno, Czech Republic, [ISBN 978-80-214-4507-9], pp. 599-612. 2012
http://rec2012.fce.vutbr.cz/documents/papers/verhaeghe.pdf
Here, as in (Klir, 2006), the equality operator is adopted. With such a definition possibilistic
independence implies possibilistic noninteraction, but not the other way around. This definition
of noninteraction or independence does not give us a measure of interaction or dependence. First
attempts to come up with such a measure are apparently found in (Fuller and Majlender, 2004).
(page 606)
A7-c6 Andrea Sgarro, Laura Franzoi, Fuzzy Arithmetics for Fuzzy n-Poles: When Is Interactivity Irrelevant?
14th International Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems, IPMU 2012, July 9-13, 2012, Catania, Italy, Communications in Computer and Information
Science, vol. 299, Springer, [ISBN: 978-3-642-31718-7], pp. 1-8. 2012
http://dx.doi.org/0.1007/978-3-642-31718-7_1
A7-c5 Irina Georgescu, Jani Kinnunen, Possibilistic Risk Aversion and Its Indicators, 11th WSEAS International Conference on APPLIED COMPUTER and APPLIED COMPUTATIONAL SCIENCE (ACACOS’12), April 18-20, 2012, Rovaniemi, Finland, [ISBN: 978-1-61804-084-8], pp. 178-183. 2012
http://www.wseas.us/e-library/conferences/2012/Rovaniemi/ACACOS/ACACOS-29.pdf
2008
A7-c4 Jan M Baeten, Bernard De Baets, Incorporating Fuzziness in Spatial Susceptible-Infected Epidemic
Models, in: J. P. Carvalho, D. Dubois, U. Kaymak and J. M. C. Sousa eds., Proceedings of the Joint 2009
International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and
Technology Conference, Lisbon, Portugal, July 20-24, 2009, [ISBN: 978-989-95079-6-8], pp. 201-206.
2009
http://www.eusflat.org/publications/proceedings/IFSA-EUSFLAT_2009/
pdf/tema_0201.pdf
A7-c3 L. Stefanini, L. Sorini, M.L. Guerra, Fuzzy Numbers and Fuzzy Arithmetic, in: W. Pedrycz, A. Skowron,
V. Kreinovich (Eds.) Handbook of Granular Computing, Studies in Computational Intelligence Series,
Wiley, [ISBN 9780470035542], pp. 249-284. 2008
2007
A7-c2 Pierpaolo D’Urso, Fuzzy Clustering of Fuzzy Data, in: J. Valente de Oliveira and W. Pedrycz eds.,
Advances in Fuzzy Clustering and its Applications, John Wiley & Sons, [ISBN 978-0-470-02760-8], pp.
155-192. 2007
2006
A7-c1 J. Fodor, B. Bede, Arithmetics with Fuzzy Numbers: a Comparative Overview, SAMI 2006 conference,
Herlany, Slovakia, [ISBN 963 7154 44 2], pp. 54-68. 2006
http://www.bmf.hu/conferences/sami2006/Fodor.pdf
in books
28
A7-c2 Adrian I Ban, Lucian Coroianu, Przemyslaw Grzegorzewski, FUZZY NUMBERS: APPROXIMATIONS,
RANKING AND APPLICATIONS, Institute of Computer Science, Polish Academy of Sciences, 2015.
Information technologies: research and their interdisciplinary applications, vol. 9, (ISBN 978-83-6315921-4). 2015
A7-c1 Marek Gagolewski, DATA FUSION THEORY, METHODS, AND APPLICATIONS, Institute of Computer Science, Polish Academy of Sciences, 2015. INFORMATION TECHNOLOGIES: RESEARCH
AND THEIR INTERDISCIPLINARY APPLICATIONS; vol 7, (ISBN 978-83-63159-20-7). 2015
in Ph.D. dissertations
• Frank H Patterson, A FUZZY FRAMEWORK FOR ROBUST ARCHITECTURE IDENTIFICATION IN
CONCEPT SELECTION, Georgia Institute of Technology, USA. 2015
https://smartech.gatech.edu/bitstream/handle/1853/54413/PATTERSON-DISSERTATION-2015.pdf
Figure 82 shows an example of calculating FPoS for a single criterion. For n criteria, the Fuzzy
Possibility of Success (FPoS) is defined by Equation 64. This definition is derived from the joint
possibility distribution outlined by Fuller [A7]. (page 202)
• Xiaolu Wang, Fuzzy Real Option Analysis in Patent Related Decision Making and Patent Valuation, Department of Information Technologies (TUCS), Åbo Akademi University, Åbo, Finland, [ISBN 978-952-123227-5]. 2015
http://urn.fi/URN:NBN:fi-fe2015061110218
In [A7], the variance of a possibility distribution à is defined as the weighted average of the
probabilistic variances of the respective uniform distributions on the α-cuts of Ã. That is, (page
47)
• József Mezei, A quantitative view on fuzzy numbers, Department of Information Technologies (TUCS), Åbo
Akademi University, Åbo, Finland, [ISBN 978-952-12-2670-0]. 2011
http://www.doria.fi/handle/10024/72548
• Angela Romagnoli, Le copule per gestire i fenomeni di dipendenza nelle assicurazioni vita: Copulas as a tool
for modelling dependencies in life insurances, Universita degli Studi di Roma ”La Sapienza”, Facolta di
Scienze Statistiche, Dipartimento di Scienze Attuariali e Finanziarie, Italy. 2007
http://hdl.handle.net/10805/2250
[A8] Christer Carlsson and Robert Fullér, A fuzzy approach to real option valuation, FUZZY SETS AND SYSTEMS, 139(2003) 297-312. [MR2006777]. doi 10.1016/S0165-0114(02)00591-2
in journals
2016
A8-c180 MING Lei, YANG Shenggang, Pricing European options based on the hesitation degree of investors,
Systems Engineering - Theory & Practice, 36: (6) pp. 1393-1398 (in Chinese). 2016
http://dx.doi.org/10.12011/1000-6788(2016)06-1392-07
A8-c179 S Muzzioli, B De Baets, Fuzzy approaches to option price modelling, IEEE TRANSACTIONS ON
FUZZY SYSTEMS (to appear). 2016
http://dx.doi.org/10.1109/TFUZZ.2016.2574906
A8-c178 Ming-Gao Dong, Shou-Yia Li, Project investment decision making with fuzzy information: A literature review of methodologies based on taxonomy, JOURNAL OF INTELLIGENT & FUZZY SYSTEMS,
30: (6) pp. 3239-3252. 2016
http://dx.doi.org/10.3233/IFS-152068
A8-c177 Hongjun Dai, Tao Sun, Wen Guo, Brownfield Redevelopment Evaluation Based on Fuzzy Real Options, SUSTAINABILITY, 8(2016), number 2, Paper 170. 10 p. 2016
http://dx.doi.org/10.3390/su8020170
29
Although the real option approach takes into account the value of investment opportunities, it
also has a disadvantage. The parameters in the model, such as the present value of future cash
flows, are assumed to be a fixed value. In fact, it is difficult to make accurate estimates of these
parameters. We can only estimate a range of these parameters. Fuzzy numbers can be expressed in
a range. The emergence of the fuzzy theory provides a new train of thought for solving real option
pricing problems. Therefore, some scholars apply fuzzy mathematics theories to the process of
real option pricing. Carlsson and Fuller are forerunners who improved the B-S pricing model by
means of fuzzy mathematics theory [32]. In 2003, Carlsson and Fuller set up a real option pricing
model for the fuzzy environment. Most of later scholars, along this way of thinking, improved
fuzzy real option pricing models and their applications [A8-35]. (page 3)
A8-c176 Junyan Guo, Zdenek Zmeskal, Valuation of the China Internet company under a real option approach,
PERSPECTIVES IN SCIENCE (to appear). 2016
http://dx.doi.org/10.1016/j.pisc.2015.11.012
2015
A8-c175 Changsheng Yi, Qiumei Jin, A Multi-stages Decision Approach for Managerial Flexibility of Energy
R&D Project under Fuzzy Environment, International Journal of Statistics and Probability, 4(2015), number
3, pp. 169-180. 2015
http://www.ccsenet.org/journal/index.php/ijsp/article/view/51350/27512
The literature about fuzzy set applied to managerial flexibility of R&D investment decision has
been developed abundantly under incomplete information. As an early application, Carlsson and
Fullér (Carlsson & Fullér, 2003) formulated a simple fuzzy real option valuation framework in
which the expected cash flows and costs are all described as trapezoidal fuzzy sets. In order to
obtain the optimal exercise time, the possibilistic mean value and variance of fuzzy numbers are
presented in a fuzzy environment. (page 170)
A8-c174 Chih-Long Lin, Jun-Liang Chen, Si-Jing Chen, Rungtai Lin, The Cognition of Turning Poetry Into
Painting, US-CHINA EDUCATION REVIEW B, 5(2015), number 8, pp. 471-487.
http://dx.doi.org/10.17265/2161-6248/2015.08.001
The application of the fuzzy approach is widespread in various fields, from behavioral and social
science to product design and human factors (Lin, 1994). Fuzzy rating allows respondents to
provide an imprecise rating that takes into account the reality of the imprecision of human thoughts
(Carlsson & Fullér, 2003). (page 479)
The result showed that the fuzzy approach can be applied for evaluating paintings effectively and
can provide artists with an idea of how to concentrate their efforts at the creation stage in order to
communicate easily with their audience. The fuzzy approach seems to be a good way to provide a
possible solution to this methodological problem (Carlsson & Fullér 2003; Chen, Lin, & Huang,
2006). (page 485)
A8-c173 Irem Ucal Sari, Cengiz Kahraman, Interval Type-2 Fuzzy Capital Budgeting, INTERNATIONAL
JOURNAL OF FUZZY SYSTEMS, 17: (4), pp. 635-646. 2015
http://dx.doi.org/10.1007/s40815-015-0040-5
A8-c172 Rupak Bhattacharyya, A Grey Theory Based Multiple Attribute Approach for R&D Project Portfolio
Selection, FUZZY INFORMATION AND ENGINEERING, 7(2015), number 2, pp. 211-225. 2015
http://dx.doi.org/10.1016/j.fiae.2015.05.006
A8-c171 Qian Wang, D Marc Kilgour, Keith W Hipel Facilitating risky project negotiation: An integrated approach using fuzzy real options, multicriteria analysis, and conflict analysis, INFORMATION SCIENCES,
295(2015), pp. 544-557. 2015
http://dx.doi.org/10.1016/j.ins.2014.10.049
Fuzzy real options were first introduced by Carlsson and Fuller [A8], who attempted to identify
optimal strategies using real options analysis with uncertain parameters. This idea can be extended
30
to tackle the private risk problem [4]. When the effects of private risk are not negligible and expert
estimation is unavoidable, fuzzy real options may be more appropriate than (crisp) real options,
even though the models are more complex. Since fuzzy real options modeling incorporates fuzzy
variables into stochastic processes, this combination meets practical needs in many applications,
especially when descriptive expert knowledge, which can be fuzzy in nature, must be used to calibrate the parameters of a stochastic process. Related mathematical concepts such as fuzzy random
variables and random fuzzy variables, and their applications, have been explored in [1214]. (page
546)
A8-c170 Qian Wang, D Marc Kilgour, Keith W Hipel, Numerical Methods to Calculate Fuzzy Boundaries for
Brownfield Redevelopment Negotiations, Group Decision and Negotiation, 24(2015), pp. 515-536. 2015
http://dx.doi.org/10.1007/s10726-014-9417-3
Fuzzy real options were first introduced to identify optimal strategies using real options analysis with fuzzy parameters (Carlsson and Fuller 2003). The possibility mean and variance were
introduced in combination with real options analysis. This idea can be extended to tackle the
private risk problem: random variables are employed to model market uncertainty, while fuzzy
representations are used for private uncertainty (Wang et al. 2009a). (page 520)
A8-c169 Tarik Driouchi, Lenos Trigeorgis, Yongling Gao, Choquet-based European option pricing with stochastic (and fixed) strikes OR Spectrum, 37: (3) pp. 787-802.. 2015
http://dx.doi.org/10.1007/s00291-014-0378-3
Alternative approaches and paradigms for representing uncertainty in investment decision-making
and option pricing include robust control (Hung and So 2010; Zymler et al. 2011), fuzzy sets
(Carlsson and Fuller 2003; Muzzioli and Torricelli 2004; Zmeskal 2010), multiple-priors (Nishimura
and Ozaki 2007; Riedel 2009), and Choquet ambiguity (Roubaud et al. 2010; Agliardi and Sereno
2011). (page 790)
2014
A8-c168 Gaston S Milanesi, Diego Broz, Fernando Tohme, Daniel Rossit, Strategic Analysis Of Forest Investments Using Real Option: The Fuzzy Pay-Off Model (Fpom), Fuzzy Economic Review, XIX(2014), issue
1, pp. 33-44. 2014
A8-c167 C C Popescu, A Fuzzy Optimization Model, ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, 48(2014), number 2, pp. 201-213. 2014
WOS: 000338090100012
A8-c166 Mingming Zhang, Dequn Zhou, Peng Zhou, A real option model for renewable energy policy evaluation with application to solar PV power generation in China, Renewable and Sustainable Energy Reviews,
40(2014), pp. 944-955. 2014
http://dx.doi.org/10.1016/j.rser.2014.08.021
Under current situation, the development of renewable energy cannot run normally without the
support of policy. So lots of authors have directed attention to the policy evaluation of renewable
energy using real option theory. Christer and Robert [34] applied real option methods to determine
the implementation time and value of environmental policy. (page 946)
A8-c165 M Modarres Yazdi, M Shafiei, S M Sahihi Oskooyi, Comprehensive Method to Determine Real Option
Utilizing Probability Distribution, International Journal of Research in Industrial Engineering, 3(2104),
number 1, pp. 11-25. 2014
http://www.nvlscience.com/nvl/Gallery/contents/d6a872c5-44f1-4520-96af-724b2e36f8c9.pdf
A8-c164 Aimin Heng, Qian Chen, Yingshuang Tan, Fuzzy Optimization of Option Pricing Model and Its Application in Land Expropriation, JOURNAL OF APPLIED MATHEMATICS 2014(2014), Paper 635898.
2014
http://dx.doi.org/10.1155/2014/635898
31
Option pricing is irreversible, fuzzy, and flexible. The fuzzy measure which is used for real option
pricing is a useful supplement to the traditional real option pricing method. Based on the review
of the concepts of the mean and variance of trapezoidal fuzzy number and the combination with
the Carlsson-Fuller model, the trapezoidal fuzzy variable can be used to represent the current price
of land expropriation and the sale price of land on the option day. Fuzzy Black-Scholes option
pricingmodel can be constructed under fuzzy environment and problems also can be solved and
discussed through numerical examples. (page 1)
As changes of the external environment make the investment on agriculture land irreversible, fuzzy
and flexible, possible profit of agriculture land bought in by potential opportunities and the added
value obtained by taking advantage of all kinds of chances in a smart way cannot be ignored when
compensating for land expropriation. And this means that attention should be paid not only to
the certain value of agriculture land but also to the uncertain value of agriculture land, namely,
the fuzzy value. On this basis and combined with Carlsson-Fuller model, we will make use of
trapezoidal fuzzy variable to show the present price and the price of land on option expiration
date during land expropriation and then we can build a B-S option pricing model by the help of
statistics to figure it out. (page 2)
After analyzing the feature of the real option of the land expropriation, we introduce the fuzzy
theory into the real option pricing model when evaluating the value of the project. By combining
the fuzzy expected value and the variance with Carlsson-Fuller model, we use the trapezoidal
fuzzy variable to indicate the present price of the city land and the price when option is expired,
constructing a Black-Scholes option pricing model in fuzzy circumstance to work it out through
number of examples. This method overcomes the impossibility of predicting model parameter
caused by lack of enough statistics and fuzziness of land expropriation by employing a series of
operations such as the fuzzy optimization of the Black-Scholes model with the same fluctuation
ratio; E. (page 6)
A8-c163 Prity Kumari, Saroj Sinha, Improving the performance of a firm through investment in intangible
assets, International Journal of Conceptions on Management and Social Sciences, 2: (1) pp. 26-32. 2014
http://www.worldairco.org/IJCMSS/March2014Paper71.pdf
In fuzzy cost and fuzzy value circumstances, Carlsson & Fuller [A8] suggest the following formula
for computing the fuzzy Real Option (FROV): (page 29)
A8-c162 G Lo Nigro, A Morreale, G Enea, Open Innovation: A Real Option To Restore Value To The Biopharmaceutical R&D, International Journal of Production Economics, Volume 149, March 2014, Pages
183-193. 2014
http://dx.doi.org/10.1016/j.ijpe.2013.02.004
Specifically, the authors adopt a fuzzy real options valuation method that is based on the method
proposed by Carlsson & Fullér (2003). They use the Geske compound options valuation model
for all 20 drugs, but we believe that the method (Geske, B&S, or simple NPV) should depend on
the remaining phases. Moreover, the authors formulate the R&D portfolio selection problem as
a fuzzy zero-one integer programming model with the aim of maximizing an objective function,
subject to budgetary constraints or constraints on the availability of human resources and other
mathematical constraints. (page 189)
2013
A8-c161 Liu S, Xu W, Hou J, Zhao M, Sun Q, Option valuation based on fuzzy theory in risk management,
International Journal of Applied Mathematics and Statistics, 48: (18) pp. 414-422. 2013
A8-c160 Catalin Cioaca, Mircea Boscoianu, Applications of Real Options Analysis in Aviation Security Investments, Applied Mechanics and Materials, 436(2013), pp. 32-39. 2013
http://dx.doi.org/10.4028/www.scientific.net/AMM.436.32
A8-c159 Giovanna Lo Nigro, Gianluca Enea, Azzurra Morreale, A user friendly real option based model to
optimize pharmaceutical R&D portfolio, Journal of Applied Operational Research, 5(2013), number 5, pp.
83-95. 2013
http://www.tadbir.ca/jaor/archive/v5/n3/jaorv5n3p83.pdf
32
In addition, according to Collan et al. (2009), there are also a number of later developed versions
of the above mentioned methods, which include the use of fuzzy variables. For example, Carlsson
and Fuller (2003) use the B&S formula, where the present values of expected cash flows and
expected costs are estimated by trapezoidal fuzzy numbers. Similarly, a fuzzy compound option
model based on the Geske model is proposed by Wang and Hwang (2007). Starting from the Cox
et al.(1979) model, Muzzioli and Reynaerts (2008), use fuzzy logic in order to investigate which
is the effect on the option price of assuming the volatility as an uncertain parameter. (page 85)
A8-c158 CAGRI TOLGA A, TUYSUZ FATIH, KAHRAMAN CENGIZ, A FUZZY MULTI-CRITERIA DECISION ANALYSIS APPROACH FOR RETAIL LOCATION SELECTION, INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING, 12(2013), issue 4, pp. 729-755.
2013
http://dx.doi.org/10.1142/S0219622013500272
A8-c157 Shashank Pushkar, Prity Kumari, Akhileshwar Mishra, IT Project Selection using Fuzzy Real Option
Optimization Model, INTERNATIONAL JOURNAL OF E-ENTREPRENEURSHIP AND INNOVATION,
3(2013), number 3, pp. 1-13. 2013
http://dx.doi.org/10.4018/jeei.2012070104
A8-c156 Yongling Gao, Tarik Driouchi, Incorporating Knightian uncertainty into real options analysis: Using
multiple-priors in the case of rail transit investment, TRANSPORTATION RESEARCH PART B, 55(2013),
pp. 23-40. 2013
http://dx.doi.org/10.1016/j.trb.2013.04.004
Rail transit projects can be subjected to many uncertain events. These could include fluctuations
in traffic demand, cost overruns, unstable socio-economic conditions, technology obsolescence,
and changes in government policy. Over time, such sources of randomness will alter the dynamics
of population in urban areas subjecting analysts to partial ignorance and fuzziness during project
planning and appraisal (Carlsson and Fuller, 2003). Because of this, and due to the close relationship between population density and the initiation of rail transit projects in a number of cities,
it is reasonable to consider deviations in population forecasts as a key source of uncertainty in
transportation and infrastructure project analysis. (page 26)
A8-c155 Srimantoorao S Appadoo, Aerambamoorthy Thavaneswaran, Recent Developments in Fuzzy Sets
Approach in Option Pricing, JOURNAL OF MATHEMATICAL FINANCE, 3(2013), pp. 312-322. 2013
http://dx.doi.org/10.4236/jmf.2013.32031
Recently there has been growing interest in fuzzy option pricing. Carlsson and Fuller [A8] were
the first to study the fuzzy real options and Thavaneswaran et al. [2] demonstrated the superiority
of the fuzzy forecasts and then derived the membership function for the European call price by
fuzzifying the interest rate, volatility and the initial value of the stock price. In this paper, we
discuss recent developments in fuzzy option pricing based on Black-Scholes models. (page 312)
In these circumstances we suggest the use of the following fuzzy weighted possibilistic (heuristic)
option formula as in Carlsson and Fuller [A8] for computing fuzzy option values. We consider the
following Black-Scholes f ormula for a dividend paying stock with exercise price K. (page 317)
A8-c154 Zhou Ke Qiu Cheng, Analysis of several models of investment value of logistics project evaluation,
ECONOMICS RESEARCH INTERNATIONAL, vol. 2013, Paper 412725. 2013
http://downloads.hindawi.com/journals/econ/aip/412725.pdf
The application of the real option to evaluate logistics project investment value is widely used.
Schwartz and moon [1] believe that real option in venture capital evaluation can make better
explanation. Dayanik [2] and so forth solved the one-dimensional diffusion process of optimal
stopping problems, and the results for American option pricing, control, and so on are suitable. At
the same time, in view of logistics project investment also having the of fuzziness, fuzzy factors
with real option theory to carry on the research is very important. Carlsson and Fullér [A8] considered the rates of fuzzy-relation-fuzzy-option formula and used the optimization theory to build
the project investment decision model of R&D optimization. (page 1)
33
A8-c153 SHEN KAO-YI, IMPLEMENTING VALUE INVESTING STRATEGY THROUGH AN INTEGRATED
FUZZY-ANN MODEL, JOURNAL OF THEORETICAL AND APPLIED INFORMATION TECHNOLOGY, 51(2013), number 1, pp. 150-157. 2013
http://www.jatit.org/volumes/Vol51No1/24Vol51No1.pdf
Due to the complicated characteristics of investment, experts need to rely on their financial knowledge and experience while considering the complex evaluation process. Fuzzy inference system
is known for being capable to tolerate imprecise data and to model nonlinear relationships of high
complexity [A8]-[20]. (page 152)
A8-c152 Andrea Capotorti, Gianna Figa-Talamanca, On an implicit assessment of fuzzy volatility in the Black
and Scholes environment, FUZZY SETS AND SYSTEMS, 223(2013), pp. 59-71. 2013
http://dx.doi.org/10.1016/j.fss.2013.01.010
By applying different methodologies both contributions derive a fuzzy price for Call and Put
options with crisp maturities and strike prices. We stress that the support, the core and the shape
of fuzzy variables in the applications suggested therein are assumed as known (or preliminarily
assigned). In [A8] the authors apply BS model to price real options; they assume both the stock
price and the strike of the option to be modelled as trapezoidal fuzzy numbers. (page 60)
2012
A8-c151 Wu Y, Qiu W-H, Zhou P, Real option model under fuzzy group decision making, Kongzhi yu Juece/Control
and Decision 27(2012), number 12, pp. 1828-1832+1838. 2012
Scopus: 84872239869
A8-c150 Yingshuang Tan and Yong Long, Option-Game Approach to Analyze Technology Innovation Investment under Fuzzy Environment, Journal of Applied Mathematics, Volume 2012, Article ID 830850. 2012
http://dx.doi.org/10.1155/2012/830850
From Carlsson and Fullér [A8] and Yoshida [7], it is easy to see that the crisp possibility mean or
expected value of A and the possibility variance of A: (page 3)
A8-c149 Danmei Zhu, Xingtong Wang, A Petroleum R&D Project Portfolio Investment Selection Model with
Project Interactions under Uncertainty, JOURNAL OF PETROLEUM SCIENCE RESEARCH, 1(2012),
number 3, pp. 44-50. 2012
http://www.jpsr.org/paperInfo.aspx?ID=3675
The value of R&D project depends on not only the cash inflow from investment in the stage of
technology development but also the value of the opportunities in the later stage of research benefit
from the initial investment. If the situation is not as optimistic as expected after the initial investment of research, decision of cutting off later investment should be made immediately to avoid
more losses. So by the fuzzy real option model of Carlsson and Fullér [A5] and the compound
option model of Geske [10], we can establish the fuzzy compound real option evaluation model
of R&D project. (page 45)
A8-c148 Faramak Zandi, Madjid Tavana, Aidan O’Connor, A strategic cooperative game-theoretic model for
market segmentation with application to banking in emerging economies, TECHNOLOGICAL AND ECONOMIC DEVELOPMENT OF ECONOMY, 18(2012), number 3, pp. 389-423. 2012
http://dx.doi.org/10.3846/20294913.2012.688072
A8-c147 Hassanzadeh F, Collan M, Modarres M, A practical approach to R&D portfolio selection using the
fuzzy pay-off method, IEEE Transactions on Fuzzy Systems, 20(2012), number 4, pp. 615-622. Paper
6109284. 2012
http://dx.doi.org/10.1109/TFUZZ.2011.2180380
Carlsson and Fullér [A8] proposed a heuristic formula to compute fuzzy real option value (FROV)
of R&D projects which was later used by several authors. For instance, Wang andHwang [20]
formulated a fuzzy R&D portfolio selection problem using a pessimistic measure where FROV
34
of selected projects was used as the objective function. Carlsson et al. [A5] used FROV concept
instead of traditional DCF and developed a fuzzy zeröone integer programming model to find
optimal R&D portfolio with the largest aggregate possibilistic deferral flexibility. Zhu et al. [22]
used FROV to develop a fuzzy model for R&D portfolio selection with the ENPV of selected
projects as the objective function. (page 616)
A8-c146 Madjid Tavana, Faramak Zandi, Applying fuzzy bi-dimensional scenario-based model to the assessment of Mars mission architecture scenarios, ADVANCES IN SPACE RESEARCH, 49(2012), issue 4, pp.
629-647.
http://dx.doi.org/10.1016/j.asr.2011.11.019
Zadeh (1965) has proposed that the key elements in human thinking are not numbers but labels
of fuzzy sets. Much knowledge in the real world is fuzzy rather than precise and fuzzy ROA can
help DMs cope with the environmental uncertainties in capital investment assessment. Carlsson
and Fullér (2003) introduced a (heuristic) real option rule in a fuzzy setting, where the expected
risks, costs and benefits were estimated by trapezoidal fuzzy numbers. (page 632)
A8-c145 Farhad Hassanzadeh, Mikael Collan, Mohammad Modarres, A practical R&D selection model using fuzzy pay-off method, INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY, 58(2011), numbers 1-4, pp. 227-236. 2012
http://dx.doi.org/10.1007/s00170-011-3364-9
Carlsson and Fullér [A8] proposed a heuristic formula based on the Black-Scholes option valuation formula to compute Fuzzy Real Option Value (FROV) of R&D projects from fuzzy inputs.
Their model assumes that the underlying process follows geometric Brownian motion which determines the probability distribution and the resulting asset value; the model is therefore a hybrid
of fuzzy inputs (possibility theory) and probability theory. (page 229)
A8-c144 Chew Jian You, C K M Lee, S L Chen, Roger J Jiao, A real option theoretic fuzzy evaluation model for
enterprise resource planning investment, JOURNAL OF ENGINEERING AND TECHNOLOGY MANAGEMENT, 29(2012), number 1, pp. 47-61. 2012
http://dx.doi.org/10.1016/j.jengtecman.2011.09.005
Applying fuzzy logic in real option evaluation, a fuzzy number is used to represent estimated future cash flow from a project or investment. Using the possibility distribution of a fuzzy number,
future cash flow is estimated with a distribution instead of an exact figure, which is quite reasonable as we are taking into consideration the attributes of uncertainties. The fuzzy mean of the
possibility distribution will hence be the expected future cash flow. Carlsson and Fullér (2003)
have described in detail about the possibilistic mean value and variance of fuzzy numbers and
while trapezoidal fuzzy number has been adopted in their paper. (page 51)
2011
A8-c143 TAN Ying-shuang, LONG Yong, CHEN Zhe, Technology innovation investment of the option-game
model under fuzzy environment, SYSTEMS ENGINEERING - THEORY & PRACTICE, 31(2011), number 1, pp. 2095-2100 (in Chinese). 2011
www.sysengi.com/CN/article/downloadArticleFile.do?attachType=PDF&id=109538
A8-c142 Shang-En Yu, Ming-Yuan Leon Li, Kun-Huang Huarng, Tsung-Hao Chen, Chen-Yuan Chen, Model
construction of option pricing based on fuzzy theory, JOURNAL OF MARINE SCIENCE AND TECHNOLOGY, 19(2011), number 5, pp. 460-469. 2011
http://jmst.ntou.edu.tw/marine/19-5/460-469.pdf
A8-c141 Shiu-Hwei Ho, Shu-Hsien Liao, A fuzzy real option approach for investment project valuation, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), issue 12, pp. 15296-15302. 2011
http://dx.doi.org/10.1016/j.eswa.2011.06.010
35
In DCF, parameters such as cash flows and discount rates are difficult to estimate (Carlsson &
Fuller, 2003). In particular, innovative investment projects may count on the subjective judgments
of decision makers due to lack of past data for reference. These parameters are essentially estimated under uncertainty. With respect to uncertainty, probability is one way to depict whereas
possibility is another.
..
.
Providing a precise volatility estimate is difficult; therefore, they used a possibility distribution
to model volatility uncertainty and to price an American option in a multiperiod binomial model.
Carlsson and Fuller (2003) mentioned that the imprecision in judging or estimating future cash
flows is not stochastic in nature, and that the use of the probability theory leads to a misleading
level of precision. Their study introduced a real option rule in a fuzzy setting in which the present
values of expected cash flows and expected costs are estimated by trapezoidal fuzzy numbers.
They determined the optimal exercise time with the help of possibilistic mean value and variance
of fuzzy numbers. The proposed model that incorporates subjective judgments and statistical
uncertainties may give investors a better understanding of the problem when making investment
decisions. (page 15297)
A8-c140 Qian Wang, D Marc Kilgour, Keith W Hipel, Fuzzy Real Options for Risky Project Evaluation Using
Least Squares Monte-Carlo Simulation, IEEE SYSTEMS JOURNAL, 5(2011), issue 3, pp. 385-395. 2011
http://dx.doi.org/10.1109/JSYST.2011.2158687
Fuzzy real options were first introduced by Carlsson and Fuller [A8], who attempted to identify
optimal strategies using real options analysis with uncertain parameters. The possibility mean and
variance were introduced in combination with real options analysis [A14]. Unlike the crisp parameters required in real options analysis, fuzzy real options allow parameters as fuzzy numbers.(page
386)
A8-c139 Faramak Zandi, Madjid Tavana, An Optimal Investment Scheduling Framework for Intelligent Transportation Systems Architecture, JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS, 15(2011),
number 3, pp. 115-132. 2011
http://www.tandfonline.com/doi/abs/10.1080/15472450.2011.594669
A8-c138 Young-Chan Lee, Seung-Seok Lee, The valuation of RFID investment using fuzzy real option, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), issue 10, pp. 12195-12201. 2011
http://dx.doi.org/10.1016/j.eswa.2011.03.076
A8-c137 David Allenotor, Ruppa K. Thulasiram, Grid resources valuation with fuzzy real option, INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING AND NETWORKING, 7(2011), number 1, pp. 1-7. 2011
http://inderscience.metapress.com/link.asp?id=15161065571r25mw
A8-c136 Faramak Zandi; Madjid Tavana; David Martin, A fuzzy group Electre method for electronic supply
chain management framework selection, INTERNATIONAL JOURNAL OF LOGISTICS: RESEARCH
AND APPLICATIONS, 14(2011), number 1, pp. 35-60. 2011
http://dx.doi.org/10.1080/13675567.2010.550872
In recent years, several researchers have combined fuzzy set theory with ROA. Carlsson and Fullér
(2003) introduced a (heuristic) real option rule in a fuzzy setting, where the present values of expected cash ows and expected costs are estimated by trapezoidal fuzzy numbers. Chen et al. (2007)
developed a comprehensive but simple methodology to evaluate technology-based investments in
a nuclear power station based on fuzzy risk analysis and real option approach. (page 39)
A8-c135 Costin-Ciprian POPESCU, Cristinca FULGA, POSSIBILISTIC OPTIMIZATION WITH APPLICATION TO PORTFOLIO SELECTION, PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A,
12(2011), number 2, pp. 88-94. 2011
http://www.acad.ro/sectii2002/proceedings/doc2011-2/02-Popescu.pdf
A8-c134 Faramak Zandi, Madjid Tavana, A fuzzy multi-objective balanced scorecard approach for selecting an
optimal electronic business process management best practice (e-BPM-BP), BUSINESS PROCESS MANAGEMENT JOURNAL, 17(2011), issue 1, pp. 147-178. 2011
36
http://dx.doi.org/10.1108/14637151111105625
A8-c133 Faramak Zandi, Madjid Tavana, A Fuzzy Goal Programming Model for Strategic Information Technology Investment Assessment, BENCHMARKING: AN INTERNATIONAL JOURNAL, 18(2011), issue
2, pp. 1-34. 2011
http://www.emeraldinsight.com/journals.htm?articleid=1905896&show=abstract
In recent years, several researchers have combined fuzzy sets theory with ROA. Carlsson and
Fullér (2003) introduced a (heuristic) real option rule in a fuzzy setting, where the present values
of expected cash flows and expected costs are estimated by trapezoidal fuzzy numbers.
A8-c132 D. Bednyagin, E. Gnansounou, Real options valuation of fusion energy R&D programme, ENERGY
POLICY, 39(2011), Issue 1, pp. 116-130. 2011
http://dx.doi.org/10.1016/j.enpol.2010.09.019
Fuzzy approach to real option valuation has been investigated in several publications. Carlsson
and Fuller (2003) introduced a heuristic real option rule in a fuzzy setting, where the present values
of expected cash flows and expected costs are estimated by trapezoidal fuzzy numbers. (page 120)
A8-c131 Farhad Hassanzadeh, Mikael Collan, Mohammad Modarres, A technical note on ”A fuzzy set approach
for R&D portfolio selection using a real options valuation model” by Wang and Hwang (2007), OMEGA,
39(2011), number 4, pp. 464-465. 2011
http://dx.doi.org/10.1016/j.omega.2010.10.001
The problem of R&D project portfolio selection is very well known and intensely studied under
uncertain environments [1,2]. An instance of this problem is considered in a paper published in
Omega 2007 by Wang and Hwang [3], where fuzzy set theory is employed to capture the natural
uncertainty of R&D decision making. The authors stress the importance of effective R&D project
valuation, criticize classical valuation methods, and adopt a fuzzy real options valuation method
that is based on the method proposed by Carlsson and Fullér [A8]. (page 464)
2010
A8-c130 YU Shao-wei, LI Xiu-hai, LIU Qing-ling, On real option pricing based on interval analysis and the
cloud model, JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 45(2010), number 5,
pp. 64-68 (in Chinese). 2010
http://d.wanfangdata.com.cn/periodical_sddxxb201005012.aspx
A8-c129 Shin-Yun Wang, Cheng Few Lee, A Fuzzy Real Option Valuation Approach To Capital Budgeting
Under Uncertainty Environment, INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY
AND DECISION MAKING, 9(2010), number 5, pp. 695-713. 2010
http://dx.doi.org/10.1142/S0219622010004056
A8-c128 Faramak Zandi; Madjid Tavana, A hybrid fuzzy real option analysis and group ordinal approach for
knowledge management strategy assessment, KNOWLEDGE MANAGEMENT RESEARCH & PRACTICE, 8(2010), pp. 216-228. 2010
http://dx.doi.org/10.1057/kmrp.2010.12
In recent years, several researchers have combined fuzzy sets theory with ROA. Carlsson & Fullér
(2003) introduced a real option heuristic in a fuzzy environment, where the present values of
expected cash flows and expected costs were estimated by trapezoidal fuzzy numbers. (page 218)
A8-c127 Zdeněk Zmeškal, Generalised soft binomial American real option pricing model (fuzzy-stochastic
approach), EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 207(2010), vol. 2, pp. 1096-1103.
2010
http://dx.doi.org/10.1016/j.ejor.2010.05.045
37
Special attention in hybrid (fuzzy-stochastic) financial modelling is paid to option valuations,
because of providing abundant and a lot of applications. Researchers has dealt with relatively new
topic of fuzzy-stochastic option valuation models which are presented, e.g., in Zmeskal (2001),
Simonelli (2001), Yoshida (2002), Carlsson and Fuller (2003), Yoshida (2003), Muzzioli and
Torricelli (2004), Wu (2005), Cheng et al. (2005), Yoshida et al. (2005), Liyan Han and Wenli
Chen (2006), Zhang et al. (2006), Wu (2007), Muzzioli and Reynaerts (2007) and Thiagarajaha et
al. (2007), Guerra et al. (2007), Chrysafis and Papadopoulos (2009). (page 1097)
A8-c126 Federica Cucchiella, Massimo Gastaldi, S C Lenny Koh, Performance improvement: an active life
cycle product management, INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 41(2010), issue 3,
pp. 301-313. 2010
http://dx.doi.org/10.1080/00207720903326886
A8-c125 Shu-Hsien Liao, Shiu-Hwei Ho, Investment project valuation based on a fuzzy binomial approach,
INFORMATION SCIENCES, 180(2010), issue 11, pp. 2124-2133. 2010
http://dx.doi.org/10.1016/j.ins.2010.02.012
Carlsson and Fuller [A8] mentioned that the imprecision in judging or estimating future cash
flows is not stochastic in nature, and that the use of the probability theory leads to a misleading
level of precision. Their study introduced a (heuristic) real option rule in a fuzzy setting in which
the present values of expected cash flows and expected costs are estimated by trapezoidal fuzzy
numbers. They determined the optimal exercise time with the help of possibilistic mean value
and variance of fuzzy numbers. The proposed model that incorporates subjective judgments and
statistical uncertainties may give investors a better understanding of the problem when making
investment decisions. (page 2125)
A8-c124 A. Çagri Tolga, C. Kahraman, M.L. Demircan, A comparative fuzzy real options valuation model using
trinomial lattice and Black-Scholes approaches: A call center application, JOURNAL OF MULTIPLEVALUED LOGIC AND SOFT COMPUTING, 16 (2010), No.1-2, pp. 135-154. 2010
http://www.oldcitypublishing.com/FullText/MVLSCfulltext/MVLSC16.1-2fulltext/MVLSCv16n12p135-154Tolga.pdf
2009
A8-c123 LI Yao-kuang, ZHANG Xiao-wei, ANG Chao-wen, Evaluation of the asset’s value by using fuzzy twostage discounted cash flow model, JOURNAL OF MODERN ACCOUNTING AND AUDITING, 5(2009),
number 11, pp. 19-27. 2009
www.accountant.org.cn/doc/acc200911/acc20091103.pdf
Zmeskal (2001) proposed a fuzzy-stochastic methodology under fuzzy numbers to appraise a firm
equity. WANG (2002) proposed a fuzzy grey prediction system to analyze stock date and to
predict stock prices. Carlsson and Fuller (2003) introduced a real option rule in a fuzzy setting to
determine the optimal exercise time by the help of possibilistic mean value and variance of fuzzy
numbers. YAO, et al (2005) proposed a fuzzy discounted cash flow model by developing a fuzzy
logic system that based on the classical discounted cash flow model. (page 20)
A8-c122 Xu Guoquan; Wang Yong, Real Options and Review of the energy field, INQUIRY INTO ECONOMIC
ISSUES, 1(2009), pp. 125-132 (in Chinese). 2009
http://d.wanfangdata.com.cn/Periodical_jjwtts200901023.aspx
A8-c121 I. Uçal; C.Kahraman, Fuzzy real options valuation for oil investments, TECHNOLOGICAL AND
ECONOMIC DEVELOPMENT OF ECONOMY, 15 (2009), issue 4, pp. 646-669. 2009
http://dx.doi.org/10.3846/1392-8619.2009.15.646-669
Traditional valuation methods are less viable under uncertainty. Hence, other methods such as real
options valuation models, which can minimize uncertainty, have become more important. In this
38
study, the hybrid approach suggested by Carlsson and Fuller is examined for the case of discrete
compounding as this approach better models risky cash flows. A new real options valuation model
that will evaluate the investment in a more realistic way is suggested by postponing the defuzzification of parameters in early stages. The suggested model has been applied to the data of an
oil field investment and in conclusion the loss of information caused by early-defuzzification has
been determined. (page 646)
Carlsson and Fuller (2003) improved a fuzzy approach for real options valuation, which is one
of the mostly used real options valuation approaches, by applying a heuristic real option rule in
a fuzzy setting, where the present values of expected cash flows and expected costs are estimated
by trapezoidal fuzzy numbers and they determined the optimal exercise time with the assistance
of possibilistic mean value and variance of fuzzy numbers. (page 650)
In this study we suggest a new model based on Carlsson & Fuller’s hybrid approach using discrete
compounding instead of continuous compounding by defuzzifying the costs and revenues at a later
stage than the based model and the based model has been improved by fuzzifying interest rates
and probabilities. (page 653)
Using real options valuation methods to analyse an investment decision reduces the uncertainty
to minimum and it ensures that the investment assessment is made in as the most realistic way
as possible. The model suggested by Carlsson and Fuller (2003) has been found to be the most
frequently used method amongst the fuzzy real options assessment methods during literature researches. In this model, however, it is observed that the fuzzy revenue and expenditure values
were defuzzified at a relatively early stage. Early defuzzification of the fuzzy parameters causes
information loss. In this study, a new model has been suggested; it postpones the defuzzification
of fuzzy parameters in the real options valuation in order to avoid this information loss. Carlsson
and Fuller’s model has been re-arranged for discrete compounding and then the defuzzification
of revenue and expenditures has been postponed and relavant equations have been formed for the
cases of early defuzzifying probabilities and defuzzifying them at the last stage. On the other hand,
the difference between the applications of this new model and of the early defuzzifying model has
been found to be the information loss due to the early defuzzification. (pages 666-667)
A8-c120 Dan-mei Zhu, Tie Zhang, Xing-tong Wang, Dong-ling Chen, Developing an R&D projects portfolio
selection decision system based on fuzzy logic, INTERNATIONAL JOURNAL OF MODELLING, IDENTIFICATION AND CONTROL, 8(2009), No. 3, pp. 205-212. 2009
http://dx.doi.org/10.1504/IJMIC.2009.029265
A8-c119 Qian Wang, Keith Hipel, and Marc Kilgour, Fuzzy Real Options in Brownfield Redevelopment Evaluation, JOURNAL OF APPLIED MATHEMATICS AND DECISION SCIENCES, Volume 2009(2009),
Article ID 817137, 19 pages. 2009
http://dx.doi.org/10.1155/2009/817137
The methods proposed to overcome the problem of private risk include utility theory [1, 7], the
Integrated Value Process [4], Monte-Carlo simulation [8, 9], and unique and private risks [10].
This paper uses fuzzy real options, developed by Carlsson and Fullér [A8], to represent private
risk. Representing private risks by fuzzy variables leaves room for information other than market
prices, such as expert experience and subjective estimation, to be taken into account. In addition,
the model of Carlsson and Fullér can be generalized to allow parameters other than present value
and exercise price [A8] to be fuzzy variables, utilizing the transformation method of Hanss [12].
(page 2)
Carlsson and Fullér assume that the present value and exercise price in the option formula are fuzzy
variables with trapezoidal fuzzy membership functions. Because inputs include fuzzy numbers,
the value of a fuzzy real options is a fuzzy number as well. A final crisp Real Option Value (ROV)
can be calculated as the expected value of the fuzzy ROV [A8].
..
.
The concise and effective fuzzy real options approach proposed by Carlsson and Fullér is widely
applicable; see [19-21]. (page 4)
39
A8-c118 Mohammad Modarres; Farhad Hassanzadeh, A Robust Optimization Approach to R&D Project Selection, WORLD APPLIED SCIENCES JOURNAL, 7(2009), No. 5, pp. 582-592. 2009
http://idosi.org/wasj/wasj7%285%29/4.pdf
A8-c117 Y.-Q. Xia, J.-F. Chen, Fuzzy optimization of real options valuation for multi-phase R&D project,
Shanghai Jiaotong Daxue Xuebao/Journal of Shanghai Jiaotong University, 43(2009), pp. 583-586. 2009
A8-c116 Konstantinos A. Chrysafis, Basil K. Papadopoulos, On theoretical pricing of options with fuzzy estimators, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 223 (2009), pp. 552-566.
2009
http://dx.doi.org/10.1016/j.cam.2007.12.006
Since the Black-Scholes option pricing formula is only approximate, it leads to considerable errors, Trenev [17] obtained a refined formula for pricing options. In [19] Wu applied fuzzy approach to the Black-Scholes formula. Zmeskal [20] applied the Black-Scholes methodology of
appraising equity as a European call option. Carlsson and Fullér [A8] used the possibility theory
for fuzzy real option valuation. (page 552)
A8-c115 A. Thavaneswaran, S.S. Appadoo, A. Paseka, Weighted possibilistic moments of fuzzy numbers
with applications to GARCH modeling and option pricing, MATHEMATICAL AND COMPUTER MODELLING, 9(2009) 352-368. 2009
http://dx.doi.org/10.1016/j.mcm.2008.07.035
Another issue is the non-synchronous record of an option price and the price of the underlying
asset. To top it off, options themselves are traded at bid/ask prices. Using models that do not
specifically account for these issues introduces errors - difference between theoretical and observed option premiums. In empirical literature examples of statistical modeling of the errors
include, among others, Jacquier and Jarrow [13] and Bakshi et al. [14]. We introduce an alternative characterization of the error. To this end, we model the uncertainty about the values of interest
rate and stock price using fuzzy numbers. Along the same lines, we model the unobserved parameter, volatility, as a fuzzy number. We replace the fuzzy interest rate, the fuzzy stock price, and
the fuzzy volatility by possibilistic mean value in the fuzzy Black-Scholes formula. The initial
stock price cannot be characterized by a single number. Thus, we assume that the initial stock
price is a fuzzy number of the form S0 = (S1 , S2 , S3 , S4 ). We use a fuzzy number of the form
e−r̃τ = (e−r4 τ , e−r3 τ , e−r2 τ , ee−r1 τ ) = [e−r4 τ + γ(e−r3 τ − e−r4 τ ), e−r1 τ − γ(e−r1 τ − e−r2 τ )]
for the discount factor and σ = (σ1 , σ1 , σ3 , σ4 ) for the volatility. Given these definitions, we suggest the use of the following fuzzy weighted possibilistic (heuristic) option formula as in Carlsson
and Fullér [A8] for computing fuzzy option values. We take an example of the Black-Scholes
formula for a dividend paying stock with exercise price K. (page 366)
2008
A8-c114 DING Si-bo; HUANG Wei-lai; ZHANG Zi-gang Real Option Pricing Method Based on Cloud, SYSTEMS ENGINEERING, 26(2008), number 10, pp. 73-76 (in Chinese). 2008
http://www.cqvip.com/qk/93285x/2008010/29012808.html
A8-c113 LI Yao-kuang; XIONG Xing-hua; XIA qiong; ZHANG Xing-yu, Fuzzy option pricing model for the
evaluation of investees in venture capital investment, JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY (NATURAL SCIENCE), 31(2008), number 9, pp. 1494-1496 (in Chinese). 2008
http://d.wanfangdata.com.cn/Periodical_hfgydxxb200809036.aspx
A8-c112 A.C. Tolga and C. Kahraman, Fuzzy multiattribute evaluation of R&D projects using a real options
valuation model, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 23(2008), pp. 11531176. 2008
http://dx.doi.org/10.1002/int.20312
40
In the literature, fuzzy real options valuation models have been developed under incomplete information. First, Carlsson and Fullér [A8] developed a heuristic real option valuation process in a
fuzzy setting. In their study, present values of expected costs and expected cash flows are calculated by trapezoidal fuzzy numbers. They determined the optimal exercise time with the help of
possibilistic mean value and variance of fuzzy numbers. (page 1155)
A8-c111 Zhu, D.-M., Zhang, T., Chen, D.-L., Gao, H.-X., New fuzzy pricing approach to real option, Dongbei
Daxue Xuebao/Journal of Northeastern University, 29(2008), pp. 1544-1547. 2008
A8-c110 A.C. Tolga, Fuzzy multicriteria R&D project selection with a real options valuation model, JOURNAL
OF INTELLIGENT AND FUZZY SYSTEMS, 19(2008), pp. 359-371. 2008
A8-c109 Onofre Martorell Cunill; Carles Mulet Forteza; Micaela Rosselló Miralles, Valuing growth strategy
management by hotel chains based on the real options approach, TOURISM ECONOMICS, Volume 14,
Number 3, September 2008 , pp. 511-526. 2008
A8-c108 Du, X.-J., Sun, S.-D., Si, S.-B., Cai, Z.-Q, Multi-objective R and D portfolio selection optimization
under uncertainty, SYSTEM ENGINEERING THEORY AND PRACTICE, Volume 28, Issue 2, February
2008, pp. 98-104. 2008
A8-c107 S.S. Appadoo, S.K. Bhatt, C.R. Bector, Application of possibility theory to investment decisions,
FUZZY OPTIMIZATION AND DECISION MAKING, vol. 7, pp. 35-57. 2008
http://dx.doi.org/10.1007/s10700-007-9023-9
A8-c106 A. Tiwari, K. Vergidis, Y. Kuo, Computer assisted decision making for new product introduction
investments, COMPUTERS IN INDUSTRY, 59(1), pp. 96-105. 2008
http://dx.doi.org/10.1016/j.compind.2007.06.014
Real options are described as the means that allow the extension of the decision making period
for an investment, without binding to a particular choice [A8]. Real options prove a strategically
life-saving approach for organisations that have to deal with alternative choices on big investments
regarding new products or services. (page 97)
2007
A8-c105 X.-J. Du, S.-D. Sun, J.-Q. Wang, J.-H. Hao, Multi-objective R and D portfolio selection optimization under uncertainty, Jisuanji Jicheng Zhizao Xitong/Computer Integrated Manufacturing Systems, CIMS
Volume 13, Issue 9, September 2007, pp. 1826-1832+1846. 2007
A8-c104 Wang JT, Hwang WL, A fuzzy set approach for R&D portfolio selection using a real options valuation
model, OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 35 (3): 247-257 JUN
2007
http://dx.doi.org/10.1016/j.omega.2005.06.002
Carlsson and Fullér [A8] have developed a fuzzy real options model to evaluate a project that only
considers a single option. However, an R&D project usually involves multiple phases. Therefore,
the compound options valuation model that involves options whose value is contingent on the
value of other options is more suitable to evaluate the R&D project. (pages 250-251)
The fuzzy value of the R&D project is defined as [A8,27]
p
p
Ṽ = S̃e−δT2 M a1 , b1 , T1 /T2 − C̃3 e−rT2 M a2 , b2 , T1 /T2 − C̃2 e−rT1 N (a2 )
(page 251)
A8-c103 Thavaneswaran A, Thiagarajah K, Appadoo SS Fuzzy coefficient volatility (FCV) models with applications, MATHEMATICAL AND COMPUTER MODELLING, 45 (7-8): 777-786 APR 2007
http://dx.doi.org/10.1016/j.mcm.2006.07.019
Following Carlsson and Fullér [B1, A8], higher order moments of fuzzy numbers are defined. We
also derive the moments and possibilistic kurtosis of the proposed FCV models. (page 778)
41
A8-c102 Thiagarajah, K., Appadoo, S.S., Thavaneswaran, A. Option valuation model with adaptive fuzzy numbers, COMPUTERS AND MATHEMATICS WITH APPLICATIONS, 53 (5), pp. 831-841. 2007
http://dx.doi.org/10.1016/j.camwa.2007.01.011
Since the Black-Scholes option pricing formula is only approximate, which leads to considerable
errors, Trenev [8] obtained a refined formula for pricing options. Due to the fluctuation of the
financial markets from time to time, some of the input parameters in the Black-Scholes formula
cannot always be expected in the precise sense. As a result, Wu [9] applied fuzzy approach to the
Black-Scholes formula. Zmeskal [10] applied Black-Scholes methodology of appraising equity
as a European call option. He used the input data in a form of fuzzy numbers in his approach
to option pricing. Carlsson and Fullér [A8] use possibility theory to fuzzy real option valuation.
(page 832)
2005
A8-c101 Yoshida, Y., Yasuda, M., Nakagami, J.-I., Kurano, M. A discrete-time American put option model with
fuzziness of stock prices, FUZZY OPTIMIZATION AND DECISION MAKING, 4 (3), pp. 191-207. 2005
http://dx.doi.org/10.1007/s10700-005-1889-9
The option pricing for stocks plays an important role in stock markets. Approaches with fuzzy
logic to European options are discussed by some authors (Carlsson and Fullér (2003), Simonelli
(2001), Yoshida (2003), Zmeskal (2001)). (page 191)
2004
A8-c100 Wang, G., Wu, C. The integral over a directed line segment of fuzzy mapping and its applications,
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 12 (4), pp. 543-556. 2004
http://dx.doi.org/10.1142/S0218488504002977
in proceedings and edited volumes
2015
A8-c69 David Allenotor, Ruppa K Thulasiram, A Discrete Time Financial Option Pricing Model for Cloud Services, Ubiquitous Intelligence and Computing, 2014 IEEE 11th International Conference on and IEEE 11th
Intl Conf on and Autonomic and Trusted Computing, and IEEE 14th Intl Conf on Scalable Computing and
Communications and Its Associated Workshops (UTC-ATC-ScalCom), IEEE, (ISBN 978-1-4799-7645-4),
pp. 629-636. 2015
http://dx.doi.org/10.1109/UIC-ATC-ScalCom.2014.53
A8-c68 Lei Ming, Shenggang Yang, Pricing European Options Based on the Hesitancy Degree of Investors,
2015 Annual Meeting of the Asian Finance Association, June 29-July, 2015, Hunan, China. 14 pages. 2015
http://dx.doi.org/10.2139/ssrn.2562849
At this time, the investors are preferred to choose the worst estimation since they can not make
sure the distribution of the stock yield [15] . Therefore, the fuzzy theory proposed by Zadeh [16]
may be a helpful tool for modeling this kind of imprecise problem. The fuzzy theory is widely
used by the scholars, such as Carlsson and Fuller [A8] , Collan et al [A48] , Lee [19] , Yoshida
[20, 21] , Wu [15], [22, 23] , Chrysafis and Papadopoulos [24] , Muzzioli and Torricelli [25] and
Zhang et al [1] . (page 3)
A8-c64 Anna Maria Gil-Lafuente, Cesar Castillo-Lopez, The Expertise on the Valuation Process Applied to the
Discounted Cash Flows in: Decision Making and Knowledge Decision Support Systems, Proceedings of the
VIII International Conference of RACEF, Barcelona, Spain, November 2013 and International Conference
MS 2013, Chania Crete, Greece, November 2013, Lecture Notes in Economics and Mathematical Systems,
vol. 675/2015, Springer, [ISBN: 978-3-319-03906-0 (Print) 978-3-319-03907-7 (Online], 2015. pp. 117124. 2015
42
http://dx.doi.org/10.1007/978-3-319-03907-7_13
2014
A8-c63 S S Appadoo, Y Gajpal, R S Bhatti, A Gaussian Fuzzy Inventory EOQ Model Subject to Inaccuracies In
Model Parameters. A Supply Chain Management Application, In: II International Conference on Business
and Management. Mumbai: Academic Research Publishers, 2014. [ISBN 978-0-9895150-3-0], pp. 7-15.
2014
A8-c62 Shu-Cheng Xiao, Jia-Feng Wu, Hong He, Zhen-Dong Yang, Xin Shen, An emergency logistics transportation path optimization model by using trapezoidal fuzzy, Proceedings of the 11th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, [ISBN 978-1-4799-5147-5], pp. 199203. 2014
http://dx.doi.org/10.1109/FSKD.2014.6980832
A8-c61 Xu Zhao, Investment Evaluation of Land Expropriation Based on the Fuzzy Binomial Tree Model, In:
Proceedings of the 2014 International Conference on Construction and Real Estate Management, American
Society of Civil Engineers, [ISBN 978-0-7844-1377-7], pp. 1526-1532. 2014
http://dx.doi.org/10.1061/9780784413777.181
A8-c60 Xian-dong Wang, Jian-min He, Reload option pricing in fuzzy framework, Proceedings of the 2014
International Conference on Management Science & Engineering (ICMSE), [ISBN 978-1-4799-5375-2],
pp. 147-152. 2014
http://dx.doi.org/10.1109/ICMSE.2014.6930222
A8-c59 Sumarti N, Wahyudi N, Stock and option portfolio using fuzzy logic approach, 4th International Conference on Mathematics and Natural Sciences: Science for Health, Food and Sustainable Energy, ICMNS
2012. (1589) American Institute of Physics Inc., [ISBN 9780735412217], pp. 504-507. 2014
http://dx.doi.org/10.1063/1.4868854
2013
A8-c58 Turek Marian, Sojda Adam, Determination of enterprise value by using the fuzzy pay-off method for
real option valuation, IEEE 7th International Conference on Intelligent Data Acquisition and Advanced
Computing Systems (IDAACS), [ISBN 978-1-4799-1426-5 ], pp. 597-600. 2013
http://dx.doi.org/10.1109/IDAACS.2013.6662994
2012
A8-c57 Tolga A Cagri, A Real Options Approach For Software Development Projects Using Fuzzy Electre,
JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING, 18: (5-6) pp. 541-560. 2012
WOS: 000305199500008
In workaday life real situations are very often vague and uncertain in several ways. When there is
a shortfall for information or unwillingness to lead the financial data out the company, a system
might not be known completely. Zadeh [7] suggested a strict mathematical outline named fuzzy
set theory that overcomes these inadequacies. The fuzzy approach to real option valuation (FROV)
was first studied by Carlsson and Fuller [A8]. This work was based on Black-Scholes’ real option
valuation, but under fuzziness. Then, Wang and Hwang [9] offered fuzzy compound options for
R&D project selection based on the Black-Scholes real option valuation. (page 543)
A8-c57 Andreea Iluzia Iacob, Costin Ciprian Popescu, An optimization model with quasi S shape fuzzy data,
2nd World Conference on Innovation and Computer Sciences 2012, AWERProcedia Information Technology & Computer Science, GLOBAL JOURNAL ON TECHNOLOGY, 2(2012), pp. 132-136. 2012
http://www.world-education-center.org/index.php/P-ITCS/article/view/634/263
A8-c56 Zdeněk Zmeškal, Modelling the sequential real options under uncertainty and vagueness (fuzzy-stochastic
approach), 30th International Conference on Mathematical Methods in Economics, 11-13 September 2012,
Karviá, Czech Republic, 127-1032. 2012
43
http://mme2012.opf.slu.cz/proceedings/pdf/176_Zmeskal.pdf
A8-c55 Anna M. Gil-Lafuente, César Castillo-López and Fabio Raúl Blanco-Mesa, A Paradigm Shift in Business Valuation Process Using Fuzzy Logic, in: Soft Computing in Management and Business Economics,
Studies in Fuzziness and Soft Computing, vol. 287/2012, Springer, [ISBN 978-3-642-30451-4], pp.177189. 2012
http://dx.doi.org/10.1007/978-3-642-30451-4_13
A8-c54 Lee Chung-Chuan, Chen Huei-Ping, A heuristic pricing formula of fuzzy lookback options in uncertain environment, 9th International Conference on Fuzzy Systems and Knowledge Discovery, Chongqing,
China, [ISBN 978-1-4673-0025-4], pp. 515-519. 2012
http://dx.doi.org/10.1109/FSKD.2012.6233717
A8-c53 Shu-xia Liu, Qin-juan Jing, Dian-yu Zhao, Fuzzy Process and the Application to Option Pricing in Risk
Mangement, In: Fuzzy Engineering and Operations Research, Advances in Intelligent and Soft Computing,
vol. 147/2012, Springer, [ISBN 978-3-642-28592-9], pp. 285-296. 2012
http://dx.doi.org/10.1007/978-3-642-28592-9_29
2011
A8-c52 Andreea Iluzia Iacob, Costin-Ciprian Popescu, Regression Using Partially Linearized Gaussian Fuzzy
Data, International Conference on Informatics Engineering and Information Science, November 14-16,
2011, Kuala Lumpur, Malaysia, [ISBN: 978-3-642-25453-6], pp. 584-595. 2011
http://dx.doi.org/10.1007/978-3-642-25453-6_48
A8-c51 Qing-e Guo, Xue-qing Wang, Zhen Wei, Fuzzy real option analysis for highway project based on credibility theory, IEEE 18th International Conference on Industrial Engineering and Engineering Management,
September 3-5, 2011, Changchun, China, [SBN: 978-1-61284-446-6], pp. 393-395. 2011
http://dx.doi.org/10.1109/ICIEEM.2011.6034762
In these literatures, the expected revenue and expected costs in construction projects were both
viewed as fixed numbers. But this is not the fact. Because many construction projects, for example,
the highway project, it’s total investment, complete time, operating costs and other variables in the
initial decision are not clear. To solve this problem, one approach is to introduce fuzzy variable
to real option. Carlsson studied a series of fuzzy real option approach [A8], the basic idea is
introduce fuzzy variable to the traditional B-S model. (page 393)
A8-c50 Tanatch Tangsajanaphakul, Junzo Watada, Fuzzy Game-Based Real Option Analysis in Competitive
Investment Situation, Fifth International Conference on Genetic and Evolutionary Computing (ICGEC),
August 29-September 1, 2011, Kitakyushu, Japan, [ISBN: 978-1-4577-0817-6], pp. 381-384. 2011
http://dx.doi.org/10.1109/ICGEC.2011.102
A8-c49 Shashank Pushkar, Akhileshwar Mishra, IT Project Selection Model Using Real Option Optimization
with Fuzzy Set Approach, International Conference on Digital Enterprise and Information Systems, July
20-22, 2011, London, England, Communications in Computer and Information Science, vol. 194/2011,
Springer, [ISBN: 978-3-642-22603-8], pp. 116-128. 2011
http://dx.doi.org/10.1007/978-3-642-22603-8_12
A8-c48 Fan Yanping, Zhang Zhe, Cloud Model of Strategic M&A Pricing Based On Real Option Method,
International Conference on E -Business and E -Government, May 6-8, 2011, Shanghai, China, [ISBN:
978-1-4244-8691-5], pp. 1-4. 2011
http://dx.doi.org/10.1109/ICEBEG.2011.5881754
The commonly used real option pricing method is basically according to a relationship mapping
to financial options to find the corresponding underlying financial assets in the financial market.
Thus the solutions can be addressed by Black-Scholes model or binomial formula. Carlsson and
Fullér had conducted a research on a might mean and variance of fuzzy number, which were
subsequently applied to the study of fuzzy real option [A8]. (page 1)
44
2010
A8-c47 Shao-Wei Yu, A Pricing Approach to Real Option Based on Normal Cloud Model, International Conference on Engineering and Business Management, March 25-27, 2010, Chengdu, China, pp. 4205-4208.
2010
ISI:000276079501442
A8-c46 Shin-Yun Wang, Cheng Few Lee, Application of Fuzzy Set Theory to Finance Research: Method and
Application, in: Cheng-Few Lee, Alice C Lee, John Lee eds., Handbook of Quantitative Finance and Risk
Management, Springer, [ISBN 978-0-387-77116-8], 2010, pp. 1183-1199. 2010
http://dx.doi.org/10.1007/978-0-387-77117-5_77
A8-c45 Shu-Hsien Liao, Shiu-Hwei Ho, Investment Project Valuation Based on the Fuzzy Real Options Approach, 2010 International Conference on Technologies and Applications of Artificial Intelligence, November 18-20, 2010, Hsinchu City, Taiwan, [ISBN 978-0-7695-4253-9], pp. 94-101. 2010
http://dx.doi.org/ 10.1109/TAAI.2010.26
Carlsson and Fuller [12] mentioned that the imprecision in judging or estimating future cash flows
is not stochastic in nature, and that the use of the probability theory leads to a misleading level
of precision. Their study introduced a real option rule in a fuzzy setting in which the present
values of expected cash flows and expected costs are estimated by trapezoidal fuzzy numbers.
They determined the optimal exercise time with the help of possibilistic mean value and variance
of fuzzy numbers. The proposed model that incorporates subjective judgments and statistical
uncertainties may give investors a better understanding of the problem when making investment
decisions. (page 95)
A8-c44 Qian Wang, K. W. Hipel, D. M. Kilgour, A numerical method of evaluating brownfields using fuzzy
boundaries and fuzzy real options, 2010 IEEE International Conference on Systems Man and Cybernetics
(SMC). October 10-13, 2010, Istanbul, Turkey, [ISBN 978-1-4244-6586-6], pp. 2901-2906. 2010
http://dx.doi.org/10.1109/ICSMC.2010.5641944
The option pricing model has a limitation. It considers only market uncertainty, which is reflected
in the observed prices [1]. In fact, brownfield redevelopment is a system of systems (SoS) problem,
and there are many private risks that cannot be estimated using market data [2]. Real option
analysis must be extended to incorporate representations of uncertainty in order to handle both
market and private risks [A8] [4]. (page 2901)
A8-c43 Shu-Hsien Liao, Shiu-Hwei Ho, Investment Appraisal under Uncertainty - A Fuzzy Real Options Approach, Neural Information Processing. Models and Applications 17th International Conference, ICONIP
2010. Sydney, Australia, November 22-25, 2010, LNCS 6444/2010, Springer, [ISBN 978-3-642-17533-6],
pp. 716-726. 2010
http://dx.doi.org/10.1007/978-3-642-17534-3_88
A8-c42 Shu-Hsien Liao, Shiu-Hwei Ho, A fuzzy real options approach for investment project valuation, Proceedings of the 5th WSEAS International Conference on Economy and Management Transformation, October 24-26, 2010, Timisoara, Romania, vol. I, pp. 86-91. 2010
http://www.wseas.us/e-library/conferences/2010/TimisoaraW/EMT/EMT1-12.pdf
Providing a precise volatility estimate is difficult; therefore, they used a possibility distribution to
model volatility uncertainty and to price an American option in a multi-period binomial model.
Carlsson and Fuller [A8] mentioned that the imprecision in judging or estimating future cash flows
is not stochastic in nature, and that the use of the probability theory leads to a misleading level of
precision. Their study introduced a real option rule in a fuzzy setting in which the present values
of expected cash flows and expected costs are estimated by trapezoidal fuzzy numbers. (pages
86-87)
45
A8-c41 Hiroshi Inoue, Masatoshi Miyake, A Default Risk Model in a Fuzzy Framework, International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU
2010), June 28-July 2, 2010, Dortmund, Germany, Springer, [ISBN 978-3-642-14057-0], pp. 280-288.
2010
http://dx.doi.org/10.1007/978-3-642-14058-7_28
A8-c40 Shu-Hsien Liao, Shiu-Hwei Ho, Investment project valuation using a fuzzy real options approach,
Proceedings of the 10th WSEAS international conference on Systems theory and scientific computation, N.
E. Mastorakis, V. Mladenov, and Z. Bojkovic eds., Mathematics And Computers In Science Engineering,
August 20-22, 2010, Taipei, Taiwan, World Scientific and Engineering Academy and Society (WSEAS),
[ISBN 978-960-474-218-9], pp. 172-177. 2010
A8-c39 Zhu Danmei, Wang Xingtong, Ren Rongrong, A heuristics R&D projects portfolio selection decision system based on data mining and fuzzy logic, International Conference on Intelligent Computation
Technology and Automation, May 11-12, 2010, Changsha, Hunan, China, [ISBN 978-0-7695-4077-1], pp.
118-121. 2010
http://doi.ieeecomputersociety.org/10.1109/ICICTA.2010.257
A8-c38 Sibo Ding, Valuation of Reverse Logistics Company Based on FRO and FMADM, in: 2nd International
Conference on e-Business and Information System Security (EBISS), Wuhan, China, May 22-23, 2010, pp.
1-4. 2010
http://dx.doi.org/10.1109/EBISS.2010.5473406
Black and Scholes [1] succeeded in establishing a option pricing formula and promoted the further development of financial derivative markets. Dixit and Pindyck [2,3] focused on multi-stage
investment analysis, in which each stage must be completed in the previous stage. They priced
the project investment opportunities at every stage of multi-phase, and figured out the lowest cost
of the next phase of the project. Carlsson and Fullér [A14, A8] studied the mean and variance of
fuzzy number and applied them to the research of fuzzy real option. Using fuzzy method, they
assumed the present value of expected cash flows and investment costs as fuzzy numbers and employed fuzzy real option to investment decision-making . . . This paper developed the combination
method that uses fuzzy real option and fuzzy multiple attribute decision making to evaluate the
value of a reverse logistics company. (page 1)
A8-c37 Yibo Sun, Sameer Tilak, Ruppa K. Thulasiram, Kenneth Chiu, Markets, Mechanisms, Games, and
Their Implications in Grids, in: Rajkumar Buyya, Kris Bubendorfer eds., Market-Oriented Grid and Utility
Computing, Wiley Series on Parallel and Distributed Computing, Wiley & Sons, [ISBN 978-0-470-287682], pp. 29-48. 2010
Carlsson and Fullér [A8] apply a hybrid approach to valuing real options. (page 46)
2009
A8-c36 Agliardi E, Guerra ML, Stefanini L, Efficient calculation of the value function in fuzzy real option
by differential evolution algorithms, Joint 2009 International Fuzzy Systems Association World Congress,
IFSA 2009 and 2009 European Society of Fuzzy Logic and Technology Conference, July 20-24, 2009,
Lisbon, Portugal, pp. 1009-1014. 2009
To the best of our knowledge, such an approach has never been discussed in the literature, with
the exception of Carlsson and Fuller [A8], that interpret the possibility of making an investment
decision in terms of a European option, while we use an American option. (page 1009)
A8-c35 WM Ma; XJ Ma, A Fuzzy Real Option Model for Information Technology Investment Evaluation, 11th
International Conference on Informatics and Semiotics in Organisations, APR 11-12, 2009, Beijing, China,
AUSSINO ACAD PUBL HOUSE, [ISBN 978-0-9806057-2-3], pp. 485-491. 2009
A8-c34 Yong Yang, An integral stage gate system and the best tool matching each phrase respectively for, R&D
project, 3rd international Conference on Risk Management and Global e-Business, August 10-12, 2009,
Incheon, Korea, [ISBN: 978-1-926642-01-7], pp. 913-917. 2009
46
A8-c33 X Bi, X F Wang, The application of fuzzy-real option theory in BOT project investment decisionmaking, IEEE 16th International Conference on Industrial Engineering and Engineering Management, October 21-23, 2009, Beijing, China, [ISBN: 978-1-4244-3670-5], pp. 289-293. 2009
http://dx.doi.org/10.1109/ICIEEM.2009.5344588
For these many reasons, this article proposed an analytical method which denotes the parameters
involved in real option with fuzzy numbers, and gave an application framework of fuzzy real
options. At present, the pricing models for real option mainly go to two categories: the binary
tree model and the B-S (Black-Scholes) model [A8]. In this article the B-S pricing model is taken
as an example to illustrate the necessity of introducing fuzzy numbers to the original real options
model as supplementation. (pages 290-291)
A8-c30 E Agliardi, M L Guerra, L Stefanini, Efficient Calculation of the Value Function in Fuzzy Real Option
by Differential Evolution Algorithms, Joint International-Fuzzy-Systems-Association World Congress/EuropeanSociety-Fuzzy-Logic-and-Technology Conference, July 27-29, 2007, Lisbon, Portugal, [ISBN: 978-98995079-6-8], pp. 1009-1014. 2009
A8-c29 Q Wang, K W Hipel, D M Kilgour, Using fuzzy real options in a brownfield redevelopment decision
support system, IEEE International Conference on Systems, Man and Cybernetics, October 11-14, 2009,
San Antonio, USA, [ISBN: 978-1-4244-2793-2], pp. 1545-1550. 2009
http://dx.doi.org/10.1109/ICSMC.2009.5346312
Soft-computing techniques have demonstrated their advantages in intelligent behavior. Fuzzy theory is especially suitable for situations in which expert knowledge is required. Hence, fuzzy real
options are proposed for dealing with private risks that are hard to objectively estimate based on
possibility theory as claimed by Carlsson and Fuller [A8] [A14]. If private risks are represented as
fuzzy variables, possibility theory can be used. In this case, both subjective and objective uncertainties are integrated into the fuzzy real options model. However, Carlsson’s fuzzy real options
are limited to the exercise price and current value in the options model [A8]. Hence, the transformation method is employed to generalize fuzzy variable representation to any parameter, which
overcomes the multiple outputs problem [22]. The idea underlying the transformation method
follows three steps: firstly, decompose fuzzy numbers into discrete form; then use an α-cut for
calculation purposes as a traditional function; and finally, search the coordinates of the points in
the hypersurfaces of the cube [22]. (page 1547)
A8-c28 Maria Letizia Guerra, Laerte Sorini, Luciano Stefanini, Value Function Computation in Fuzzy Real
Options by Differential Evolution, Ninth International Conference on Intelligent Systems Design and Applications, November 30 - December 02, 2009, Pisa, Italy, [ISBN 978-0-7695-3872-3], pp. 324-329. 2009
http://dx.doi.org/10.1109/ISDA.2009.232
We present a real options that will be evaluated within a fuzzy setting; more specifically, the
present values of expected cash flows and expected costs are estimated by fuzzy numbers. To
the best of our knowledge, such an approach has never been discussed in the literature, with
the exception of Carlsson and Fullér [A8], that interpret the possibility of making an investment
decision in terms of a European option, while we use an American option. (page 324)
A8-c27 Wei Li, Liyan Han, The fuzzy binomial option pricing model under Knightian uncertainty, 6th International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2009 Volume 4, [ISBN 978076953735-1], 14-16, August, Tianjin, China, Article number 5359195, pp. 399-403. 2009
http://dx.doi.org/10.1109/FSKD.2009.252
A8-c26 Miao Jing-yi; Sun Zhen-hua; Miao Miao, The Technological Investment Decision Study Based on
Fuzzy Real Option, Proceedings - 2009 International Symposium on Information Engineering and Electronic Commerce, IEEC 2009, 16-17 May, 2009, art. no. 5175103, pp. 202-206. 2009
http://dx.doi.org/10.1109/IEEC.2009.47
Therefore, fuzzy set theory plays an important role in investment decision of project. As a result,
we combine the theory of the fuzzy set and B-S equation as the basis of further studies [A8], set
up one corresponding fuzzy real option assessment model, and develop the calculation procedures
using the assessment model to evaluate real option. (page 203)
47
A8-c25 Yibo Sun, Sameer Tilak, Ruppa K. Thulasiram, and Kenneth Chiu, Markets, Mechanisms, Games, and
Their Implications in Grids, in: Rajkumar Buyya, Kris Bubendorfer eds., Market-Oriented Grid and Utility
Computing, Wiley, [ISBN: 978-0-470-28768-2], pp. 29-48. 2009
A8-c24 Qian Wang, Keith W. Hipel, D. Marc Kilgour, Solving the Private Risk Problem in Brownfield Redevelopment using Fuzzy Real Options, Proceedings of GDN 2009: International Conference on Group Decision
and Negotiation Toronto, Canada, pp. 178-180. 2009
This proposed approach is based on Carlsson and Fullér’s article on the fuzzy real options [A8].
But since the private risk is usually reflected as the volatility (σ), the transformation method developed by Hanss [5] is integrated in order to be able to make σ a fuzzy variable. (page 179)
2008
A8-c23 C Kahraman, I Ucal, Fuzzy real options valuation for oil investments, 8th International Conference
on Fuzzy Logic and Intelligent Technologies in Nuclear Science, September 21-24, 2008, Madrid, Spain,
[ISBN: 978-981-279-946-3], pp. 1027-1032. 2008
A8-c22 Zhengbiao Qin, Yun Pu, and Minjie Hu, Investment Decisions in the BOT Transport Infrastructure
Applying Fuzzy Real Option, in: Proceedings of the 8th International Conference of Chinese Logistics and
Transportation Professionals - Logistics: The Emerging Frontiers of Transportation and Development in
China, pp. 1584-1589. 2008
http://dx.doi.org/10.1061/40996(330)231
A8-c21 D. Allenotor, R.K. Thulasiram, Grid resources pricing: A novel financial option based quality of serviceprofit quasi-static equilibrium model, 9th IEEE/ACM International Conference on Grid Computing, pp.
75-84. 2008
http://dx.doi.org/10.1109/GRID.2008.4662785
Carlsson and Fullér in [A8] apply a hybrid approach to valuing real options. Their method incorporates real option, fuzzy logic, and probability to account for the uncertainty involved in the
valuation of future cash flow estimates. The results of the research efforts given in [A8] and [18]
have no formal reference to the QoS that characterize a decision system. Carlsson and Fullér
[A8] apply fuzzy methods to measure the level of decision uncertainties and did not price grid
resources. (pages 76-77)
A8-c20 A.C. Tolga, C. Kahraman, Fuzzy multi-criteria evaluation of R&D projects and a fuzzy trinomial lattice
approach for real options, in: Proceedings of the 3rd International Conference on Intelligent System and
Knowledge Engineering, ISKE 2008, November 17-19, 2008, Xiamen, China, Article number 4730966,
pp. 418-423. 2008
http://dx.doi.org/10.1109/ISKE.2008.4730966
Real options give a right but not an obligation to make or not to make an investment for a certain
period. For instance, organizing a Research and Development (R&D) laboratory investment gives
the company right to research and develop new products now but not the obligation at future. Real
options were first introduced by Trigeorgis [2]. Huchzermeier and Loch’s [3] model built real
option for R&D managers as to when it is and when it is not worthwhile to delay commitments.
The lack of past data and vague information drives us to use fuzzy models. In the literature, fuzzy
real options valuation (FROV) models have been developed under incomplete information. First,
Carlsson and Fullér [A8] developed a heuristic real option valuation process in a fuzzy setting. In
their study present values of expected costs and expected cash flows are calculated by trapezoidal
fuzzy numbers. (page 418)
A8-c19 P. Majlender, Soft decision support systems for evaluating real and financial investments, in: Fuzzy
Engineering Economics with Applications, Studies in Fuzziness and Soft Computing series, 233/2008, pp.
307-338. 2008
http://dx.doi.org/10.1007/978-3-540-70810-0_17
48
A8-c18 D. Kuchta, Optimization with fuzzy present worth analysis and applications, in: Fuzzy Engineering
Economics with Applications, Studies in Fuzziness and Soft Computing, vol. 233/2008, Springer, [ISBN
978-3-540-70809-4], pp. 43-69. 2008
http://dx.doi.org/10.1007/978-3-540-70810-0_2
A8-c17 A. Dimitrovski, M. Matos, Fuzzy present worth analysis with correlated and uncorrelated cash flows,
in: Studies in Fuzziness and Soft Computing, vol. 233, pp. 11-41. 2008
http://dx.doi.org/10.1007/978-3-540-70810-0_2
2007
A8-c16 J Guo, F J Wei, A fuzzy sequential exchange option model to IT investment valuation and portfolio
management, 1st International Conference on Management Innovation, June 4-6, 2007, Shanghai, China,
[ISBN: 978-0-9783350-0-7], pp. 397-402. 2007
A8-c15 David Allenotor, Ruppa K. Thulasiram, G-FRoM: Grid Resources Pricing A Fuzzy Real Option Model
In: IEEE International Conference on e-Science and Grid Computing, December 10-13, 2007, Bangalore,
India, pp. 388-395. 2007
http://dx.doi.org/10.1109/E-SCIENCE.2007.37
Current literature on real option approaches to valuing projects presents real options framework in
eight categories [15]: option to defer, time-to-build option, option to alter, option to expand, option
to abandon, option to switch, growth options, and multiple integrating options. There are also
efforts reported towards improving the selection and decision methods used in the prediction of
the capital that an investment may consume. Carlsson and Fullér in [A8] apply a hybrid approach
to valuing real options. Their method incorporates real option and fuzzy logic and some aspects
of probability to account for the uncertainty involved in the valuation of future cash ow estimates.
The results of the research efforts given in [15] and [8] have no formal reference to the QoS that
characterize a decision system. Carlsson and Fullér [8] apply fuzzy methods to measure the level
of decision uncertainties, however, there is a lack of indication on how accurate the decisions
could be. (page 389)
A8-c14 Cheng, Jao-Hong Lee, Chen-Yu , Product Outsourcing under Uncertainty: an Application of Fuzzy
Real Option Approach, IEEE International Fuzzy Systems Conference, 2007 (FUZZ-IEEE 2007), 23-26
July 2007, London, [ISBN: 1-4244-1210-2], pp. 2023-2028. 2007
http://dx.doi.org/10.1109/FUZZY.2007.4295675
Carlsson and Fullér [A8] stated that the relevance of historic data diminished very quickly after
2-3 years, so it was not worthwhile to claim the predictive value of time series after 5 years (and
even much more so for 15-25 years ahead). (page 2)
A8-c13 Chen, Tao; Zeng, Yurong; Wang, Lin; Zhang, Jinlong, Evaluating IT Investment Using a Hybrid Approach of Fuzzy Risk Analysis and Real Options, Fourth International Conference on Fuzzy Systems and
Knowledge Discovery (FSKD 2007), Haikou, Hainan, China, 24-27 Aug. 2007, vol.1, pp.135-139. 2007
http://dx.doi.org/10.1109/FSKD.2007.276
A8-c12 David Allenotor and Ruppa K. Thulasiram, A Grid Resources Valuation Model Using Fuzzy Real
Option, in: Ivan Stojmenovic; Ruppa K.Thulasiram; Laurence T.Yang; Weijia Jia; Minyi Guo; Rodrigo
Fernandes de Mello eds., Parallel and Distributed Processing and Applications, 5th International Symposium, ISPA2007, Niagara Falls, Canada, August 29-31, 2007, Lecture Notes in Computer Science, vol.
4742, Springer, pp. 622-632. 2007
http://dx.doi.org/10.1007/978-3-540-74742-0_56
Carlsson and Fullér in [A8] apply a hybrid approach (real option, fuzzy logic, and probability
theory) to value future options. The results given in [2] and [A8] have no formal reference to
the QoS that characterize a decision system. Carlsson and Fullér [A8] apply fuzzy methods to
measure the level of decision uncertainties, however, there is a lack of indication on how accurate
the decisions could be. (page 624)
49
A8-c11 Chen Tao, Zhang Jinlong, Yu Benhai, and Liu Shan A Fuzzy Group Decision Approach to Real Option
Valuation, in: Aijun An, Jerzy Stefanowski, Sheela Ramanna, Cory J. Butz, Witold Pedrycz, Guoyin Wang
(Eds.): Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, 11th International Conference,
RSFDGrC 2007, Toronto, Canada, May 14-16, 2007, Lecture Notes in Computer Science, Sublibrary:
Lecture Notes in Artificial Intelligence, vol. 4482, Springer, [ISBN 978-3-540-72529-9], pp. 103-110.
2007
http://dx.doi.org/10.1007/978-3-540-72530-5_12
A8-c10 Chen Tao, Zhang Jinlong, Liu Shan, and Yu Benhai, Fuzzy Real Option Analysis for IT Investment
in Nuclear Power Station, Y. Shi et al. (Eds.): ICCS 2007, Part III, Lecture Notes in Computer Science,
Volume 4489/2007, Springer, [ISBN 978-3-540-72587-9], pp. 953-959. 2007
http://dx.doi.org/10.1007/978-3-540-72588-6_152
Step 5: the real option valuation of the investment
In the last step, we can assess the real option value of the investment based on the result obtained
above. For the purpose of simplicity, we assume that only the expected payoff is uncertain and
utilize the Black-Scholes pricing model. Then the fuzzy real option value of an investment is [A8]
FROV = V N (d1 ) − Xe−rT N (d2 )
where
d1 =
ln(E(V )/X) + (r + σ 2 /2)T
√
,
σ T
√
d2 = d1 − σ T ,
Only V is a fuzzy number. E(V ) and σ represent, respectively, the possibilistic expected value
and the standard deviation of fuzzy figure V . The computing result FROV is also a fuzzy number,
representing the real option value of the investment under consideration. (page 955)
2006
A8-c9 Yoshida, Y. Option pricing theory in financial engineering from the viewpoint of fuzzy logic, in: Kahraman, Cengiz (Ed.) Fuzzy Applications in Industrial Engineering, Series: Studies in Fuzziness and Soft
Computing , Vol. 201, pp. 229-243. 2006
http://dx.doi.org/10.1007/3-540-33517-X_8
A8-c8 Zhang JL, Du HB, Tang WS, Pricing R&D option with combining randomness and fuzziness, in: Computational Intelligence, International Conference on Intelligent Computing, ICIC 2006, Kunming, China,
August 16-19, 2006. Proceedings, Part II, LECTURE NOTES IN ARTIFICIAL INTELLIGENCE, vol.
4114, pp. 798-808. 2006
http://dx.doi.org/10.1007/11816171_100
Carlsson and Fullér [A8] gianed the present value of expected cash flow could not usually be
characterized by a single number. However, their experiences with the practical projects showed
that managers were able to estimate the present value of expected cash flows by using a trapezoidal
fuzzy variable. (page 799)
A8-c7 E.E. Karsak, A generalized fuzzy optimization framework for R&D project selection using real options
valuation, in: Computational Science and Its Applications - ICCSA 2006, LECTURE NOTES IN COMPUTER SCIENCE 3982: 918-927 2006
http://dx.doi.org/10.1007/11751595_96
Lately, options valuation approach has been proposed as a more suitable alternative for determining the benefits from R&D projects [9]. Options approach deviates from the conventional DCF
approach in that it views future investment opportunities as rights without obligations to take some
50
action in the future [3]. The asymmetry in the options expands the NPV to include a premium beyond the static NPV calculation, and thus presumably increase the total value of the project and
the probability of justification. Carlsson and Fullér [A8] further extended the use of options approach in R&D project valuation by considering the possibilistic mean and variance of fuzzy cash
flow estimates. This paper presents a novel fuzzy formulation for R&D project selection accounting for project interactions with the objective of maximizing the net benefit based on expanded
net present value which incorporates the real options inherent in R&D projects in a fuzzy setting. Although a fuzzy optimization model is provided for R&D portfolio selection in [14], the
project interactions are completely ignored. Compared with the real options valuation procedures
delineated in [A8, 14], the valuation approach utilized in this paper models exercise price as a
stochastic variable enabling to deal with technological uncertainties in real options analysis, and
considers both the benefits of keeping the development option alive and the opportunity cost of
delaying development. (page 919)
2005
A8-c6 Z. Zmeskal, Approach to Real Option Model Application on Soft Binomial Basis Fuzzy - stochastic
approach, 23rd International Conference on Mathematical Methods in Economics, September 14-16, 22005,
Hradec Kralove, Czech Pepublic, [ISBN: 978-80-7041-535-1] pp. 433-439. 2005
ISI:000260962400070
A8-c5 T. Sato, S. Takahashi, C. Huang and H. Inoue, Option pricing with fuzzy barrier conditions, in: Y. Liu,
G. Chen and M. Ying eds., Proceedings of the Eleventh International Fuzzy systems Association World
Congress, July 28-31, 2005, Beijing, China, 2005 Tsinghua University Press and Springer, [ISBN 7-30211377-7] pp. 380-384. 2005
2004
A8-c4 Garcia, F.A.A., Fuzzy real option valuation in a power station reengineering project, Soft Computing
with Industrial Applications - Proceedings of the Sixth Biannual World Automation Congress, [ISBN 1889335-21-5], pp. 281-287. 2004
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1439379
A8-c3 L Ran, J L Li, Z Q Zhao, A fuzzy approach to compound R&D option valuation, International Conference
on Management Science and Engineering, August 8-10, 2004, Harbin, China, [ISBN: 7-5603-1855-X], pp.
1214-1218. 2004
in books
A8-c1 Ketty Peeva; Yordan Kyosev, Fuzzy relational calculus: Theory, applications and software, Advances in
Fuzzy Systems - Applications and Theory, Vol. 22, World Scientific. 2004
in Ph.D. dissertations
• Fabio Raul Blanco Mesa, Técnicas para la toma de decisiones en contextos inciertos: identificacin de oportunidades socio-económicas en el ámbito deportivo, University of Barcelona, Spain. 2015
http://www.tdx.cesca.cat/bitstream/handle/10803/322786/FRBM TESIS.pdf
Also in the DCF model, it has been applied a fuzzy binomial approach to estimate the associated
uncertainty with these cash flows when facing the decision-making (Ho and Liao, 2011, 15 301).
Smith and Trigeorgis (2006, p.110), concerned about the importance of creating shareholder value,
apply a combination of real options and analysis of set theory to make value creation to flow from
an strictly financial point of view to the strategic one. Thus, the real options make it the preferred
methodology of academic literature at a time to minimize the effects of uncertainty, over the
traditional methods of valuation (Ucal and Kahraman, 2009, p. 666) or probabilistic approaches
(Carlsson and Fuller, 2003, p. 310). In some studies it has been used ”Subtle Sets” to measure the
value of goodwill, leaving the accounting methods that do not properly handle uncertainty, and
thus determine a more adjusted company’s value (Ionita and Stoica, 2009, p. 122). (page 264)
51
• Xiaolu Wang, Fuzzy Real Option Analysis in Patent Related Decision Making and Patent Valuation, Department of Information Technologies (TUCS), Åbo Akademi University, Åbo, Finland, [ISBN 978-952-123227-5]. 2015
http://urn.fi/URN:NBN:fi-fe2015061110218
Carlsson and Fullér [A8] propose a different approach to the Black-Scholes model extension.
That is, they allow the extended model to directly take on fuzzy numbers (e.g., fuzzy underlying
asset price and fuzzy exercise price) as input. Such modification has great practical merit of
being useful in valuing real options as ”from a computational point of view it is easier to use
linear membership functions and, more importantly, our experience shows that senior managers
prefer trapezoidal fuzzy numbers to Gaussian ones when they estimate the uncertainties associated
with future cash inflows and outflows” [A8]. Indeed, the extended model further improve the
Black-Scholes formula by taking into consideration the practical difficulties in characterizing the
present value of expected cash flows with one single number, which is especially the case when the
underlying is a real asset such as real estate, agricultural land, special purpose machinery or when
the underlying asset has lower liquidity or no established market such as intellectual properties.
The proposed pricing model for a European-style call option is given as follows: (page 69)
• József Mezei, A quantitative view on fuzzy numbers, Department of Information Technologies (TUCS), Åbo
Akademi University, Åbo, Finland, [ISBN 978-952-12-2670-0]. 2011
http://www.doria.fi/handle/10024/72548
• Jan Edelmann, Experiences in using a structured method in finding and defining new innovations: the strategic
options approach, Lappeenranta University of Technology, Finland, ISBN 978-952-265-097-9. 2011
http://www.doria.fi/handle/10024/69761
When strategic investments are in future innovations it is difficult or impossible to calculate the
expected rate of return beforehand. Such investments are often termed ’faith-alone’ investments,
and are decided at top-management level. The benefits are expected to spread over many phases of
the firm’s activities and to stretch into the distant future, and the main objective may be ”a strategic
defense or attack” (Dean, 1951; Kasanen, 1993). Large-scale investments (or giga-investments,
Carlsson & Fullér, 2003; Collan, 2004) are often considered strategic investments that are highly
irreversible and uncertain in nature. (page 34)
A research stream allowing decision makers to utilize the advances in real options valuation to handle imprecise information is emerging. The projection approach (including, e.g., fuzzy logic and
outcome scenarios) has been suggested as a solution to the one-point evaluation problem involving a range of estimates showing the best, most likely and worst outcomes (see e.g., Carlsson &
Fullér, 2003; Büyüközkan & Feyzolu, 2003; Mathews et al., 2007; Wang & Hwang, 2007; Collan
et al., 2009; Jaimungal & Lawryshyn, 2011). This simple change in logic could strongly enhance
the usefulness of real options theory with regard to highly uncertain strategic opportunities. (page
78)
• Qian Wang, Facilitating Brownfield Redevelopment Projects: Evaluation, Negotiation, and Policy. University
of Waterloo, Canada, 2011.
http://uwspace.uwaterloo.ca/bitstream/10012/5948/1/Wang_Qian.pdf
This research attempts to employ and customize the option pricing model for better evaluation of
brownfield redevelopment projects. But as options become ”real”, the underlying uncertainties
become more difficult to deal with. Some risks associated with real options are not priced in
the market, challenging the validity of using option pricing models. Hence, volatilities in real
options usually cannot be accurately estimated. These risks are usually referred to as private
risk, which are prevalent in brownfield redevelopment projects. The private risk problem places a
major obstacle on adopting the real options approach to evaluate brownfields. Fuzzy real options,
initialized by Carlsson and Fullér [A8], are employed to accommodate private risks in brownfield
redevelopment. The proposed model is able to tackle private risks and preferences, making it more
suitable for employment in risky project evaluations, such as the brownfields. (page 2)
52
Fuzzy real options were first introduced by Carlsson and Fullér [A8], who attempted to identify
optimal strategies using real options analysis with uncertain parameters. The possibility mean
and variance were introduced in combination of real options analysis [31] [11]. Unlike the crisp
parameters required in real options analysis, fuzzy real options allow parameters as fuzzy numbers.
(page 30)
• Markku Heikkilä, R&D investment decisions with real options - Profitability and Decision Support, Åbo
Akademi University, Åbo, Finland, [ISBN 978-952-12-2379-2]. 2009
• Péter Majlender, A Normative Approach to Possibility Theory and Soft Decision Support, Turku Centre for
Computer Science, Institute for Advanced Management Systems Research, Åbo Akademi University, No
54, [ISBN 952-12-1409-0]. 2004
[A9] Robert Fullér and Péter Majlender, On weighted possibilistic mean and variance of fuzzy numbers, FUZZY
SETS AND SYSTEMS, 136(2003) 363-374. [MR1984582]. doi 10.1016/S0165-0114(02)00216-6
in journals
2016
A9-c177 Abel Rubio, Jose D Bermudez, Enriqueta Vercher, Forecasting portfolio returns using weighted fuzzy
time series, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 75(2016), pp. 1-12. 2016
http://dx.doi.org/10.1016/j.ijar.2016.03.007
Other possibility moments could be used if the expert decides to apply weights to the γ-level cuts
of the membership function of the fuzzy returns [A14, A9]. (page 3)
A9-c176 Dong J-Y, Wan S-P, A new method for prioritized multi-criteria group decision making with triangular
intuitionistic fuzzy numbers, JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 30: (3) pp. 17191733. 2016
http://dx.doi.org/10.3233/IFS-151882
A9-c175 Mikael Collan, Mario Fedrizzi, Pasi Luukka, Possibilistic risk aversion in group decisions: theory with
application in the insurance of giga-investments valued through the fuzzy pay-off method, APPLIED SOFT
COMPUTING (to appear). 2016
http://dx.doi.org/10.1007/s00500-016-2069-2
To determine the possibilistic risk premiums we will use the notions of possibilistic expected value
and possibilistic variance, as introduced by Carlsson and Fullér (2001), Carlsson et al. (2002) and
Fullér and Majlender (2003).
A9-c174 Shu-Ping Wan, Feng Wang, Li-Lian Lin, Jiu-Ying Dong, Some new generalized aggregation operators for triangular intuitionistic fuzzy numbers and application to multi-attribute group decision making,
COMPUTERS AND INDUSTRIAL ENGINEERING, 93(2016), pp. 286-301. 2016
http://dx.doi.org/10.1016/j.cie.2015.12.027
The main works and features of this paper are illuminated as follows:
(1) According to the possibility theory (Fullér and Majlender, 2003), we define the weighted
possibility attitudinal expected values of TIFNs and thereby present a new risk attitudinal ranking
method of TIFNs. This ranking method can sufficiently consider DMs’ risk attitude and make
the results more consistent with real situations. The sensitivity analyses on attitudinal character
parameter are also given.
A9-c173 Jing Liu, Yizeng Chen, Jian Zhou, Xiajie Yi An Exact Expected Value-Based Method to Prioritize
Engineering Characteristics in Fuzzy Quality Function Deployment, INTERNATIONAL JOURNAL OF
FUZZY SYSTEMS (to appear). 2016
http://dx.doi.org/10.1007/s40815-015-0118-0
A9-c172 Franco Molinari, A new criterion of choice between generalized triangular fuzzy numbers, FUZZY
SETS AND SYSTEMS, 296(2016), pp. 51-69. 2016
http://dx.doi.org/10.1016/j.fss.2015.11.022
53
In this paper we consider a new criterion of choice between generalized (or rounded) triangular
fuzzy numbers based on the concept of the weighted possibilistic mean introduced by Fullér and
Majlender. First we introduce a preference relation which establishes a partial order on the family
of generalized triangular fuzzy numbers. Second, we present a weak preference relation which
leads to a total order on this family. Then we consider the special case of triangular fuzzy fuzzy
number. Finally we compare our results with a number of new approaches recently discussed in
the literature. (page 51)
In keeping with this research, in this paper we propose a new criterion of choice between generalized triangular fuzzy numbers based on the concept of the weighted possibilistic mean introduced
by Fullér and Majlender [A9]. We consider the weighted possibilistic mean to be the best numerical index that characterizes a fuzzy number. (page 51)
A9-c171 Jiuying Dong, Shuping Wan, A new method for multi-attribute group decision making with triangular
intuitionistic fuzzy numbers, KYBERNETES, 45: (1) pp. 158-180. 2016
http://dx.doi.org/10.1108/K-02-2015-0058
A9-c170 Ruben Saborido, Ana B Ruiz, Jose D Bermdez, Enriqueta Vercher, Mariano Luque, Evolutionary
multi-objective optimization algorithms for fuzzy portfolio selection, APPLIED SOFT COMPUTING,
39(2016), pp. 48-63.. 2016
http://dx.doi.org/10.1016/j.asoc.2015.11.005
Since the fuzzy number Q induces a possibility distribution that matches with its membership
function Q(y) [26], we consider power LR-fuzzy numbers to approximate the uncertain return
on the portfolio x, and we directly approximate the possibility distribution of its return instead
of aggregating the possibility distributions of the individual assets that compose x. Then, to approximate the expected return on a given portfolio, the concept of interval-valued expectation [45]
is applied, with the usual defuzzification approach for a crisp representation of their possibilistic moments. It must be mentioned that other weighted mean-interval definitions could be used
analogously [A9]. (page 51)
2015
A9-c170 Yue W, Wang YP, Dai C, An Evolutionary Algorithm for Multiobjective Fuzzy Portfolio Selection
Models with Transaction Cost and Liquidity, MATHEMATICAL PROBLEMS IN ENGINEERING, Paper
569415. 15 p. 2015
http://dx.doi.org/10.1155/2015/569415
In this paper, we regard a new weighted possibilistic mean value, variance, and skewness [26]
of fuzzy return to characterize the return level, risk level, and the corresponding asymmetry as
alternative approach, respectively. It is just because the weighted possibilistic mean (WPM) and
variance (WPV) of fuzzy number have all the properties of the possibilistic mean value and variance stated in [A9, 25], and the WPV has all necessities and important properties for defining of
the possibilistic variance of a fuzzy number. In addition, WPM is the nearest weighted point to
the fuzzy number via minimizing a new weighted distance quantity; moreover, WPV of a fuzzy
number is consistent with the physical interpretation of the variance and well-known de nition
of variance in probability theory so that it can simply introduce the possibilistic moments about
the mean of fuzzy numbers [26]. Furthermore, Pasha et al. [26] pointed out that this definition
of weighted possibilistic moments on fuzzy number is more suitable for all fuzzy numbers than
the definitions of possibilistic moments introduced in [A9, 25]. is indicates that WPM and WPV
are suitable and applicable and play an important role in fuzzy data analysis. For this reason, we
quantify the return, risk, and skewness by using the WPMs. (page 3)
A9-c169 I-Fei Chen, Ruey-Chyn Tsaur, Fuzzy Portfolio Selection Using a Weighted Function of Possibilistic
Mean and Variance in Business Cycles, INTERNATIONAL JOURNAL OF FUZZY SYSTEMS (to appear).
2015
http://dx.doi.org/10.1007/s40815-015-0073-9
54
A9-c168 Pasi Luukka, Mikael Collan, New Fuzzy Insurance Pricing Method for Giga-Investment Project Insurance, INSURANCE MATHEMATICS & ECONOMICS, 65(2015), pp. 22-29. 2015
http://dx.doi.org/10.1016/j.insmatheco.2015.08.002
A9-c167 P Rajarajeswari, M Sangeetha, An Effect for Solving Fuzzy Transportation Problem Using Hexagonal
Fuzzy Numbers, International Journal of Research in Information Technology, 3(2015), number 6, pp. 295307. 2015
A9-c166 J Dong, D Y Yang, S P Wan, Trapezoidal intuitionistic fuzzy prioritized aggregation operators and
application to multi-attribute decision making, IRANIAN JOURNAL OF FUZZY SYSTEMS, 12(2015),
number 4, pp. 1-32. 2015
http://ijfs.usb.ac.ir/pdf_2083_b0bfd4eb1264f73143bcf1b0715c6d2f.html
A9-c165 Enriqueta Vercher, Jose D Bermudez, Portfolio optimization using a credibility mean-absolute semideviation model, EXPERT SYSTEMS WITH APPLICATIONS, 42(2015), number 20, pp. 7121-7131.
2015
http://dx.doi.org/10.1016/j.eswa.2015.05.020
Note that the results proved in Propositions 2 and 3 are only established between the crisp possibilistic expected values of LR-type fuzzy numbers (in the sense of Dubois and Prade) and the
credibility expected values of LR-type fuzzy variables. That is, when non-unit constant weights
are considered for different c-cuts of the membership function of a fuzzy number, these equivalencies may disappear (see, for instance, Fullér & Majlender, 2003; Saedifar & Pasha, 2009); this
may also be the case if fuzzy variables other than LR-type are used for quantifying uncertainty.
(page 7124)
A9-c164 Praveenprakash A, Raman Kanimozhi, Sumathi R, Application of Three Estimates Fuzzy TOPSIS(TEFTOPSIS)
Method using pentagonal Fuzzy Number in Analyzing the Causes for increase in Old Age Home, INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN COMPUTER SCIENCE, 6(2015), number 2,
pp. 77-83. 2015
A9-c163 Shang Rui, Research on Science Award Judgment, International Journal of u- and e- Service, Science
and Technology, 8(2015), number 3, pp. 99-106. 2015
http://dx.doi.org/10.14257/ijunesst.2015.8.3.09
A9-c162 Shu-Ping Wan, Jiu-Ying Dong, Power geometric operators of trapezoidal intuitionistic fuzzy numbers
and application to multi-attribute group decision making, Applied Soft Computing, 29(2015), pp. 153-168.
2015
http://dx.doi.org/10.1016/j.asoc.2014.12.031
Motivated by [A9], we give the definitions of the weighted possibility means of TrIFNs as follows.
(page 156)
A9-c161 Ruey-Chyn Tsaur, Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions
International Journal of Systems Science, 46(2015), number 3, pp. 438-450. 2015
http://dx.doi.org/10.1080/00207721.2013.784820
A9-c160 Zhi-Yuan Feng, Johnson T -S Cheng, Yu-Hong Liu, I-Ming Jiang, Options pricing with time changed
Lévy processes under imprecise information, Fuzzy Optimization and Decision Making, 14: (1) pp. 97-119.
2015
http://dx.doi.org/10.1007/s10700-014-9191-3
This section briefly introduces fuzzy set theory, the fuzzy random variable, and the crisp weighted
possibilistic mean values of continuous possibility distributions. Zadeh (1965) first proposed the
fuzzy set theory, and used it to describe sets of variables without clear boundaries. For a more
extensive application of this approach using probability theory, Puri and Ralescu (1986) proposed
fuzzy random variables. Fullér and Majlender (2003) then introduced crisp weighted possibilistic
mean to deal with the problem of expectations regarding fuzzy numbers. (pages 100-101)
2014
55
A9-c159 Irina Georgescu, Risk aversion, prudence and mixed optimal saving models, Kybernetika 50:(2014),
number 5, pp. 706-724. 2014
http://dx.doi.org/10.14736/kyb-2014-5-0706
A9-c158 Shuping Wang, Jiuying Dong, Multi-Attribute Group Decision Making with Trapezoidal Intuitionistic
Fuzzy Numbers and Application to Stock Selection, INFORMATICA 25: pp. 663-697. 2014
http://dx.doi.org/10.15388/Informatica.2014.34
In statistics, central tendency and distribution dispersion are considered to be the important measures. For fuzzy numbers, two of the most useful measures are the mean and variance of fuzzy
numbers. The possibility mean and variance are the important mathematical characteristics of
fuzzy numbers. The possibilistic mean, variance and covariance of fuzzy numbers, defined by
Carlsson and Fullér (2001) and Fullér and Majlender (2003) are usually used to the research of
fuzzy optimal portfolio selection (Zhang et al., 2009). (page 666)
A9-c157 Ana Maria Lucia Casademunt, Irina Georgescu, The Optimal Saving with Mixed Parameters, Procedia
Economics and Finance, 15(2014), pp. 326-333. 2014
http://dx.doi.org/10.1016/S2212-5671(14)00517-6
A9-c156 Thanh T Nguyen, Lee Gordon-Brown, Abbas Khosravi, Douglas Creighton, Saeid Nahavandi, Fuzzy
Portfolio Allocation Models through a New Risk Measure and Fuzzy Sharpe Ratio, IEEE TRANSACTIONS ON FUZZY SYSTEMS (to appear). 2014
http://dx.doi.org/10.1109/TFUZZ.2014.2321614
A9-c155 Adel Azar, Hossein Sayyadi Tooranloo, Ali Rajabzadeh, Laya Olfat, A Model for Assessing Agility
Drivers with Possibility Theory, Applied mathematics in Engineering, Management and Technology, June
2014: (1119) p. 1134. 2014
http://amiemt.megig.ir/test/sp2/136.pdf
A9-c154 Dabuxilatu Wang, Pinghui Li, Masami Yasuda, Construction of Fuzzy Control Charts Based on
Weighted Possibilistic Mean, Communications in Statistics - Theory and Methods, 43(2014), number 15,
pp. 3186-3207. 2014
http://dx.doi.org/10.1080/03610926.2012.695852
A9-c153 Wang X, He J, Li S, Compound option pricing under fuzzy environment, Journal of Applied Mathematics, 2014: Paper 875319. 2014
http://dx.doi.org/10.1155/2014/875319
Fullér and Majlender [A9] defined the crisp possibilistic mean value of a fuzzy number (page 2)
A9-c152 S Sefi, R Saneifard, Fuzzy Risk Analysis Based on Measure of Fuzzy Numbers and Its Application in
the Extended Air Fighter Selection Problem, Advances in Environmental Biology 8(2014), number 10, pp.
513-518. 2014
A9-c4151 Belles-Sampera J, Merigo JM, Guillén M, Santolino M, Indicators for the characterization of discrete
Choquet integrals, Information Sciences, 267(2014), pp. 201-216. 2014
http://dx.doi.org/10.1016/j.ins.2014.01.047
Initially, Yager [41] introduced the orness/andness indicators and the entropy of dispersion for just
this purpose. Later, he proposed complementary indicators, including the balance indicator [42]
and the divergence [44], to be used in exceptional situations. Meanwhile, Fullér and Majlender
[11] suggested the use of a variance indicator and Majlender [21] introduced the Rnyi entropy
[32] as a generalization of the Shannon entropy [33] in the framework of the OWA operator. (page
202)
A9-c150 Piotr Nowak, Maciej Romaniuk, Application of Levy processes and Esscher transformed martingale measures for option pricing in fuzzy framework, Journal of Computational and Applied Mathematics,
263(2014), pp. 129-151. 2014
http://dx.doi.org/10.1016/j.cam.2013.11.031
Fuller and Majlender A9] introduced weighted interval-valued and crisp possibilistic mean values
of fuzzy numbers. (page 132)
56
A9-c4149 Shu-Ping Wan, Jiu-Ying Dong, Possibility Method for Triangular Intuitionistic Fuzzy Multi-attribute
Group Decision Making with Incomplete Weight Information, International Journal of Computational Intelligence Systems, 7(2014), number 1, pp. 65-79. 2014
http://dx.doi.org/10.1080/18756891.2013.857150
2013
A9-c148 Weijun Xu Xiaolong Peng, Weilin Xiao, The Fuzzy Jump-Diffusion Model to Pricing European Vulnerable Options, International Journal of Fuzzy Systems, 15(2013), number 3, pp. 317-325. 2013
http://www.ijfs.org.tw/ePublication/2013_paper_3/
ijfs13-3-r-6-20130911111142_v2.pdf
Fuller and Majlender [28] defined the crisp possibilistic mean value of a fuzzy number (page 321)
A9-c147 Wan S-P, Wang Q-Y, Dong J-Y, The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers, Knowledge-Based Systems, 52(2013), pp. 65-77. 2013
http://dx.doi.org/10.1016/j.knosys.2013.06.019
Motivated by [A9], we give the definitions of the crisp weighted possibility mean of TIFNs as
follows. (page 67)
A9-c146 Gong Yanbing, The new weighted magnitude mean value and variance of fuzzy numbers, Journal of
Intelligent and Fuzzy Systems, 26(2014), number 5, pp. 2303-2313. 2014
http://dx.doi.org/10.3233/IFS-130903
Fullér and Majlender (Fuzzy Sets and Systems 136 (2003) 363374) introduced the notation of
weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-valued probabilistic mean. In this paper, we introduce the new notation of
lower and upper weighted magnitude mean values of a fuzzy number. The new interval-valued
weighted magnitude mean and variance are defined, which differs from the one given by Fullér
and Majlender. We will show the relationship of interval-valued weighted magnitude mean and
interval-valued weighted possibilistic mean. Furthermore, we shall also introduce the notations
of crisp weighted magnitude mean value, variance and covariance of fuzzy numbers, which are
consistent with the extension principle.
A9-c145 Liu Wen-qiong, Li Sheng-hong, European option pricing model in a stochastic and fuzzy environment,
Applied Mathematics - A Journal of Chinese Universities, 8(2013), number 3, pp. 321-334. 2013
http://dx.doi.org/10.1007/s11766-013-3030-0
We shall list a collection of basic definitions of weighted possibilistic mean of a fuzzy number.
For more details and examples on this one can referred to Fullér and Majlender [A9]. (page 323)
A9-c144 Luca Anzilli, Gisella Facchinetti, The Total Variation of Bounded Variation Functions to Evaluate and
Rank Fuzzy Quantities, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 28(2013), issue
10, pp. 927-956. 2013
http://dx.doi.org/10.1002/int.21604
A9-c143 Collan M, Fedrizzi M, Luukka P, A multi-expert system for ranking patents: An approach based on
fuzzy pay-off distributions and a TOPSIS-AHP framework, Expert Systems with Applications, 40(2013),
number 12, pp. 4749-4759. 2013
http://dx.doi.org/10.1016/j.eswa.2013.02.012
A9-c142 Irina Georgescu, A new notion of possibilistic covariance, NEW MATHEMATICS AND NATURAL
COMPUTATION, 9(2013), number 1, pp. 1-11. 2013
http://dx.doi.org/10.1142/S1793005713500014
A9-c141 Gao S, Zhang Z, Cao C, Program evaluation and review technique based on fuzzy numbers, JOURNAL
OF CONVERGENCE INFORMATION TECHNOLOGY, 8(2013), number 2, pp. 652-659. 2013
http://dx.doi.org/10.4156/jcit.vol8.issue2.78
57
A9-c140 Matteo Brunelli, József Mezei, How different are ranking methods for fuzzy numbers? A numerical
study, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 54(2013), number 5, pp. 627639. 2013
http://dx.doi.org/10.1016/j.ijar.2013.01.009
Fullér and Majlender [A9] extended the original definition by replacing the weight with a general
weighting function f (α).
A9-c139 Enriqueta Vercher, Jose D Bermudez, A Possibilistic Mean-Downside Risk-Skewness model for efficient portfolio selection, IEEE TRANSACTIONS ON FUZZY SYSTEMS (to appear). 2013
http://dx.doi.org/10.1109/TFUZZ.2012.2227487
Other weighted mean-interval definitions based on the α-cuts could be used, those introduced in
[A9] also allow incorporation of the importance of the α-level sets (see [5] for several relationships
between these two types of interval-valued expectations).
A9-c138 Jixiang Xu, Yanhua Tan, Enmin Feng, Jinggui Gao, Pricing currency option based on the extension
principle and defuzzification via weighting parameter identification, JOURNAL OF APPLIED MATHEMATICS, vol. 2013, Paper 623945. 2013
http://www.hindawi.com/journals/jam/aip/623945/
2012
A9-c137 Gao S, Zhang Z, Cao C, Square operation of triangular fuzzy number, ADVANCES IN INFORMATION SCIENCES AND SERVICE SCIENCES, Volume 4, Issue 14, August 2012, Pages 16-24. 2012
http://dx.doi.org/10.4156/AISS.vol4.issue14.3
A9-c136 Wan S-P, Zhang X-L, Method based on weighted possibility mean for solving matrix games with payoffs of intuitionistic trapezoidal fuzzy numbers Kongzhi yu Juece/Control and Decision, 27(2012), number
8, p. 1121-1126+1132. 2012
Scopus: 84867050763
A9-c135 Ching-Hsue Cheng, Chen-Tung Chen, Sue-Fen Huang, Combining fuzzy integral with order weight
average (OWA) method for evaluating financial performance in the semiconductor industry, AFRICAN
JOURNAL OF BUSINESS MANAGEMENT 6(2012), number 21, pp. 6358-6368. 2012
http://dx.doi.org/10.5897/AJBM11.534
A9-c134 I. Georgescu, Expected utility operators and possibilistic risk aversion, SOFT COMPUTING, Volume
16, Issue 10, September 2012, Pages 1671-1680. 2012
http://dx.doi.org/10.1007/s00500-012-0851-3
A9-c133 Zhang L -H, Zhang W -G, Xu W -J, Xiao W -L, The double exponential jump diffusion model for
pricing European options under fuzzy environments, Economic Modelling, 29(2012), number 3, pp. 780786. 2012
http://dx.doi.org/10.1016/j.econmod.2012.02.005
Fullér and Majlender (2003) defined the crisp possibilistic mean value of a fuzzy number (page
783)
A9-c132 Gao S, Zhang Z, Cao C, Maximum and minimum of fuzzy numbers and application in fuzzy shortest
path problem, INTERNATIONAL JOURNAL OF ADVANCEMENTS IN COMPUTING TECHNOLOGY,
4(2012), number 13, pp. 1-11. 2012
Scopus: 84865344171
A9-c131 J D Bermúdeza, J V Segurab, E Vercher, A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection, FUZZY SETS AND SYSTEMS, 188(2012), number 1, pp. 16-26. 2012
http://dx.doi.org/10.1016/j.fss.2011.05.013
A9-c130 Chung-Tsen Tsao, Fuzzy net present values for capital investments in an uncertain environment, COMPUTERS & OPERATIONS RESEARCH, 39(2102), issue 8, pp. 1885-1892. 2012.
http://dx.doi.org/10.1016/j.cor.2011.07.015
2011
58
A9-c129 Appadoo S S, Bector C R, Bhatt S K, Possibilistic characterization of (m,n)-Trapezoidal fuzzy numbers
with applications, Journal of Interdisciplinary Mathematics, 14(2011), number 4, pp. 347-372. 2011
Scopus: 84856195004
A9-c88 Jinquan Li, Xuehai Yuan, E S Lee, Dehua Xu, Setting due dates to minimize the total weighted possibilistic mean value of the weighted earliness - tardiness costs on a single machine, COMPUTERS AND
MATHEMATICS WITH APPLICATIONS, 62(2011), number 11, pp. 4126-4139. 2011
http://dx.doi.org/10.1016/j.camwa.2011.09.063
A9-c87 A Saeidifar, Application of weighting functions to the ranking of fuzzy numbers, COMPUTERS AND
MATHEMATICS WITH APPLICATIONS 62(2011), number 5, pp. 2246-2258. 2011
http://dx.doi.org/10.1016/j.camwa.2011.07.012
A9-c128 Shiu-Hwei Ho, Shu-Hsien Liao, A fuzzy real option approach for investment project valuation, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), issue 12, pp. 15296-15302. 2011
http://dx.doi.org/10.1016/j.eswa.2011.06.010
A9-c127 Rahim Saneifard, A new algorithm for selecting equip system based on fuzzy operations, INTERNATIONAL JOURNAL OF THE PHYSICAL SCIENCES, 6(2011), number 14, pp. 3279-3287. 2011
http://www.academicjournals.org/IJPS/PDF/pdf2011/18Jul/Saneifard.pdf
A9-c126 Irina Georgescu; Jani Kinnunen, Credibility measures in portfolio analysis: From possibilistic to
probabilistic models, JOURNAL OF APPLIED OPERATIONAL RESEARCH, 3(2011), number 2, pp.
91-102.
http://www.tadbir.ca/jaor/archive/v3/n2/jaorv3n2p91.pdf
A9-c125 Ondřej Pavlačka, Modeling uncertain variables of the weighted average operation by fuzzy vectors,
INFORMATION SCIENCES, 1 81(2011), number 22, pp. 4969-4992. 2011
http://dx.doi.org/10.1016/j.ins.2011.06.022
A9-c124 Irina Georgescu, Jani Kinnunen, Possibilistic risk aversion with many parameters, PROCEDIA COMPUTER SCIENCE 4(2011), pp. 1735-1744. 2011
http://dx.doi.org/10.1016/j.procs.2011.04.188
A9-c123 Dug Hun Hong, The relationship between the minimum variance and minimax disparity rim quantifier
problems, FUZZY SETS AND SYSTEMS, 181(2011), number 1, pp. 50-57. 2011
http://dx.doi.org/10.1016/j.fss.2011.05.014
A9-c122 Irina Georgescu; Jani Kinnunen, Multidimensional possibilistic risk aversion, MATHEMATICAL
AND COMPUTER MODELLING, 54(2011), issues 1-2, pp. 689-696. 2011
http://dx.doi.org/10.1016/j.mcm.2011.03.011
A9-c121 Irina Georgescu, A possibilistic approach to risk aversion, SOFT COMPUTING, 15(2011), pp. 795801. 2011
http://dx.doi.org/10.1007/s00500-010-0634-7
A9-c120 Zhang Qiansheng, Jiang Shengyi, Probabilistic interval-valued fuzzy sets and its application in pattern
recognition APPLIED MATHEMATICS 26(2011), number 1, pp. 111-120. 2011
http://www.math.zju.edu.cn/amjcu/A/201101/111-120.pdf
2010
A9-c119 Seung Hoe Choi; Jin Hee Yoon, General fuzzy regression using least squares method, INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 41(2010), issue 5, pp. 477-485. 2010
http://dx.doi.org/10.1080/00207720902774813
A9-c118 Zhang Qian-Sheng; Jiang Sheng-Yi, On Weighted Possibilistic Mean, Variance and Correlation of
Interval-valued Fuzzy Numbers, COMMUNICATIONS IN MATHEMATICAL RESEARCH, 26(2010),
number 2, pp. 105-118. 2010
http://www.cqvip.com/qk/96600A/201002/34084956.html
59
A9-c117 Jinquan Li, Kaibiao Sun, Dehua Xu, Hongxing Li, Single machine due date assignment scheduling
problem with customer service level in fuzzy environment, APPLIED SOFT COMPUTING, 10(2010),
issue 3, pp. 849-858. 2010
http://dx.doi.org/10.1016/j.asoc.2009.10.002
A9-c116 Shu-Hsien Liao, Shiu-Hwei Ho, Investment project valuation based on a fuzzy binomial approach,
INFORMATION SCIENCES, 180(2010), issue 11, pp. 2124-2133. 2010
http://dx.doi.org/10.1016/j.ins.2010.02.012
A9-c115 Weijun Xu, Weidong Xu, Hongyi Li, Weiguo Zhang, A study of Greek letters of currency option under
uncertainty environments, Mathematical and Computer Modelling, Volume 51, Issues 5-6, March 2010, pp.
670-681. 2010
http://dx.doi.org/10.1016/j.mcm.2009.10.041
A9-c114 Chung-Tsen Tsao, The revised algorithms of fuzzy variance and an application to portfolio selection,
SOFT COMPUTING , 14(2010), pp. 329-337. 2010
http://dx.doi.org/10.1007/s00500-009-0407-3
The discussion of fuzzy statistical measures and fuzzy statistical inference have been found in
many previous studies (Carlsson and Fuller 2001; Chiang and Lin 1999; Dubois and Prade 1986;
Feng et al. 2001; Fruhwirth-Schnatter 1992; Fuller and Majlender 2003; Hong 2006; Hryniewicz
2006; Kwakernaak 1978, 1979; Lee 2001; Liu and Kao 2002; Puri and Ralescu 1986; Wu 2003).
(page 329)
It has been entirely accepted that the arithmetic mean of a set of fuzzy data is a fuzzy number (Puri
and Ralescu 1986), but the opinions regarding the fuzziness of the variance and covariance rest
on both sides of the fence. Feng et al. (2001), Fuller and Majlender (2003), and Chiang and Lin
(1999) treated the variance of fuzzy random variables to be crisp values, i.e., with no fuzziness.
Contrarily, Lee (2001), Wu (2003), Liu and Kao (2002), and Hong (2006) stood for the side of
fuzziness. In these previous studies the computation methods for crisp variance seem to be sound,
but those for fuzzy variance are controversial. This work herein does not focus on stating which
side is more reasonable, but rather concentrates on mending the controversy of fuzzy computation.
(page 330)
2009
A9-c113 Irina Georgescu, Possibilistic risk aversion, FUZZY SETS AND SYSTEMS, 160(2009), pp. 26082619. 2009
http://dx.doi.org/10.1016/j.fss.2008.12.007
A9-c112 Srabani Sarkar and Madhumangal Pal, Multiple Regression of Fuzzy-Valued Variable, JOURNAL OF
PHYSICAL SCIENCES, 13(2009), pp. 57-66.
http://www.vidyasagar.ac.in/journal/maths/vol13/Art05.pdf
A9-c111 Wei Chen, Weighted portfolio selection models based on possibility theory, FUZZY INFORMATION
AND ENGINEERING, 1(2009), pp. 115-127. 2009
http://dx.doi.org/10.1007/s12543-009-0010-4
A9-c110 G. Facchinetti and N. Pacchiarotti, A general defuzzification method for a fuzzy system output depending on different t-norms, ADVANCES IN FUZZY SETS AND SYSTEMS, Volume 4, Issue 2, Pages
167-187. 2009
http://pphmj.com/references/4120.htm
A9-c109 Srabani Sarkar and Madhumangal Pal, Measure of fuzziness involved in fuzzy-valued variable, ADVANCES IN FUZZY MATHEMATICS, Volume 4, Number 2 (2009), pp. 85-100. 2009
http://www.ripublication.com/afm/afmv4n2_1.pdf
A9-c108 Shang Gao, Zaiyue Zhang, Cungen Cao, Multiplication Operation on Fuzzy Numbers, JOURNAL OF
SOFTWARE, VOL. 4, NO. 4, JUNE 2009, pp. 331-338. 2009
http://academypublisher.com/jsw/vol04/no04/jsw0404331338.pdf
60
A9-c107 Weidong Xu, Chongfeng Wu, Weijun Xu, Hongyi Li, A jump-diffusion model for option pricing under
fuzzy environments, INSURANCE: MATHEMATICS AND ECONOMICS, 44(2009), pp. 337-344. 2009
http://dx.doi.org/10.1016/j.insmatheco.2008.09.003
A9-c106 Wei-Guo Zhang and Wei-Lin Xiao, On weighted lower and upper possibilistic means and variances
of fuzzy numbers and its application in decision, KNOWLEDGE AND INFORMATION SYSTEMS,
18(2009), pp. 311-330. 2009
http://dx.doi.org/10.1007/s10115-008-0133-7
The contributions of this paper are as follows. Corresponding to the weighted lower and upper
possibilistic means introduced by Fullér and Majlender [A9], we will define the weighted lower
and upper possibilistic variances and possibilistic covariances of fuzzy numbers and show that
many properties of variance and covariance in probability theory are preserved by the proposed
notions. (page 312)
A9-c105 A. Saeidifar, E. Pasha, The possibilistic moments of fuzzy numbers and their applications, JOURNAL
OF COMPUTATIONAL AND APPLIED MATHEMATICS, 223 (2009), pp. 1028-1042. 2009
http://dx.doi.org/10.1016/j.cam.2008.03.045
In statistics, measures of central tendency and measures dispersion of distribution are considered
important. For fuzzy numbers, one of the most common and useful measures of central tendency
is the mean of fuzzy numbers, Carlsson, Fullér and Majlender [A6,A9] defined the weighted lower
possibilistic and upper possibilistic mean values, crisp possibilistic mean value, the variance and
covariance of fuzzy numbers.
..
.
The main results of Sections 4 and 5 are new and interesting alternative justifications to the definitions of the f-weighted interval-valued possibilistic mean and f-weighted possibilistic mean value
of a fuzzy number that introduced by Fullér and Majlender [A6,A9]. (page 1028)
A9-c104 Konstantinos A. Chrysas, Basil K. Papadopoulos, On theoretical pricing of options with fuzzy estimators, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 223 (2009), pp. 552-566.
2009
http://dx.doi.org/10.1016/j.cam.2007.12.006
A9-c103 A. Thavaneswaran, S.S. Appadoo, A. Paseka, Weighted possibilistic moments of fuzzy numbers
with applications to GARCH modeling and option pricing, MATHEMATICAL AND COMPUTER MODELLING, 9(2009) 352-368. 2009
http://dx.doi.org/10.1016/j.mcm.2008.07.035
2008
A9-c102 S S Appadoo, S K Bhatt, C R Bector, Application of possibility theory to investment decisions, FUZZY
OPTIMIZATION AND DECISION MAKING, vol. 7(2008), pp. 35-57. 2008
http://dx.doi.org/10.1007/s10700-007-9023-9
A9-c101 Michele Lalla; Gisella Facchinetti; Giovanni Mastroleo, Vagueness evaluation of the crisp output in a
fuzzy inference system, FUZZY SETS AND SYSTEMS, 159(2008) 3297-3312. 2008
http://dx.doi.org/10.1016/j.fss.2008.03.002
A9-c100 HOU Shi-wang; TONG Shu-rong, The Study of Control Chart for Fuzzy Process Quality Control
Based on Fuzzy Number, JOURNAL OF ZHENGZHOU UNIVERSITY: ENGINEERING SCIENCES,
29(2008), number 1, pp. 39-43 (in Chinese). 2008
http://www.cqvip.com/qk/95571b/2008001/26834315.html
A9-c99 Michele Lalla; Gisella Facchinetti; Giovanni Mastroleo, Vagueness evaluation of the crisp output in a
fuzzy inference system, FUZZY SETS AND SYSTEMS, 159(2008) pp. 3297-3312. 2008
http://dx.doi.org/10.1016/j.fss.2008.03.002
61
A9-c98 Enriqueta Vercher, Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 217(2008) 381-393. 2008
http://dx.doi.org/10.1016/j.cam.2007.02.017
Recently, weighted mean values have been introduced [A9], which also allow us to incorporate
the importance of the α-level sets. All these interval-valued expectations remain additive in the
sense of the addition of fuzzy numbers. (page 384)
2007
A9-c97 D.H. Hong and K.T. Kim, A note on the maximum entropy weighting function problem, JOURNAL
OF APPLIED MATHEMATICS AND COMPUTING, 23(2007), No. 1-2, pp. 547-552. 2007
http://www.mathnet.or.kr/mathnet/thesis_file/DHHong0613F.pdf
A9-c96 S Sudradjat, On the possibilistic approach to a portfolio selection problem, MATHEMATICAL REPORTS, 9(2007), pp. 305-317. 2007
http://www.csm.ro/reviste/Mathematical_Reports/Pdfs/2007/3/supian.pdf
A9-c95 Martin O, Klir G J, Defuzzification as a special way of dealing with retranslation, INTERNATIONAL
JOURNAL OF GENERAL SYSTEMS, 36: (6), pp. 683-701. 2007
http://dx.doi.org/10.1080/03081070701456088
A9-c94 Zhang W -G, Wang Y -L, A comparative analysis of possibilistic variances and covariances of fuzzy
numbers FUNDAMENTA INFORMATICAE, 79: (1-2), pp. 257-263. 2007
A9-c93 Xinwang Liu and Hsinyi Lin, Parameterized approximation of fuzzy number with minimum variance
weighting functions, MATHEMATICAL AND COMPUTER MODELLING, 46 (2007) 1398-1409. 2007
http://dx.doi.org/10.1016/j.mcm.2007.01.011
Apart from the weighting function that put different emphasis on the possible values of a fuzzy
number, we can also put different emphasis on the cut-level set of a fuzzy number. This method
was proposed by Fullér and Majlender [A9]. The method was extended to a more general form
without the monotonic condition in the weighting function definition by Liu recently [19], and a
parameterized weighting function with maximum entropy was proposed. (page 1406)
A9-c92 Thavaneswaran A, Thiagarajah K, Appadoo SS Fuzzy coefficient volatility (FCV) models with applications MATHEMATICAL AND COMPUTER MODELLING, 45 (7-8): 777-786 APR 2007
http://dx.doi.org/10.1016/j.mcm.2006.07.019
A9-c91 Vercher E, Bermudez JD, Segura JV Fuzzy portfolio optimization under downside risk measures FUZZY
SETS AND SYSTEMS, 158 (7): 769-782 APR 1 2007
http://dx.doi.org/10.1016/j.fss.2006.10.026
Weighted mean values introduced in [A9] are a generalization of those possibilistic ones and
allow us to incorporate the importance of α-level sets. It shows that for LR-fuzzy numbers, any
f -weighted interval-valued possibilistic mean value is a subset of the interval-valued mean of a
fuzzy number in the sense of Dubois and Prade. (page 770)
A9-c90 Supian Sudradjat, The Weighted Possibilistic Mean Variance and Covariance of Fuzzy Numbers, JOURNAL OF APPLIED QUANTITATIVE METHODS, Volume 2, Issue 3, pp. 342-349, September 30, 2007
http://jaqm.ro/issues/volume-2,issue-3/pdfs/sudradjat.pdf
A9-c89 Thiagarajah, K., Appadoo, S.S., Thavaneswaran, A. Option valuation model with adaptive fuzzy numbers, COMPUTERS AND MATHEMATICS WITH APPLICATIONS, 53 (5), pp. 831-841. 2007
http://dx.doi.org/10.1016/j.camwa.2007.01.011
In the next section, in the line of Fullér and Majlender [A9] we discuss weighted possibilistic
moment of the adaptive fuzzy number. (page 834)
62
Viewing the fuzzy numbers as random sets, Dubois and Prade [5] defined their interval-valued expectation. However, Carlsson and Fullér [A14] defined a possibilistic interval-valued mean value
of fuzzy numbers by viewing them as possibility distributions. Furthermore, weighted possibilistic mean, variance and weighted interval-valued possibilistic mean value of fuzzy numbers are all
introduced in Fullér and Majlender [A9]. Furthermore, weighted possibilistic mean, variance and
weighted interval-valued possibilistic mean value of fuzzy numbers are all introduced in Fullér
and Majlender [A9]. (page 835)
2006
A9-c88 D. Dubois, Possibility theory and statistical reasoning COMPUTATIONAL STATISTICS & DATA
ANALYSIS, 51 (1): 47-69 NOV 1 2006
http://dx.doi.org/10.1016/j.csda.2006.04.015
Fullér and colleagues (Carlsson and Fullér, 2001; Fullér and Majlender, 2003) consider introducing a weighting function on [0, 1] in order to account for unequal importance of cuts when
computing upper and lower expectations. (page 63)
The notion of variance has been extended to fuzzy random variables (Koerner, 1997), but little
work exists on the variance of a fuzzy interval. Fullér and colleagues (Carlsson and Fullér, 2001;
Fullér and Majlender, 2003) propose a definition as follows
Z
1
V̄ (M ) =
0
sup Mγ − inf Mγ
2
2
f (γ) dγ
where f is a weight function. (page 63)
A9-c87 Stefanini L, Sorini L, Guerra ML Parametric representation of fuzzy numbers and application to fuzzy
calculus FUZZY SETS AND SYSTEMS, 157 (18): 2423-2455 SEP 16 2006
http://dx.doi.org/10.1016/j.fss.2006.02.002
Other functions can be calculated numerically; examples are the covariance and variance of fuzzy
numbers u, v (see [3, A9]); (page 2437)
A9-c86 Matia F, Jimenez A, Al-Hadithi BM, et al. The fuzzy Kalman filter: State estimation using possibilistic
techniques, FUZZY SETS AND SYSTEMS, 157 (16): 2145-2170 AUG 16 2006
http://dx.doi.org/10.1016/j.fss.2006.05.003
A9-c85 Xinwang Liu, On the maximum entropy parameterized interval approximation of fuzzy numbers,
FUZZY SETS AND SYSTEMS, 157(2006) 869-878. 2006
http://dx.doi.org/10.1016/j.fss.2005.09.010
This paper extends the interval-valued weighted possibilistic mean of a fuzzy number of Fullér and
Majlender to a general weighting function without the monotonic increasing assumption. This
weighting function determines a weighted average aggregation of the cuts of the fuzzy number
according to the preference of a decision-maker. Some properties of the weighting function are
provided and a preference index that qualifies this aggregation and can serve as a parameter for
the definition of interval approximation of a fuzzy number is proposed. A special class of parameterized weighting functions satisfying the maximal entropy principle is proposed. (page 869)
Fullér and Majlender [A9] further extended these results to the notion of weighted possibilistic
mean with the weighting function method. (page 870)
Based on this interval aggregation idea, the definition of the weighting function in [A9] is extended
without the monotonic increasing assumption. In fact, the increasing weighting function in [A9]
can be seen as the weighted average of the level sets which places more emphasis on the level sets
with higher membership grades. (page 870)
63
The property of the f-weighted interval-valued possibilistic mean is also extended directly:
Theorem 1 (Fullér and Majlender [A9]). Let A, B ∈ F and let f be a weighting function, and let
µ be a real number, then,
Mf (A + B) = Mf (A) + Mf (B),
Mf (µA) = µMf (A).
(page 871)
Regarding the weighting function as an aggregation operator for the fuzzy number level sets, the
paper extends the concept of a weighting function proposed by Fullér and Majlender to a general
form without the monotonic increasing assumption. (page 878)
2005
A9-c84 Ayala G, Leon T, Zapater V, Different averages of a fuzzy set with an application to vessel segmentation,
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 13(3): 384-393 JUN 2005
http://dx.doi.org/10.1109/TFUZZ.2004.839667
A9-c83 Cheng CB, Fuzzy process control: construction of control charts with fuzzy numbers, FUZZY SETS
AND SYSTEMS, 154 (2): 287-303 SEP 1 2005
http://dx.doi.org/10.1016/j.fss.2005.03.002
Fullér and Majlender [A9] further generalized the above definition by introducing a weighting
function, ω(γ), to measure the importance of the γ-level set of F , and defined the ω-weighted
R 1 eu (γ) − el (γ) 2
possibilistic variance of F as Varω (F ) = 0
ω(γ)dγ, where the weighting
2
R1
function is nonnegative, monotonically increasing and satises 0 ω(γ)dγ = 1. (page 291)
However, to allow the use of the given scores in this estimation, the present study re-defines the
γ-weighted possibilistic variance of a triangular fuzzy number based on the definitions of Carlsson
and Fullér [A14] and Fullér and Majlender [A9],
Z 1
Z 1
1
[m − el (γ)]2 ω(γ)dγ +
[m − eu (γ)]2 ω(γ)dγ
(4)
Varω (F ) =
2 0
0
In Eq. (4), the mode of the fuzzy number, m, replaces the arithmetic mean of the γ-level set used
in the definition of Carlsson and Fullér [A14]. When F is symmetric, the γ-weighted possibilistic
variance defined in Eq. (4) equals to the variance defined by Fullér and Majlender [A9]. (pages
291-292)
A9-c82 Wu Lihua; Cai-Ming Fu, Finite Element Simulation of Stress and Strain of Teeth Based on Different Loading Method, MACHINE BUILDING & AUTOMATION, 34(2005), number 1, pp. 102-105 (in
Chinese). 2005
http://d.wanfangdata.com.cn/Periodical_jxzzyzdh200501030.aspx
A9-c81 Bodjanova S, Median value and median interval of a fuzzy number, INFORMATION SCIENCES, 172
(1-2): 73-89 JUN 9 2005
http://dx.doi.org/10.1016/j.ins.2004.07.018
Weighted possibilistic mean, variance, and covariance of fuzzy numbers can be found in the work
of Fullér and Majlender [A9]. (page 74)
2004
A9-c80 Hong DH, Kim KT, A note on weighted possibilistic mean, FUZZY SETS AND SYSTEMS, 148 (2):
333-335 DEC 1 2004
http://dx.doi.org/10.1016/j.fss.2004.04.011
64
in proceedings and edited volumes
2015
A9-c44 Luca Anzilli, Gisella Facchinetti, A general fuzzy set representation for decision making, In: Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and the 9th
Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Atlantis Press, (ISBN
978-94-62520-77-6), pp. 857-864. 2015
http://dx.doi.org/10.2991/ifsa-eusflat-15.2015.121
A9-c43 A Rubio, J D Bermudez, E Vercher, Comparative analysis of forecasting portfolio returns using Soft
Computing technologies, In: Proceedings of the 16th World Congress of the International Fuzzy Systems
Association (IFSA) and the 9th Conference of the European Society for Fuzzy Logic and Technology
(EUSFLAT), Atlantis Press, (ISBN 978-94-62520-77-6), pp. 617-623. 2015
http://dx.doi.org/10.2991/ifsa-eusflat-15.2015.88
The f-weighted interval-valued possibilistic mean value of a fuzzy number [A10] can be considered as a generalization of both the interval-valued mean [19] and the interval-valued possibilistic
mean [A14], using the weighting functions f (γ) = 1 and f (γ) = 2γ, respectively. The authors
also noted that their definition of the f-weighted possibilistic mean value coincides with the value
of a fuzzy number (with respect to the reducing function 0.5f) introduced by Delgado et al. [23].
(page 618)
A9-c42 Irina Georgescu, Jani Kinnunen, Ana Maria Lucia-Casademunt, Possibilistic Models of Risk Management, In: Intelligent Techniques in Engineering Management, Intelligent Systems Reference Library, vol.
87/2015, Springer, (ISBN 978-3-319-17905-6) pp. 21-44. 2015
http://dx.doi.org/10.1007/978-3-319-17906-3_2
A9-c41 Andrea Barbazza, Mikael Collan, Mario Fedrizzi, Pasi Luukka, Consensus Modeling in Multiple Criteria Multi-expert Real Options-Based Valuation of Patents, In: Intelligent Systems’2014, Proceedings of the
7th International Conference Intelligent Systems IEEE IS’2014, September 24?26, 2014, Warsaw, Poland,
Volume 1: Mathematical Foundations, Theory, Analyses, Advances in Intelligent Systems and Computing
vol. 322, Springer, (ISBN 978-3-319-11312-8) pp. 269-278. 2015
http://dx.doi.org/10.1007/978-3-319-11313-5 25
2013
A9-c40 Wang Dabuxilatu, A soft control chart based on weighted measurement of fuzzy data, In: Proceedings
of the 2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE
Computer Society Press, 2013. (ISBN 978-1-4673-5253-6) pp. 299-303. 2013
http://dx.doi.org/10.1109/FSKD.2013.6816211
Fullér et al. [A9] introduced the weighted possibilistic mean and variance for fuzzy numbers.
(page 299)
A9-c39 Bayaraa S-O, Delgersaikhan U, Dalaisaikhan N, Utility maximization problem using curve trapezoidal
fuzzy number, Proceedings of the 8th International Forum on Strategic Technology 2013, IFOST 2013,
Ulaanbaatar, [ISBN 978-1-4799-0931-5], pp. 393-395. 2013
http://dx.doi.org/10.1109/IFOST.2013.6616992
A9-c38 Alfred M Mbairadjim, Jules Sadefo Kamdem, Michel Terraza, Hedge Funds Risk-Adjusted Performance Evaluation: A Fuzzy Set Theory-Based Approach, In: Virginie Terraza, Hery Razafitombo eds., Understanding Investment Funds: Insights from Performance and Risk Analysis, Palgrave Macmillan, 2013,
[ISBN 9781137273604], pp. 57-71. 2013
2012
65
A9-c37 Irina Georgescu, Combining probabilistic and possibilistic aspects of background risk, 2012 IEEE 13th
International Symposium on Computational Intelligence and Informatics (CINTI), 20-22 Nov. 2012, Budapest, [ISBN 978-1-4673-5205-5], pp. 225,229. 2012
http://dx.doi.org/10.1109/CINTI.2012.6496765
A9-c36 Enriqueta Vercher, José D Bermúdez, Fuzzy Portfolio Selection Models: A Numerical Study, in: Financial Decision Making Using Computational Intelligence, Springer Optimization and Its Applications Ser,
[ISBN 978-1-4614-3773-4], pp. 253-280. 2012
http://dx.doi.org/10.1007/978-1-4614-3773-4_10
In order to incorporate the importance of α-level sets into the definition of mean value of a fuzzy
quantity, Fullér and Majlender [A9] introduce the concept of weighted possibilistic expectation of
fuzzy numbers, extending the definition of interval-valued possibilistic mean and variance given
by Carlsson and Fullér [A14]. (page 262)
A9-c35 B. Ying, Evaluation system of organization quality culture development based on fuzzy similarity,
Proceeding of 2012 International Conference on Information Management, Innovation Management and
Industrial Engineering, ICIII 2012, October 20-21, 2012, Sanya, [ISBN: 978-146731932-4], pp. 141-145.
2012
Scopus: 84870587639
A9-c34 Luca Anzilli, A Possibilistic Approach to Evaluating Equity-Linked Life Insurance Policies, in: Advances in Computational Intelligence, 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, July 9-13, 2012, Catania, Italy, Communications in Computer and Information Science, vol. 300/2012, Springer, [ISBN 978-3-642-31724-8,
pp. 44-53. 2012
http://dx.doi.org/10.1007/978-3-642-31724-8_6
A9-c33 Irina Georgescu, Jani Kinnunen, Possibilistic Risk Aversion and Its Indicators, 11th WSEAS International Conference on APPLIED COMPUTER and APPLIED COMPUTATIONAL SCIENCE (ACACOS’12), April 18-20, 2012, Rovaniemi, Finland, [ISBN: 978-1-61804-084-8], pp. 178-183. 2012
http://www.wseas.us/e-library/conferences/2012/Rovaniemi/ACACOS/ACACOS-29.pdf
A9-c32 M Collan, K Kyläheiko, Strategic Patent Portfolios: Valuing the Bricks of the Road to the Future, 17th
International Working Seminar on Production Economics, February 20-24, 2012, Innsbruck, Austria, 12
pages. 2012
http://www.medifas.net/IGLS/Papers2012/Paper029.pdf
A9-c31 I Georgescu, J Kinnunen, A Mixed Portfolio Selection Problem, 9th International Conference on Distributed Computing and Artificial Intelligence, March 28-30, 2012, Salamanca, Spain, Advances in Intelligent and Soft Computing, vol. 151/2012, Springer, [ISBN: 978-3-642-28764-0], pp. 95-102. 2012
http://dx.doi.org/10.1007/978-3-642-28765-7_13
A9-c30 I Georgescu, J Kinnunen, A Generalized 3-Component Portfolio Selection Model, 11th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (AIKED ’12),
February 22-24, 2012, Cambridge, England, [ISBN: 978-1-61804-068-8], pp. 142-147. 2012
http://www.wseas.us/e-library/conferences/2012/CambridgeUK/AIKED/AIKED-22.pdf
2011
A9-c29 Irina Georgescu, Comparing Possibilistically Multidimensional Risk Aversions, 12th IEEE International
Symposium on Computational Intelligence and Informatics, November 21-22, 2011, Budapest, Hungary,
[ISBN: 978-1-4577-0045-3], pp. 183-188. 2011
http://dx.doi.org/10.1109/CINTI.2011.6108496
66
A9-c28 Irina Georgescu, Jani Kinnunen, Multidimensional risk aversion with mixed parameters, In: 6th IEEE
International Symposium on Applied Computational Intelligence and Informatics, May 19-21, 2011, Timisoara,
Romania, [ ISBN: 978-1-4244-9108-7], pp. 63-66. 2011
http://dx.doi.org/10.1109/SACI.2011.5872974
A9-c27 Irina Georgescu, Mixed risk aversion: Probabilistic and possibilistic aspects, 2011 IEEE 9th International Symposium on Applied Machine Intelligence and Informatics (SAMI), January 27-29, 2011,
Smolenice, Slovakia, [ISBN: 978-1-4244-7429-5], pp. 279-283. Paper 11883948. 2011
http://dx.doi.org/10.1109/SAMI.2011.5738889
2010
A9-c26 Irina Georgescu, A possibilistic Pratt theorem, 8th International Symposium on Intelligent Systems and
Informatics (SISY), 10-11 September 2010, Subotica, Serbia, [ISBN 978-1-4244-7394-6], pp. 193-196.
2010
http://dx.doi.org/10.1109/SISY.2010.5647299
A9-c25 Irina Georgescu, Jani Kinnunen, Multidimensional Possibilistic Risk Aversion, 11th International Symposium on Computational Intelligence and Informatics (CINTI), November 18-20, 2010, Budapest, Hungary, [ISBN 978-1-4244-9279-4], pp. 163-168. 2010
http://dx.doi.org/10.1109/CINTI.2010.5672253
A9-c24 Shu-Hsien Liao, Shiu-Hwei Ho, Investment Project Valuation Based on the Fuzzy Real Options Approach, 2010 International Conference on Technologies and Applications of Artificial Intelligence, November 18-20, 2010, Hsinchu City, Taiwan, [ISBN 978-0-7695-4253-9], pp. 94-101. 2010
http://dx.doi.org/ 10.1109/TAAI.2010.26
A9-c23 Ying-yu He, Portfolio selection model with transaction costs based on fuzzy information, 2nd IEEE
International Conference on Information and Financial Engineering (ICIFE), 17-19 Sept. 2010, Chongqing,
China, [ISBN 978-1-4244-6927-7], pp. 148-152. 2010
http://dx.doi.org/10.1109/ICIFE.2010.5609270
In this paper, we concentrate on three fundamental factors. One is the expected rate of return and
the risk. The uncertainty of the returns on the assets is modeled by means of fuzzy quantities.
Weighted mean values introduced in [A9] are a generalization of those possibilistic [A14] ones
and allow us to incorporate the importance of γ-level sets. We use weighted possibilistic means
to express the rate of the expected rate. Based on this point, we obtain the weighted possibilistic
variances to express the risk of a portfolio. (page 149)
A9-c22 Shu-Hsien Liao, Shiu-Hwei Ho, Investment Appraisal under Uncertainty - A Fuzzy Real Options Approach, Neural Information Processing. Models and Applications 17th International Conference, ICONIP
2010. Sydney, Australia, November 22-25, 2010, LNCS 6444/2010, Springer, [ISBN 978-3-642-17533-6],
pp. 716-726. 2010
http://dx.doi.org/10.1007/978-3-642-17534-3_88
A9-c21 Shu-Hsien Liao, Shiu-Hwei Ho, A fuzzy real options approach for investment project valuation, Proceedings of the 5th WSEAS International Conference on Economy and Management Transformation, October 24-26, 2010, Timisoara, Romania, vol. I, pp. 86-91. 2010
http://www.wseas.us/e-library/conferences/2010/TimisoaraW/EMT/EMT1-12.pdf
A9-c20 Guixiang Wang; Zhenju Mu, The fuzzy degrees of fuzzy n - cell numbers, Seventh International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 10-12 August 2010, Yantai, Shandong, [ISBN
978-1-4244-5931-5 ], pp. 349-353. 2010
http://dx.doi.org/10.1109/FSKD.2010.5569651
In [A9, A14], Carlsson, Fullér and Majlender studied the problems of variances for 1-dimension
fuzzy numbers. In this paper, for fuzzy n - cell numbers, we study the problems with respect to
fuzzy degrees. Firstly, we introduce concepts of vector-valued fuzzy degrees and weight (numbervalued) fuzzy degrees of fuzzy n - cell numbers, and then investigate their properties. At last, in
67
order to be conveniently used in applications, we give out the formula of calculating these fuzzy
degrees for pyramid fuzzy n - cell numbers. (page 349)
A9-c19 Shu-Hsien Liao, Shiu-Hwei Ho, Investment project valuation using a fuzzy real options approach,
Proceedings of the 10th WSEAS international conference on Systems theory and scientific computation, N.
E. Mastorakis, V. Mladenov, and Z. Bojkovic eds., Mathematics And Computers In Science Engineering,
August 20-22, 2010, Taipei, Taiwan, World Scientific and Engineering Academy and Society (WSEAS),
[ISBN 978-960-474-218-9], pp. 172-177. 2010
A9-c18 Irina Georgescu; Jani Kinnunen, Credibility measures in portfolio analysis, in: Mikael Collan ed.,
Proceedings of the 2nd International Conference on Applied Operational Research - ICAOR’10, Lecture
Notes in Management Science, vol. 2/2010, August 25-27, 2010 Turku, Finland, [ISBN: 978-952-12-24140], pp. 6-18. 2010
A9-c17 Ying-yu He, The comparison of the optimal portfolio corresponding to different weight functions, The
Third International Conference on Business Intelligence and Financial Engineering, August 13-15, 2010,
Hong Kong, pp. 196-200. 2010
http://dx.doi.org/10.1109/BIFE.2010.54
In this paper, we concentrate on three fundamental factors. One is the expected rate of return. The
uncertainty of the returns on the assets is modeled by means of fuzzy quantities. Weighted mean
values introduced in [A9] are a generalization of those possibilistic [A14] ones and allow us to
incorporate the importance of α-level sets. The other one is the risk. We could consider evaluating
its risk using a measure of the fuzziness of the return. (page 196)
2009
A9-c16 Gisella Facchineti, Nicoletta Pacchiarotti, Evaluation of fuzzy quantities by means of a weighting functions, In: Bruno Apolloni, Simone Bassis, Maria Marinaro eds., New Directions in Neural Networks - 18th
Italian Workshop on Neural Networks: WIRN 2008, Frontiers in Artificial Intelligence and Applications
Volume 193, 2009, IOS Press, pp. 194-204. 2009
http://dx.doi.org/10.3233/978-1-58603-984-4-194
A9-c15 G.-X. Wang; Y.-L. Liu; X.-N. Gao, The means of fuzzy n-cell numbers and the pre-orders on fuzzy ncell number space, 2009 International Conference on Machine Learning and Cybernetics, Volume 2, 12-15
July 2009, pp. 866-870. 2009
http://dx.doi.org/10.1109/ICMLC.2009.5212360
In [10], for 1-dimension fuzzy numbers, Dubois and Prade defined an interval-valued expectation.
In [A14, A9], Carlsson, Fullér and Majlender also studied the problems of means for 1-dimension
fuzzy numbers. On the other hand, it is well know that order, ranking and evaluating are all also
important research fields. In these aspects, plentiful research achievements have been obtained. In
this paper, for fuzzy n?cell numbers, we study the problems with respect to means and pre-orders.
(page 866)
A9-c14 Yan-qiu Guo and Shi-chang Lu, The Research of Multi-objective Asset Allocation Model with Complex
Constraint Conditions in a Fuzzy Random Environment, in: Fuzzy Information and Engineering Volume 2,
Advances in Soft Computing, vol. 62/2009, Springer, [ISBN 978-3-642-03663-7], pp. 1405-1415. 2009
http://dx.doi.org/10.1007/978-3-642-03664-4_149
2008
A9-c13 Irina Georgescu, Risk Aversion through Fuzzy Numbers, First International Conference on Complexity
and Intelligence of the Artificial and Natural Complex Systems. Medical Applications of the Complex
Systems. Biomedical Computing, November 08-10, 2008, Targu Mures, Romania, [ISBN 978-0-76953621-7], pp. 174-182. 2008
http://doi.ieeecomputersociety.org/10.1109/CANS.2008.27
68
A9-c12 A Saeidifar, Point and interval estimators of fuzzy numbers, 9th Iranian Statistics Conference, 20-22
August 2008, Isfahan, Iran, pp. 574-584. 2008
http://www.irstat.ir/Files/ISC/ISC9/ISC9%20-%20Proceedings
%20(English).pdf#page=583
2007
A9-c11 Cheng, Jao-Hong Lee, Chen-Yu , Product Outsourcing under Uncertainty: an Application of Fuzzy
Real Option Approach, IEEE International Fuzzy Systems Conference, 2007 (FUZZ-IEEE 2007), 23-26
July 2007, London, [ISBN: 1-4244-1210-2], pp. 1-6. 2007
http://dx.doi.org/10.1109/FUZZY.2007.4295675
2005
A9-c10 Wenyi Zeng, Hongxing Li, Weimin Ye, On the weighted interval approximation of a fuzzy number In:
10th International Conference on Fuzzy Theory and Technology (FTT 2005), 2005.
http://fs.mis.kuas.edu.tw/˜cobol/JCIS2005/papers/44.pdf
A9-c9 Wang X, Xu WJ, Zhang WG, et al., Weighted possibilistic variance of fuzzy number and its application
in portfolio theory, in: Fuzzy Systems and Knowledge Discovery, LECTURE NOTES IN ARTIFICIAL
INTELLIGENCE, vol. 3613, pp. 148-155. 2005
http://dx.doi.org/10.1007/11539506_18
Abstract. Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing
them as consonant random sets. Fullér and Majlender then proposed an weighted possibility mean
value, variance and covariance of fuzzy numbers, viewing them as weighted possibility distributions. In this paper, we define a new weighted possibilistic variance and covariance of fuzzy
numbers based on Fullér and Majlenders’ notations. We also consider the weighted possibilistic
mean-variance model of portfolio selection and introduce the notations of the weighted possibilistic efficient portfolio and efficient frontier. Moreover, a simple example is presented to show the
application of our results in security market. (page 148)
In 2003, Fullér and Majlender proposed an weighted possibility mean value of fuzzy numbers,
viewing them as weighted possibility distributions [A9]. Moreover, Zhang considered alternative
notations of the possibilistic variance and covariance of fuzzy numbers. In fact, Zhang’s notations
are the extension of Carlsson and Fullérs’ mean values and variances [A14]. In this paper, we
develop the notations of the weighted possibilistic variances and covariances of fuzzy numbers
based on Fullér and Majlenders’ notations in Section 2, and some properties of these notations
can be discussed in a similar manner as in probability theory. (page 148)
A9-c8 Zhang WG, Wang YL, Portfolio selection: Possibilistic mean-variance model and possibilistic efficient
frontier, in: Megiddo, N.; Xu, Y.; Alonstioti, N.; Zhu, B. (Eds.) Algorithmic Applications in Management
First International Conference, AAIM 2005, Xian, China, June 22-25, 2005, Proceedings Series: Lecture
Notes in Computer Science , Vol. 3521 Sublibrary: Information Systems and Applications, incl. Internet/Web, and HCI, Springer, [ISBN: 978-3-540-26224-4], 2005, pp. 203-213. 2005
http://dx.doi.org/10.1007/11496199_23
Fullér and Majlender [A9] defined the weighted possibilistic mean value of A as
Z 1
MfL (A) + MfU (A)
a(γ) + b(γ)
M̄f (A) =
f (γ)
dγ =
.
2
2
0
(page 204)
A9-c7 Zhang, J.-P., Li, S.-M. Portfolio selection with quadratic utility function under fuzzy environment, International Conference on Machine Learning and Cybernetics, ICMLC 2005, pp. 2529-2533. 2005
http://dx.doi.org/10.1109/ICMLC.2005.1527369
69
A9-c6 Blankenburg, B., Klusch, M. BSCA-F: Efficient fuzzy valued stable coalition forming among agents
Proceedings - 2005 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT’05,
2005, art. no. 1565632, pp. 732-738. 2005
http://dx.doi.org/10.1109/IAT.2005.48
2004
A9-c5 F. Augusto Alcaraz Garcia, Fuzzy real option valuation in a power station reengineering project Soft
Computing with Industrial Applications - Proceedings of the Sixth Biannual World Automation Congress,
June 28 - July 1, 2004, Seville, Spain, [ISBN 1-889335-21-5], vol. 17, pp. 281-287. 2004
http://ieeexplore.ieee.org/iel5/9827/30981/01439379.pdf?
A9-c4 Wang, X., Xu, W.-J., Zhang, W.-G. A class of weighted possibilistic mean-variance portfolio selection
problems Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 4, pp. 20362040. 2004
http://ieeexplore.ieee.org/iel5/9459/30104/01382130.pdf?arnumber=1382130
in books
A9-c2 Jiuping Xu and Xiaoyang Zhou, Fuzzy-Like Multiple Objective Decision Making, Studies in Fuzziness
and Soft Computing, Volume 263/2011, Springer, [ISBN 978-3-642-16894-9], 2011.
http://dx.doi.org/10.1007/978-3-642-16895-6
A9-c1 Elisabeth Rakus-Andersson, Fuzzy and Rough Techniques in Medical Diagnosis and Medication, Studies
in Fuzziness and Soft Computing series, vol. 212/2007, Springer, [ISBN 978-3-540-49707-3], 2007.
in Ph.D. dissertations
• Xiaolu Wang, Fuzzy Real Option Analysis in Patent Related Decision Making and Patent Valuation, Department of Information Technologies (TUCS), Åbo Akademi University, Åbo, Finland, [ISBN 978-952-123227-5]. 2015
http://urn.fi/URN:NBN:fi-fe2015061110218
• József Mezei, A quantitative view on fuzzy numbers, Department of Information Technologies (TUCS), Åbo
Akademi University, Åbo, Finland, [ISBN 978-952-12-2670-0]. 2011
http://www.doria.fi/handle/10024/72548
[A10] Robert Fullér and Péter Majlender, On obtaining minimal variability OWA operator weights, FUZZY SETS
AND SYSTEMS, 136(2003) 203-215. [MR1980864]. doi 10.1016/S0165-0114(02)00267-1
in journals
2016
A10-c235 Hong-Tao Yu, Shou-Hui Wang, Qing-Qing Ma, Link prediction algorithm based on the Choquet
fuzzy integral, INTELLIGENT DATA ANALYSIS, 20: (4) pp. 809-824. 2016
http://dx.doi.org/10.3233/IDA-160833
A10-c234 Zeng Shouzhen, An Extension of OWAD Operator and Its Application to Uncertain Multiple-Attribute
Group Decision-Making, CYBERNETICS AND SYSTEMS (to appear). 2016
http://dx.doi.org/10.1080/01969722.2016.1182362
A10-c233 Emad A Mohammed, Christopher T Naugler, Behrouz H Far, Breast Tumor Classification Using a
New OWA Operator, EXPERT SYSTEMS WITH APPLICATIONS, 6182016), pp. 302-313. 2016
http://dx.doi.org/10.1016/j.eswa.2016.05.037
70
Maximal entropy OWA weight vector (Fullér and Majlender, 2001) is one of the first methods
for obtaining the weight vector of an OWA, which selects the weight vector that maximizes the
entropy of the OWA operator; as it is based on the solution of a constrained optimization problem
that requires computational efforts to find the optimal weight. An extension of this method was
proposed to obtain minimal variability (Fullér and Majlender, 2003) OWA weighting vector for
any level of optimism.
A10-c232 R Amin Gholam, Hajjami Mohaddeseh, Application of Optimistic and Pessimistic OWA and DEA
Methods in Stock Selection, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS (to appear).
2016
http://dx.doi.org/10.1002/int.21824
A10-c231 Dug Hun Hong, A Note on Properties of the Continuous Weighted OWA Operator, APPLIED MATHEMATICAL SCIENCES, 10: (31) pp. 1537-1547. 2016
http://dx.doi.org/10.12988/ams.2016.6271
A10-c230 Kuei-Hu Chang, A novel reliability allocation approach using the OWA tree and soft set, ANNALS
OF OPERATIONS RESEARCH (to appear). 2016
http://dx.doi.org/10.1007/s10479-016-2178-4
The parametric OWA operator can grasp the subtle preferences of the decision-maker, based on
the context, by choosing between multiple aggregation results. The key issue in applying the OWA
operator for decision-making problems is determining their associated weights. O’Hagan (1988)
proposed the concept of maximum entropy to determine OWA operator weights with a given level
of orness. Wang and Parkan (2005) developed the minimax disparity approach to obtain OWA
operator weights by minimizing the maximum difference between any 2 adjacent weights. Fuller
and Majlender (2003) used the concept of minimum variance to determine OWA operator weights
with a given level of orness.
The key issue in implementing OWA operators is determining the OWA operator weights. Fuller
and Majlender (2003) used the concept of minimum variance for OWA operator weights under
a given level of orness. This approach is based on the solution of the following mathematical
programming model:
A10-c229 Ronald R Yager, Naif Alajlan, Some Issues on the OWA Aggregation with Importance Weighted
Arguments, KNOWLEDGE-BASED SYSTEMS, 100(2016), pp. 89-96. 2016
http://dx.doi.org/10.1016/j.knosys.2016.02.009
A10-c228 Gurbinder Kaur, Joydip Dhar, Rangan Kumar Guha, Minimal variability OWA operator combining
ANFIS and fuzzy c-means for forecasting BSE index, MATHEMATICS AND COMPUTERS IN SIMULATION, 122(2016), pp. 69-80. 2016
http://dx.doi.org/10.1016/j.matcom.2015.12.001
The OWA first introduced by Yager [35], has gained much interest among researchers. In recent years, many related studies have been conducted. Fuller and Majlender [A13] use Lagrange
multipliers to solve constrained optimization problem and determine the optimal weighing vector. Fuller and Majlender [A10], employ the Kuhn-Tucker second order sufficiency conditions to
optimize and derive OWA weights. (page 70)
2.1.2 Fuller and Majlender’s OWA
Fuller and Majlender [A10] transform Yager’s OWA equation to a polynomial equation by using
Kuhn-Tucker second order sufficiency conditions. According to their approach, the associated
weight vectors can be obtained as: (page 71)
A10-c227 Bin Zhu, Zeshui Xu, Ren Zhang, Mei Hong, Hesitant analytic hierarchy process, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 250(2016), pp. 602-614. 2016
http://dx.doi.org/10.1016/j.ejor.2015.09.063
Based on the attitudinal character, many models have been developed to determine the weights
(Fullér and Majlender, 2001, Fullér and Majlender, 2003, Liu, 2006, Liu and Chen, 2004, Liu and
Yu, 2012, Majlender, 2005 and O’Hagan, 1988). (page 608)
71
2015
A10-c226 Dug Hun Hong, A Note on Maximum Rényi Entropy OWA Problem, INTERNATIONAL JOURNAL
OF MATHEMATICAL ANALYSIS, 9: (51) pp. 2505-2511. 2015
http://dx.doi.org/10.12988/ijma.2015.58201
A number of approaches have been suggested for obtaining the associated weights, i.e., quantifier guided aggregation [6, 7], exponential smoothing [1] and learning [8]. Another approaches,
suggested by O?Hagan [3], determines a special class of OWA operators having maximal entropy
of the OWA weights for a given level of orness; algorithmically it is based on the solution of a
constrained optimization problem. Fullér and Majlender [2] presented a class of OWA operators
that have minimal variability OWA weights under any level of orness. Hong [4] provided a new
proof supporting the minimum variance problem. Recently, Majlender [5], based on the fundamental concept of parameteric entropy introduced by Rényi, extended and unify the former results
by presenting a special class of OWA operators having maximal Rényi entropy of the associated
weights for any level of compensation. (page 2506)
A10-c225 ZHU Bo, LINGJuanping, ZHONG Honghua, Chaotic Transport for Single Particle in Tilted Optical
Latice with Periodical Modulation Journal of Jishou University (Natural Science Edition), 36: (6) pp. 1539. (in Chinese). 2015
http://dx.doi.org/10.3969/j.cnki.jdxb.2015.06.004
A10-c224 Dug Hun Hong, The Least Absolute Deviation Problem for OWA Operator Weights, APPLIED
MATHEMATICAL SCIENCES, 9: (136), pp. 6767-6772. 2015
http://dx.doi.org/10.12988/ams.2015.59589
The ordered weighted averaging (OWA) operators were introduced by Yager [11] and have attracted much interest among researchers. An important issue in the theory of OWA operators
is the determination of the associated weights. The minimum variance problem was proposed by
Fullér and Majlender [A10], which minimizes the variance of OWA operator weights under a given
level of orness. Their method requires the solution of the following mathematical programming
model: (pages 6767-6768)
A10-c223 Ahmed El Bouri, Gholam R Amin, A combined OWA-DEA method for dispatching rule selection,
COMPUTERS AND INDUSTRIAL ENGINEERING, 88: pp. 470-478. 2015
http://dx.doi.org/10.1016/j.cie.2015.08.007
One important issue in the theory and application of OWA operators is the determina- tion of the
corresponding OWA weights. A number of methods have been introduced for generating the OWA
weights, see Fuller and Majlender (2003), Xu (2005), Wang and Parkan (2005), Emrouznejad and
Amin (2010), Amin and Emrouznejad (2011), and Liu (2012). (page 472)
A10-c222 Manish Aggarwal, On Learning of Weights through Preferences, INFORMATION SCIENCES,
321(2015), pp. 90-102. 2015
http://dx.doi.org/10.1016/j.ins.2015.05.034
A10-c221 G Tohidi, M Khodadadi, The OWA Weights of Improved Minimax Disparity Model, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 30: (7) pp. 781-797. 2015
http://dx.doi.org/10.1002/int.21711
A10-c220 Yao Ouyang, Improved minimax disparity model for obtaining OWA operator weights: Issue of
multiple solutions, INFORMATION SCIENCES, 320: pp. 101-106. 2015
http://dx.doi.org/10.1016/j.ins.2015.05.021
Fullér and Majlender [5] suggested a minimum variance approach, which requires to solve the
following constrained non-linear optimization problem: (page 102)
A10-c219 Jianhua Guo, The Private Enterprises’ Competitiveness Evaluation and Promoting Path Based on
Dynamic TOPSIS Method, ADVANCED MANAGEMENT SCIENCE, 4(2015), number 1, pp. 53-57.
2015
http://dx.doi.org/10.7508/ams.2015.01.010
72
A10-c218 Fang Liu, Yu-Fan Shang, Li-Hua Pan, A Modified TOPSIS Method for Obtaining the Associated
Weights of the OWA-Type Operators, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 30:
(10) pp. 1101-1116. 2015
http://dx.doi.org/10.1002/int.21737
A10-c217 Christophe Labreuche, Brice Mayag, Bertrand Duqueroie, Extension of the MACBETH approach to
elicit an ordered weighted average operator, EURO Journal on Decision Processes, 3: (1-2) pp. 65-105.
2015
http://dx.doi.org/10.1007/s40070-015-0041-5
A10-c216 Jie Cao, Xiaobing Yu, Zhifei Zhang, Integrating OWA and data mining for analyzing customers churn
in E-commerce, Journal of Systems Science and Complexity, 28(215), number 2, pp. 381-392. 2015
http://dx.doi.org/10.1007/s11424-015-3268-0
A10-c215 Jianwei Gao, Ming Li, Huihui Liu, Generalized ordered weighted utility proportional averaginghyperbolic absolute risk aversion operators and their applications to group decision-making, Applied Mathematics and Computation, 252(2015), pp. 114-132. 2015
http://dx.doi.org/10.1016/j.amc.2014.12.009
A10-c214 Jianwei Gao, Ming Li, Huihui Liu, Generalized ordered weighted utility averaging-Hyperbolic Absolute Risk Aversion operators and their applications to group decision-making, European Journal of Operational Research, 243(2015), number 1, pp. 258-270. 2015
http://dx.doi.org/10.1016/j.ejor.2014.11.039
Fullér and Majlender (2003a) provided a minimum variance method, which demands the solution
of the following quadratic programming problem for minimizing the variance of the OWA operator
weights under a given orness measure: (page 264)
A10-c213 Danielle Morais, Adiel Teixeira de Almeida, Luciana Hazin, Tharcylla R N Clemente, Ceres Cavalcanti, PROMETHEE - ROC MODEL FOR ASSESSING THE READNESS OF TECHNOLOGY FOR
GENERATING ENERGY, Mathematical Problems in Engineering, Paper 530615. 11 p. 2015
http://downloads.hindawi.com/journals/mpe/aip/530615.pdf
A10-c212 Dipti Dubey, Suresh Chandra, Aparna Mehra, Computing a Pareto-optimal solution for multi-objective
flexible linear programming in a bipolar framework, International Journal of General Systems, 44(2015),
number 4, pp. 457-470. 2015
http://dx.doi.org/10.1080/03081079.2014.969253
A10-c211 Milad Moradi, Mahmoud Reza Delavar, Behzad Moshiri, A GIS-based multi-criteria decision-making
approach for seismic vulnerability assessment using quantifier-guided OWA operator: a case study of
Tehran, Iran, Annals of GIS (to appear). 2015
http://dx.doi.org/10.1080/19475683.2014.966858
A10-c210 Yu-lin He, James N K Liu, Yan-xing Hu, Xi-zhao Wang, OWA Operator Based Link Prediction
Ensemble for Social Network, EXPERT SYSTEMS WITH APPLICATIONS, 42(2015), pp. 21-50. 2015
http://dx.doi.org/10.1016/j.eswa.2014.07.018
Fuller and Majlender’s minimum variance method (MVM) [A10] is to solve the following mathematical programming model (page 29).
A10-c209 Nassim Ammour, Naif Alajlan, A dynamic weights OWA fusion for ensemble clustering, SIGNAL,
IMAGE AND VIDEO PROCESSING, 9: (3) pp. 727-734. 2015
http://dx.doi.org/10.1007/s11760-013-0499-1
Fuller and Majlender [A10] suggested the minimum variance for OWA operator determination.
(page 730)
2014
A10-c208 Li Qiang, Niu Wensheng, A Direct Trust Aggregation Algorithm Based on the Minimum Variance
Time Sequence Weight, The Open Cybernetics & Systemics Journal 8(2014), pp. 349-356. 2014
http://dx.doi.org/10.2174/1874110X01408010349
73
In order to make the weight sequence {w(k)} (k = 1, 2, ..., h) more effective, it uses the minimum
variance model to determine the weight vector time sequence [A10] to determine the weight vector
of time sequence {w(k)} (k = 1, 2, ..., h), and gain the weight of minimum variance of time
sequence [20]. (page 351)
A10-c207 Belles-Sampera J, Merigo JM, Guillen M, Santolino M, Indicators for the characterization of discrete
Choquet integrals, INFORMATION SCIENCES, 267(2014), pp. 201-216. 2014
http://dx.doi.org/10.1016/j.ins.2014.01.047
Initially, Yager [41] introduced the orness/andness indicators and the entropy of dispersion for just
this purpose. Later, he proposed complementary indicators, including the balance indicator [42]
and the divergence [44], to be used in exceptional situations. Meanwhile, Fullér and Majlender
[A10] suggested the use of a variance indicator and Majlender [21] introduced the Rényi entropy
[32] as a generalization of the Shannon entropy [33] in the framework of the OWA operator. (page
202)
A10-c206 Ali Emrouznejad, Marianna Marra, Ordered Weighted Averaging Operators 1988?2014: A CitationBased Literature Survey, International Journal of Intelligent Systems, 29(12014), number 11, pp. 994-1014.
2014
http://dx.doi.org/10.1002/int.21673
A10-c205 Huchang Liao, Zeshui Xu, Jiuping Xu, An approach to hesitant fuzzy multi-stage multi-criterion
decision making, Kybernetes, 43(2014), number 9/10. Paper K-11-2013-0246. 2014
http://dx.doi.org/10.1108/K-11-2013-0246
A10-c204 Liu Xiaojun, The study of history aging model in network trust evaluation, Journal of Chemical and
Pharmaceutical Research, 6(2014, number 9, pp. 449-455. 2014
http://jocpr.com/vol6-iss9-2014/JCPR-2014-6-9-449-455.pdf
A10-c203 Bazi Y, Alajlan N, Melgani F, AlHichri H, Yager R, Robust Estimation of Water Chlorophyll Concentrations With Gaussian Process Regression and IOWA Aggregation Operators, IEEE Journal of Selected
Topics in Applied Earth Observations and Remote Sensing, 7(2014), number 7. Article 2327003. 2014
http://dx.doi.org/10.1109/JSTARS.2014.2327003
With the application of OWA operator and more specifically the IOWA operator in various areas, the determination of the associated weight parameters became an active topic of research
in recent years. Numerous approaches have been suggested for obtaining these weights such as
argument-based methods, optimization methods, sample learning methods, and function-based
methods [29]-[A10]. In this paper, we propose three different approaches for obtaining these
weights. In the first approach, we investigate the minimum variance optimization method which
minimizes the variance of the weights under a given fixed level of orness [A10].
A10-c202 Osman Mohammadpour, Yousef Hassanzadeh, Ahmad Khodadadi, Bahram Saghafian, Selecting
the Best Flood Flow Frequency Model Using Multi-Criteria Group Decision-Making, Water Resources
Management (to appear). 2014
http://dx.doi.org/10.1007/s11269-014-0720-1
Different methods of OWA weight generation have been proposed (Liu 2011). One major methodology is the optimization method. Two well-known methods, maximum entropy and minimum
variance, use a constraint nonlinear optimization problem with a predefined degree of orness as
constraint and entropy and variability OWA operator weights as the objective functions. The minimal variability OWA operator weights are defined as (Fuller and Majlender 2003):
A10-c201 Giuseppe De Marco, Jacqueline Morgan, On Ordered Weighted Averaging Social Optima, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 160(2014), issue 2, pp. 623-635. 2014
http://dx.doi.org/10.1007/s10957-013-0376-7
A10-c200 Wei Zhou, Jian Min He, Interval-valued intuitionistic fuzzy ordered precise weighted aggregation
operator and its application in group decision making, Technological and Economic Development of Economy, 20(2014), number 4, pp. 648-672. 2014
http://dx.doi.org/10.3846/20294913.2013.869516
74
Other approaches include the genetic algorithm weighted method (Nettleton, Torra 2001), the
minimum variance weighted method (Fuller, Majlender 2003), the parametric geometric weighted
method (Liu, Chen 2004), the mini-max disparity weighted method (Wang, Parkan 2005), the
maximal Renyi entropy weighted method (Majlender 2005), the preemptive goal programming
weighted method (Wang, Parkan 2007), the deviation entropy weight method (Han, Liu 2011),
and the distance measure weighted method (Yue 2011).
A10-c199 Gholam R Amin, Sujeet Kumar Sharma, Measuring batting parameters in cricket: A two-stage
regression-OWA method MEASUREMENT, 53(2014), pp. 56-61. 2014
http://dx.doi.org/10.1016/j.measurement.2014.03.029
A number of methods have been introduced for generating of the OWA weights, Fuller and Majlender (2003), Xu (2005), Wang and Parkan (2005), Emrouznejad and Amin (2010). Wang and
Parkan (2005) introduced the first linear programming (LP) model, minimax disparity model, to
determine the OWA weights. (page 58)
A10-c198 K. Guo, Quantifiers Induced by Subjective Expected Value of Sample Information, IEEE Transactions on Cybernetics (to appear). 2014
http://dx.doi.org/10.1109/TCYB.2013.2295316
A10-c197 Xiuzhi Sang, Xinwang Liu, Lianghua Chen, Parametric Weighting Function for WOWA Operator
and Its Application in Decision Making, International Journal of Intelligent Systems, 29(2014), number 2,
pp. 119-136. 2013
http://dx.doi.org/10.1002/int.21629
A10-c196 W Zhou, Two Atanassov intuitionistic fuzzy weighted aggregation operators based on a novel weighted
method and their application, Journal of Intelligent and Fuzzy System, 26: (4) pp. 1787-1798. 2014
http://dx.doi.org/10.3233/IFS-130858
A10-c195 Byeong Seok Ahn, Ronald R Yager, The use of ordered weighted averaging method for decision
making under uncertainty, International Transactions in Operational Research, Volume 21, Issue 2, pages
247262, March 2014
http://dx.doi.org/10.1111/itor.12042
A10-c194 Ahn Byeong Seok, Developing Group Ordered Weighted Averaging Operator Weights for Group
Decision Support, Group Decision and Negotiation, 23: (5) pp. 1127-1143. 2014
http://dx.doi.org/10.1007/s10726-013-9366-2
To start with, the proposed method determines, without solving any linear or nonlinear program,
a group’s OWA operator weights for either multiple certain or uncertain attitudinal characters by
using extreme points due to the theories developed in the paper. This is more evident when considering a programming-based approach which employs diverse complicated objective functions,
linear (e.g., minimax disparity) or nonlinear (e.g., maximum entropy, minimal variability, maximal Renyi entropy, least square method, or chi-square method) while consistently maintaining
the attitudinal character constraint (Ahn 2008; Filev and Yager 1995; Fuller and Majlender 2003;
O’Hagan 1990; Majlender 2005; Wang and Parkan 2005; Wang et al. 2007). (page 1128)
2013
A10-c193 S. Charles and L. Arockiam, Fuzzy Weighted Gaussian Mixture Model for Feature Reduction, International Journal of Computer Applications, 64(2013), number 18, pp. 9-15. 2013
http://cirworld.com/index.php/ijct/article/view/1170/0
A Minimum variance method is adopted for finding the minimum variability weights of the variables identified by this approach [A10]. (page 11)
A10-c192 AlHichri Haikel, Bazi Yakoub, Alajlan Naif, Melgani Farid, Malek Salim, Yager Ronald R, A novel
fusion approach based on induced ordered weighted averaging operators for chemometric data analysis,
Journal of Chemometrics, 27(2013), number 12, pp. 447-456. 2013
http://dx.doi.org/10.1002/cem.2557
75
A10-c191 Sang Xiuzhi, Liu Xinwang, An analytic approach to obtain the least square deviation OWA operator
weights, Fuzzy Sets and Systems, 240(2014), pp. 103-116. 2014
http://dx.doi.org/10.1016/j.fss.2013.08.007
A10-c190 Feng-Mei Ma, Ya-Jun Guo, Determination of the Attitudinal Character by Self-Evaluation for the
Maximum Entropy OWA Approach, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 28(2013),
number 11, pp. 1089-1098. 2013
http://dx.doi.org/10.1002/int.21618
A10-c189 Ronald R Yager, Naif Alajlan, On characterizing features of OWA aggregation operators, Fuzzy
Optimization and Decision Making (to appear). 2013
http://dx.doi.org/10.1007/s10700-013-9167-8
A10-c188 Xiuzhi Sang, Xinwang Liu, Parametric extension of the most preferred OWA operator and its application in search engine’s rank, JOURNAL OF APPLIED MATHEMATICS (to appear). 2013
http://downloads.hindawi.com/journals/jam/aip/273758.pdf
A10-c187 M. Rahmanimanesh and S. Jalili, ADAPTIVE ORDERED WEIGHTED AVERAGING FOR ANOMALY
DETECTION IN CLUSTER-BASED MOBILE AD HOC NETWORKS, Iranian Journal of Fuzzy Systems,
10(2013), number 2, pp. 83-109. 2013
http://www.sid.ir/en/VEWSSID/J_pdf/90820130206.pdf
A10-c186 Hu-Chen Liu, Ling-Xiang Mao, Zhi-Ying Zhang, Ping Li, Induced aggregation operators in the
VIKOR method and its application in material selection, APPLIED MATHEMATICAL MODELLING,
37(2013), issue 9, pp. 6325-6338. 2013
http://dx.doi.org/10.1016/j.apm.2013.01.026
A10-c185 Mohammad Amir Rahmani, Mahdi Zarghami, A New Approach to Combine Climate Change projections by Ordered Weighting Averaging Operator; Applications to Northwestern Provinces of Iran, GLOBAL
AND PLANETARY CHANGE, 102(2013), pp. 41-50. 2013
http://dx.doi.org/10.1016/j.gloplacha.2013.01.007
A10-c184 Qingxing Dong, Yajun Guo, Multiperiod multiattribute decision-making method based on trend incentive coefficient, INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, 20(2013),
number 1, pp. 141-152. 2013
http://dx.doi.org/10.1111/j.1475-3995.2012.00853.x
2012
A10-c183 Xu ZS, A Survey and Prospects of OWA Aggregation with Intuitionistic Fuzzy Information, INFORMATIONAN INTERNATIONAL INTERDISCIPLINARY JOURNAL, 15(2012), number 11B, pp. 4763-4776. 2012
WOS:000311066500005
A10-c182 Ahn BS, Programming-based OWA operator weights with quadratic objective function, IEEE Transactions on Fuzzy Systems, 20(2012), number 5, pp. 986-992. Paper 6220246. 2012
http://dx.doi.org/10.1109/TFUZZ.2012.2205155
A10-c181 Feng-Mei Ma, Ya-Jun Guo, Ping-Tao Yi, Cluster-reliability-induced OWA operators, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 27(2012), number 9, pp. 823-8367. 2012
http://dx.doi.org/10.1002/int.21549
A10-c180 Wang Y, Ren L, Sun Z, Novel dynamic TOPSIS method in evaluation for quality of medical care
Journal of Central South University (Medical Sciences) 37(2012), number 10, pp. 1071-1076 (in Chinese).
2012
http://dx.doi.org/10.3969/j.issn.1672-7347.2012.10.018
A10-c179 P. N. Smith, Applications of intuitionistic fuzzy set aggregation operators in transport multi-factor
project evaluation TRANSPORTATION PLANNING AND TECHNOLOGY, 35(2012), issue 4, pp. 427447. 2012
http://dx.doi.org/10.1080/03081060.2012.680815
76
A10-c178 Feng-Mei Ma, Ya-Jun Guo, Xiang Shan, Analysis of the impact of attitudinal character on the multicriteria decision making with OWA operators, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 27(2012), number 5, pp. 502-518. 2012
http://dx.doi.org/10.1002/int.21533
A10-c177 Cuiping Wei, Xijin Tang, Generalized prioritized aggregation operators, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 27(2012), number 6, pp. 578-589. 2012
http://dx.doi.org/10.1002/int.21537
A10-c176 Dug Hun Hong, The relationship between the maximum entropy and minimax ratio RIM quantifier
problems, FUZZY SETS AND SYSTEMS, 202(2012), pp. 110-117. 2012
http://dx.doi.org/10.1016/j.fss.2012.01.014
A10-c175 Chang K -H, Chang Y -C, Wen T -C, Cheng C -H, An innovative approach integrating 2-tuple and
lowga operators in process failure mode and effects analysis, INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING, INFORMATION AND CONTROL, 8(2012), number 1B, pp. 747-761. 2012
Scopus: 84856948976
A10-c174 Xinwang Liu, Models to determine parameterized ordered weighted averaging operators using optimization criteria, INFORMATION SCIENCES, 190(2012), pp. 27-55. 2012
http://dx.doi.org/10.1016/j.ins.2011.12.007
In addition to the MEOWA operator, Fullér and Majlender [A10] formulated a minimal variability OWA operator problem in quadratic programming and gave an analytical solution. Liu [24]
proposed an OWA operator generation method using the equidifferent OWA operator, which is an
extension of the work in [A10]. (page 28)
A10-c173 Xinwang Liu, Shui Yu, On the Stress Function-Based OWA Determination Method With Optimization Criteria, IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS,
42(2012), number 1, pp. 246-257. 2012
http://dx.doi.org/10.1109/TSMCB.2011.2162233
A10-c172 M Teresa Lamata, E Cables Pérez, Obtaining OWA operators starting from a linear order and preference quantifiers INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 27(2012), number 3, pp.
242-258. 2012
http://dx.doi.org/10.1002/int.21520
A10-c171 M. Q. Suo, Y. P. Li, G. H. Huang, Multicriteria decision making under uncertainty: An advanced ordered weighted averaging operator for planning electric power systems, ENGINEERING APPLICATIONS
OF ARTIFICIAL INTELLIGENCE, 25(2012), number 1, pp. 72-81. 2012
http://dx.doi.org/10.1016/j.engappai.2011.08.007
In order to obtain a unique weighting vector for optimization, the Kuhn?Tucker second-order
sufficiency conditions can be used for solving the above model (Fullér and Majlender, 2003), and
the results can be formulated as follows: (page 73)
2011
A10-c170 Alvydas Balezentis, Tomas Balezentis, A Novel Method for Group Multi-attribute Decision Making with Two-tuple Linguistic Computing: Supplier Evaluation under Uncertainty, JOURNAL OF ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, 4(2011),
pp. 5-30. 2011
http://www.ecocyb.ase.ro/nr4%20eng/Alvydas%20Balezentis.pdf
A10-c169 Yanbing Gong, A combination approach for obtaining the minimize disparity OWA operator weights,
FUZZY OPTIMIZATION AND DECISION MAKING,10(2011), number 4, pp. 311-321. 2011
http://dx.doi.org/10.1007/s10700-011-9107-4
77
Fullér and Majlender (2003) proposed a minimum variance method, which minimizes the variance
of OWA operator weights under a given level of orness. Their method requires the solution of the
following mathematical programming model: (page 314)
A10-c168 Zhi-xin Su, Ming-yuan Chen, Guo-ping Xia, Li Wang, An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making, EXPERT SYSTEMS WITH APPLICATIONS, t 38(2011),
issue 12, pp. 15286-15295. 2011
http://dx.doi.org/10.1016/j.eswa.2011.06.022
A10-c167 Dug Hun Hong, The relationship between the minimum variance and minimax disparity rim quantifier problems, FUZZY SETS AND SYSTEMS, 181(2011), number 1, pp. 50-57. 2011
http://dx.doi.org/10.1016/j.fss.2011.05.014
A10-c166 Feng-Mei Ma, Ya-Jun Guo, Density-Induced Ordered Weighted Averaging Operators, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 26(2011), issue 9, pp. 866-886. 2011
http://dx.doi.org/10.1002/int.20500
A10-c165 Efendi Nasibov, Cagin Kandemir-Cavas, OWA-based linkage method in hierarchical clustering: Application on phylogenetic trees, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), number 10, pp.
12684-12690. 2011
http://dx.doi.org/10.1016/j.eswa.2011.04.055
A10-c164 Byeong Seok Ahn, Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 212(2011),
pp. 552-559. 2011
http://dx.doi.org/10.1016/j.ejor.2011.02.017
Fuller and Majlender (2003) first presented the minimal variability objective function instead of
the entropy in (9). (page 555)
A10-c163 Dug Hun Hong, On proving the extended minimax disparity OWA problem, FUZZY SETS AND
SYSTEMS, 168(2011), issue 1, pp. 35-46. 2011
http://dx.doi.org/10.1016/j.fss.2010.08.008
A10-c162 Xiaoyong Li, Feng Zhou, Xudong Yang, A multi-dimensional trust evaluation model for large-scale
P2P computing, JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING, 71(2011), issue 6, 837847. 2011
http://dx.doi.org/10.1016/j.jpdc.2011.01.007
2010
A10-c161 X. Liu, The relationships between two variability and orness optimization problems for OWA operator
with RIM quantifier extensions, INTERNATIONAL JOURNAL OF UNCERTAINTY, FUZZINESS AND
KNOWLEDGE-BASED SYSTEMS, 18: (5) 515-538. 2010
http://dx.doi.org/10.1142/S0218488510006684
Apart from the researches on the MEOWA operator, Fullér and Majlender [A10] suggested a
minimum variance approach to obtain the minimal variability OWA operator weighting vector of
a fixed orness level with a quadratic programming problem. An analytical method to obtain the
optimal solution was proposed. (page 516)
A10-c160 Byeong Seok Ahn, Parameterized OWA operator weights: An extreme point approach, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 51(2010), pp. 820-831. 2010
http://dx.doi.org/10.1016/j.ijar.2010.05.002
A10-c159 Byeong Seok Ahn, A priori identification of preferred alternatives of OWA operators by relational
analysis of arguments, INFORMATION SCIENCES, 180(2010), Issue 23, pp. 4572-4581. 2010
http://dx.doi.org/10.1016/j.ins.2010.08.010
A10-c158 Ronald R. Yager, Including a diversity criterion in decision making, INTERNATIONAL JOURNAL
OF INTELLIGENT SYSTEMS, 25(2010), pp. 958-969. 2010
http://dx.doi.org/10.1002/int.20426
78
Here, we draw upon the results provided in Refs. 5 and A10 to suggest some alternative formulation for the measure of diversity. (page 963)
A10-c157 R. A. Nasibova; E. N. Nasibov, Linear Aggregation with Weighted Ranking, AUTOMATIC CONTROL AND COMPUTER SCIENCES, 44(2010), Number 2, pp. 96-102. 2010
http://dx.doi.org/10.3103/S0146411610020057
A10-c156 Y.-J. Guo; H.-Y. Tang; D.-G. Qu, Dynamic comprehensive evaluation method and its application
based on minimal variability, SYSTEMS ENGINEERING AND ELECTRONICS, 32(2010), issue 6, pp.
1225-1228 (in Chinese). 2010
http://dx.doi.org/10.3969/j.issn.1001-506X.2010.06.025
A10-c155 Qiong Pei Zheng; Yi Liang Zhong; Wei Dongmei; Kong Mingming, Attribute Relative Reduction of
Set-valued Information Systems Based on λ-Approximations, FUZZY SYSTEMS AND MATHEMATICS,
6(2010) (in Chinese). 2010.
http://d.wanfangdata.com.cn/periodical_mhxtysx201006023.aspx
2009
A10-c154 Jian Wu, Bo-Liang Sun, Chang-Yong Liang, Shan-Lin Yang, A linear programming model for determining ordered weighted averaging operator weights with maximal Yager’s entropy, COMPUTERS &
INDUSTRIAL ENGINEERING, Volume 57, Issue 3, October 2009, pp. 742-747. 2009
http://dx.doi.org/10.1016/j.cie.2009.02.001
Fullér and Majlender (2003) suggested a minimum variance approach, which minimizes the variance of OWA operator weights under a given level of orness. A set of OWA operator weights with
minimal variability could then be generated. Their approach requires the solution of the following
mathematical programming problem: (page 743)
A10-c153 Byeong Seok Ahn, Some remarks on the LSOWA approach for obtaining OWA operator weights,
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Volume 24 Issue 12, Pages 1265-1279.
2009
http://dx.doi.org/10.1002/int.20384
Fullér and Majlender [A10] presented a method of deriving the minimal variability weighting vector for any level of orness, using Kuhn-Tucker second-order sufficiency conditions for optimality.
Although the minimum variance approach generates the OWA operator weights in an analytical
way, it still needs to partition the unit interval (0, 1) into a number of subintervals in order to judge
which subinterval the given orness value lies in. (page 1268)
A10-c152 S. Zadrozny, J. Kacprzyk, Issues in the practical use of the OWA operators in fuzzy querying, JOURNAL OF INTELLIGENT INFORMATION SYSTEMS, 33(2009), No. 3, pp. 307-325. 2009
http://dx.doi.org/10.1007/s10844-008-0068-1
A10-c151 Zeshui Xu, Multi-period multi-attribute group decision-making under linguistic assessments, INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 38(2009), Issue 8, pp. 823-850. 2009
http://dx.doi.org/10.1080/03081070903257920
A10-c150 Yu Yi, Thomas Fober, Eyke Hüllermeier, Fuzzy Operator Trees for Modeling Rating Functions, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE AND APPLICATIONS, 8(2009),
pp. 423-428. 2009
http://dx.doi.org/10.1142/S1469026809002679
The issue of model selection and parameter estimation has been addressed, though, for simpler
types of decision models, especially for models using a single aggregation operator. For example,
the problem of fitting parameters on the basis of exemplary outputs has been studied for weighted
mean and OWA operators, [7,29] the WOWA (weighted OWA) operator, [30] the Choquet integral,
[18,31] and the Sugeno integral. [14] Besides, attempts have been made to identify the parameters
of such models using other types of information, such as the so-called ”orness” or degree of
disjunction [A10, A13] as well as preferences and order relations. [4,19] (page 426)
79
A10-c149 E. Cables Pérez, M.Teresa Lamata, OWA weights determination by means of linear functions,
MATHWARE & SOFT COMPUTING, 16(2009), 107-122. 2009
http://ic.ugr.es/Mathware/index.php/Mathware/article/view/398/pdf-16-2-art1-final
A10-c148 R.R. Yager, On the dispersion measure of OWA operators, INFORMATION SCIENCES, 179(2009),
pp. 3908-3919. 2009
http://dx.doi.org/10.1016/j.ins.2009.07.015
An additional variation on the approach suggested by O’Hagan is to consider alternative measures
of dispersion, a pioneering development in this direction was the work of Fuller and Majlender
[A10]. (page 3909)
A10-c147 Ronald R. Yager, Weighted Maximum Entropy OWA Aggregation With Applications to Decision
Making Under Risk, IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICSPART A:
SYSTEMS AND HUMANS, VOL. 39, NO. 3, pp. 555-564. 2009
http://dx.doi.org/10.1109/TSMCA.2009.2014535
A10-c146 S.-M. Chen, C.-H. Wang, A generalized model for prioritized multicriteria decision making systems,
EXPERT SYSTEMS WITH APPLICATIONS, Volume 36, Issue 3 PART 1, April 2009, pp. 4773-478.
2009
http://dx.doi.org/10.1016/j.eswa.2008.06.021
A10-c145 X. Liu, Parameterized defuzzification with continuous weighted quasi-arithmetic means - An extension, INFORMATION SCIENCES, 179(2009), pp. 1193-1206. 2009
http://dx.doi.org/10.1016/j.ins.2008.12.005
A10-c144 B.S. Ahn, H. Park, An efficient pruning method for decision alternatives of OWA operators, IEEE
TRANSACTIONS ON FUZZY SYSTEMS, 16 (2009), pp. 1542-1549. 2009
http://dx.doi.org/10.1109/TFUZZ.2008.2005012
A10-c143 Jos M. Merigó, and Anna M. Gil-Lafuente OWA Operators in Generalized Distances, INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE, 5(2009) pp. 11-18.
2009
http://www.waset.org/ijamcs/v5/v5-1-3.pdf
A10-c142 S.-J. Chuu, Group decision-making model using fuzzy multiple attributes analysis for the evaluation
of advanced manufacturing technology, FUZZY SETS AND SYSTEMS, 160(2009) pp. 586-602. 2009
http://dx.doi.org/10.1016/j.fss.2008.07.015
2008
A10-c141 Jos M. Merigó, and Anna M. Gil-Lafuente, On the Use of the OWA Operator in the Euclidean
Distance, INTERNATIONAL JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, 2(2008) pp.
170-176. 2008
http://www.waset.org/ijcse/v2/v2-4-31.pdf
A10-c140 Ronald R. Yager, Time Series Smoothing and OWA Aggregation, IEEE TRANSACTIONS ON
FUZZY SYSTEMS, 16(2008) pp. 994-1007. 2008
http://dx.doi.org/10.1109/TFUZZ.2008.917299
A10-c139 Ali Emrouznejad, MP-OWA: The most preferred OWA operator, KNOWLEDGE-BASED SYSTEMS,21 (2008), pp. 847-851. 2008
http://dx.doi.org/10.1016/j.knosys.2008.03.057
The minimax disparity approach was also extended by Amin and Emrouznejad [1] and Amin [2].
It is observed that most of the above methods produce regular weight distributions, which vary either in the form of exponential (geometric progression) or in the form of arithmetical progression.
For example, the maximum entropy weights vary in the form of exponential, while the minimal
variability weights [A10] and the minimax disparity weights vary in the form of equidistance. Although regular weight distributions make sense, there is no reason to believe that OWA operator
weights can vary regularly [12].
80
A10-c138 Xinwang Liu A general model of parameterized OWA aggregation with given orness level INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, vol. 48, pp. 598-627. 2008
http://dx.doi.org/10.1016/j.ijar.2007.11.003
Liu and Chen [31] proposed general forms of the MEOWA operator with a parametric geometric
approach, and discussed its aggregation properties. Apart from maximum entropy OWA operator,
Fullér and Majlender [A10] suggested the minimal variability OWA operator problem in quadratic
programming, and proposed an analytical method for solving it. (page 599)
A10-c137 M Zarghami, R Ardakanian, A Memariani, F. Szidarovszky, Extended OWA Operator for Group
Decision Making on Water Resources Projects, JOURNAL OF WATER RESOURCES PLANNING AND
MANAGEMENT-ASCE, Volume 134, Issue 3, pp. 266-275. 2008
http://dx.doi.org/10.1061/(ASCE)0733-9496(2008)134:3(266)
A10-c136 M. Zarghami, F. Szidarovszky, R. Ardakanian, Sensitivity Analysis of the OWA Operator IEEE
TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS, vol. 38(2008),
pp. 547-552. 2008
http://dx.doi.org/10.1109/TSMCB.2007.912745
A10-c135 Mahdi Zarghami, Ferenc Szidarovszky Fuzzy quantifiers in sensitivity analysis of OWA operator
COMPUTERS & INDUSTRIAL ENGINEERING, vol. 54(2008), pp.1006-1018. 2008
http://dx.doi.org/10.1016/j.cie.2007.11.012
A10-c134 Byeong Seok Ahn, Some Quantier Functions From Weighting Functions With Constant Value of Orness, IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART B: CYBERNETICS,
38(2008), pp. 540-546. 2008
http://dx.doi.org/10.1109/TSMCB.2007.912743
A10-c133 Xinwang Liu and Shilian Han, Orness and parameterized RIM quantifier aggregation with OWA operators: A summary, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, Volume 48(2008),
Issue 1, Pages 77-97. 2008
http://dx.doi.org/10.1016/j.ijar.2007.05.006
A10-c132 Ronald R. Yager, A knowledge-based approach to adversarial decision making, INTERNATIONAL
JOURNAL OF INTELLIGENT SYSTEMS, Volume 23(2008), Issue 1, pp. 1-21. 2008
http://dx.doi.org/10.1002/int.20254
A10-c131 R.R. Yager, Prioritized aggregation operators, INTERNATIONAL JOURNAL OF APPROXIMATE
REASONING, Volume 48(2008), Issue 1, April 2008, Pages 263-274. 2008
http://dx.doi.org/10.1016/j.ijar.2007.08.009
A10-c130 B.S. Ahn, H. Park, Least-squared ordered weighted averaging operator weights, INTERNATIONAL
JOURNAL OF INTELLIGENT SYSTEMS, 23(2008), pp. 33-49. 2008
http://dx.doi.org/10.1002/int.20257
A10-c129 B.S. Ahn, Preference relation approach for obtaining OWA operators weights, INTERNATIONAL
JOURNAL OF APPROXIMATE REASONING, 47(2008), pp. 166-178. 2008
http://dx.doi.org/10.1016/j.ijar.2007.04.001
Instead of maximizing the degree of dispersion, Fullér and Majlender A10] presented a method
for deriving the minimal variability weighting vector for any level of orness, using Kuhn-Tucker
second-order sufficiency conditions for optimality. (page 167)
A10-c128 LU Zhen-bang; ZHOU Li-hua, Probabilistic Fuzzy Cognitive Maps Based on Ordered Weighted
Averaging Operators, COMPUTER SCIENCE, 35(2008), number 12, pp. 187-189 (in Chinese). 2008
http://d.wanfangdata.com.cn/Periodical_jsjkx200812049.aspx
2007
81
A10-c127 D.H. Hong and K.T. Kim, A note on the maximum entropy weighting function problem, JOURNAL
OF APPLIED MATHEMATICS AND COMPUTING, 23(2007), No. 1-2, pp. 547-552. 2007
http://www.mathnet.or.kr/mathnet/thesis_file/DHHong0613F.pdf
A10-c126 Zhenbang Lv and Lihua Zhou, Advanced Fuzzy Cognitive Maps Based on OWA Aggregation, INTERNATIONAL JOURNAL OF COMPUTATIONAL COGNITION, 5(2007) pp. 31-34. 2007
http://www.yangsky.com/ijcc/pdf/ijcc524.pdf
A10-c125 Xinwang Liu, Hongwei Lou, On the equivalence of some approaches to the OWA operator and RIM
quantier determination, FUZZY SETS AND SYSTEMS, vol. 159(2007), pp. 1673-1688. 2007
http://dx.doi.org/10.1016/j.fss.2007.12.024
The idea of OWA operator with variance was proposed by Yager [24]. Fullér and Majlender [A10]
proposed the problem of minimum variance OWA operator. (page 1678)
A10-c124 X. Liu, Some OWA operator weights determination methods with RIM quantifier, Journal of Southeast University (English Edition), vol. 23 (SUPPL.), pp. 76-82. 2007
A10-c123 B.S. Ahn, The OWA aggregation with uncertain descriptions on weights and input arguments, IEEE
TRANSACTIONS ON FUZZY SYSTEMS, 15(2007), pp. 1130-1134. 2007
http://dx.doi.org/10.1109/TFUZZ.2007.895945
A10-c122 L. Zhenbang, Z. Lihua, A hybrid fuzzy cognitive model based on weighted OWA operators and
single-antecedent rules, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 22(2007), pp.
1189-1196. 2007
http://dx.doi.org/10.1002/int.20243
A10-c121 Xinwang Liu and Hsinyi Lin, Parameterized approximation of fuzzy number with minimum variance
weighting functions, MATHEMATICAL AND COMPUTER MODELLING, 46 (2007) 1398-1409. 2007
http://dx.doi.org/10.1016/j.mcm.2007.01.011
The problem of getting the minimum variance OWA weighting vector was proposed by Fullér and
Majlender [A10] to get minimum variance OWA weighting vector with a given orness level. (page
1400)
A10-c120 Llamazares, B., Choosing OWA operator weights in the field of Social Choice, INFORMATION
SCIENCES, 177 (21), pp. 4745-4756. 2007
http://dx.doi.org/10.1016/j.ins.2007.05.015
To avoid the resolution of a nonlinear optimization problem, Yager [32] introduces a simpler
procedure that tries to keep the spirit of maximizing the entropy for a given level of orness. Similar
approaches (through a fixed orness level) have also been proposed by Fullér and Majlender [A10],
(page 4746)
A10-c119 Leon, T., Zuccarello, P., Ayala, G., de Ves, E., Domingo, J., Applying logistic regression to relevance
feedback in image retrieval systems, PATTERN RECOGNITION, 40 (10), pp. 2621-2632. 2007
http://dx.doi.org/10.1016/j.patcog.2007.02.002
A10-c118 Wang, Y.-M., Luo, Y., Hua, Z., Aggregating preference rankings using OWA operator weights, INFORMATION SCIENCES, 177 (16), pp. 3356-3363. 2007
http://dx.doi.org/10.1016/j.ins.2007.01.008
The minimum variance method proposed by Fullér and Majlender [A10], which minimizes the
variance of OWA operator weights under a given level of orness and requires the solution of the
following mathematical programming model: (page 3358)
A10-c117 Amin, G.R., Notes on properties of the OWA weights determination model, COMPUTERS & INDUSTRIAL ENGINEERING, 52 (4), pp. 533-538. 2007
http://dx.doi.org/10.1016/j.cie.2007.03.002
82
An important issue related to the theory and application of OWA operators is the determination of
the weights of the operators, (Amin & Emrouznejad, 2006; Fullér & Majlender, 2003; O’Hagan,
1988; Wang & Parkan, 2005). (page 533)
A10-c116 Liu, X., The solution equivalence of minimax disparity and minimum variance problems for OWA
operators, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 45 (1), pp. 68-81. 2007
http://dx.doi.org/10.1016/j.ijar.2006.06.004
Apart from MEOWA operator, Fullér and Majlender [A10] suggested a minimum variance approach to obtain the minimal variability OWA weighting vector under given orness level with a
quadratic programming problem. They also proposed an analytical method to get the optimal
solution. (page 69)
In this section, we will prove the MSEOWA operator is the optimal solution of the minimum
variance problem for OWA operator which was proposed by Fullér and Majlender [A10]. (page
73)
Fullér and Majlender [A10] proposed an analytical approach for (23) by dividing (0, 1] into 2n − 1
subintervals to decide which subinterval the given level of orness lies in. The MSEOWA weighting
vector generating method can be seen as an alternative expression of the unique optimal solution,
with the parameters being expressed directly. (page 75)
A10-c115 Wang YM, Parkan C, A preemptive goal programming method for aggregating OWA operator weights
in group decision making, INFORMATION SCIENCES, 177 (8): 1867-1877 APR 15 2007
http://dx.doi.org/10.1016/j.ins.2006.07.023
Other approaches include Nettleton and Torra’s [7] genetic algorithm (GA), Fullér and Majlender’s
[A10] minimum variance method, which produces minimum variability OWA operator weights,
and Liu and Chen’s [5] parametric geometric method, which could be used to obtain maximum
entropy weights. (page 1868)
Other approaches Fullér and Majlender [A10] suggested a minimum variance approach, which
minimizes the variance of OWA operator weights under a given degree of orness. A set of OWA
operator weights with minimal variability could then be generated. (page 1869)
A10-c114 Wang YM, Luo Y, Liu XW, Two new models for determining OWA operator weights, COMPUTERS
& INDUSTRIAL ENGINEERING, 52 (2): 203-209 MAR 2007
http://dx.doi.org/10.1016/j.cie.2006.12.002
Fullér and Majlender (2003) also suggested a minimum variance method to obtain the minimal
variability OWA operator weights. (page 203)
A10-c113 Wu J, Liang CY, Huang YQ An argument-dependent approach to determining OWA operator weights
based on the rule of maximum entropy INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 22
(2): 209-221 FEB 2007
http://doi.wiley.com/10.1002/int.20201
2006
A10-c112 D.H. Hong, A note on the minimal variability OWA operator weights, INTERNATIONAL JOURNAL
OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 14 (6): 747-752 DEC 2006
http://dx.doi.org/10.1142/S0218488506004308
One important issue in the theory of ordered weighted averaging (OWA) operators is the determination of the associated weighting vector. Recently, Fuller and Majlender derived the minimal
variability weighting vector for any level of orness using the Kuhn-Tucker second-order sufficiency conditions for optimality. In this note, we give a new proof of the problem. (page 747)
Another approach, suggested by O’Hagan , determines a special class of OWA operators having
maximal entropy of the OWA weights for a given level of orness; algorithmically it is based on
83
the solution of a constrained optimization problem. Recently, to obtain minimal variability OWA
weights under given level of orness, Fuller and Majlender mathematical programming problem
minimize
subject to
n n
1 X
1 X
1 2
1
D (W ) = ·
= ·
wi −
w2 − 2
n i=1
n
n i=1 i
n
2
orness(w) =
n
X
n−i
· wi = α, 0 ≤ α ≤ 1,
n−1
i=1
w1 + · · · + wn = 1, 0 ≤ wi , i = 1, . . . , n.
where E(W ) = (w1 + · · · wn )/n stands for the arithmetic mean of weights. And they solved
problem (1) analytically and derived the exact minimal variability OWA weights for any level of
orness using the Kuhn-Tucker second-order sufficiency conditions for optimality. In this note, we
give a new method deriving the exact minimal variability OWA weights for the problem (1). (page
748)
In this note, we introduced a new method of deriving the main result of Fuller and Majlender
concerning obtaining minimal variability OWA operator weights. (page 752)
A10-c111 Liu XW An orness measure for quasi-arithmetic means, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 14 (6): 837-848 DEC 2006
http://dx.doi.org/10.1109/TFUZZ.2006.879990
Among these, one class is the ordered weighted averaging (OWA) operator, which was proposed
by Yager [10] has attracted much interest of researchers. Many extensions and applications have
been proposed [11]-[14]. One of the appealing points in OWA operator is the concept of orness
[10]. The orness measure reects the and-like or or-like aggregation result of an OWA operator,
which is very important both in theory and in applications [15]-[A10]. (page 837)
A10-c110 Liu XW, Lou HW Parameterized additive neat OWA operators with different orness levels, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 21 (10): 1045-1072 OCT 2006
http://doi.wiley.com/10.1002/int.20176
The idea of getting the minimum variance weighting vector was proposed by Yager. [38] Then
it was applied to the OWA operator by Fullér and Majlender [A10] to get the minimum variance
OWA weighting vector with a given orness level. (pages 1061-1062)
A10-c109 Liu, X. Reply to ”Comments on the paper: On the properties of equidifferent OWA operator”, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 43 (1), pp. 113-115. 2006
http://dx.doi.org/10.1016/j.ijar.2006.02.004
A10-c108 Liu XW On the properties of equidifferent OWA operator, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 43 (1): 90-107 SEP 2006
http://dx.doi.org/10.1016/j.ijar.2005.11.003
First, we will prove the equivalence of MSEOWA operator and the minimum variance OWA operator proposed by Fullér and Majlender [A10]. (page 96)
A10-c107 Amin GR, Emrouznejad A, An extended minimax disparity to determine the OWA operator weights,
COMPUTERS & INDUSTRIAL ENGINEERING, 50 (3): 312-316 JUL 2006
http://dx.doi.org/10.1016/j.cie.2006.06.006
An important issue related to the theory and application of OWA operators is the determination of
the weights of the operators (Fullér & Majlender, 2003; O’Hagan, 1988; Wang & Parkan, 2005).
(page 312)
A10-c106 Ahn BS On the properties of OWA operator weights functions with constant level of orness, IEEE
TRANSACTIONS ON FUZZY SYSTEMS, 14 (4): 511-515 AUG 2006
http://dx.doi.org/10.1109/TFUZZ.2006.876741
84
It is clear that the actual results of aggregation performed by the OWA operators depend on the
forms of the weighting vectors, which play a key role in the aggregation process. Filev and Yager
[3] presented a way of obtaining the weights associated with the OWA aggregation in a situation in
which data on the arguments and the aggregated value have been observed (see [2], [A13], [A10],
and [7] for the methods of determining the OWA weights). (page 511)
A10-c105 Marchant T Maximal orness weights with a fixed variability for owa operators, INTERNATIONAL
JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 14 (3): 271-276
JUN 2006
http://dx.doi.org/10.1142/S021848850600400X
Anyone willing to use the ordered weighted average operator (OWA) must at some point choose
a weight vector. Several approaches exist for this. For instance, [5] suggested that, in some cases,
it might be interesting to choose the weight vector maximizing the entropy of the operator while
guaranteeing some predetermined orness. He also proposed a technique achieving this goal. [1]
studied the same problem. [A13] followed the same approach and suggested a different algorithm
for the maximal entropy weight vector given a fixed orness. Since entropy is not the only possible
measure for the variability, [A10] presented an algorithm for finding the minimal-variance weight
vector given a fixed orness. (page 271)
A10-c104 Liu XW, Some properties of the weighted OWA operator, IEEE TRANSACTIONS ON SYSTEMS
MAN AND CYBERNETICS PART B - CYBERNETICS, 36(1): 118-127 FEB 2006
http://dx.doi.org/10.1109/TSMCA.2005.854496
A10-c103 Smith PN, Flexible aggregation in multiple attribute decision making: Application to the Kuranda
Range Road upgrade, CYBERNETICS AND SYSTEMS, 37(1): 1-22 JAN-FEB 2006
2005
A10-c102 Liu XW, On the properties of equidifferent RIM quantifier with generating function, INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 34 (5): 579-594 OCT 2005
http://dx.doi.org/10.1080/00268970500067880
From the discussion above, we can see that, the generating function f (x) in the RIM fuzzy quantifier Q plays the role of weights vector W in OWA operator. A kind of OWA operator is the
minimum variance OWA operator that was proposed by Fullér and Majlender (2003), which was
based on the idea of Yager (1995). (page 589)
A10-c101 Ying-Ming Wang, Celik Parkan, A minimax disparity approach for obtaining OWA operator weights,
INFORMATION SCIENCES, 175(2005) 20-29. 2005
http://dx.doi.org/10.1016/j.ins.2004.09.003
Fullér and Majlender [A10] suggested a minimum variance approach, which minimizes the variance of OWA operator weights under a given level of orness. A set of OWA operator weights with
minimal variability could then be generated. Their approach requires the solution of the following
mathematical programming problem:
n n
1 2
1 X 2
1
1 X
2
wi −
= ·
wi − 2
minimize D (W ) = ·
n i=1
n
n i=1
n
subject to
orness(w) =
n
X
n−i
· wi = α, 0 ≤ α ≤ 1,
n−1
i=1
w1 + · · · + wn = 1, 0 ≤ wi , i = 1, . . . , n.
(page 23)
A10-c100 P.N. Smith, Andness-directed weighted averaging operators: Possibilities for environmental project
evaluation, JOURNAL OF ENVIRONMENTAL SYSTEMS, 30(2003), pp. 333-348. 2003
http://dx.doi.org/10.2190/18H8-9362-3363-3120
85
in proceedings and edited volumes
2016
A10-c47 Chuan-yang Ruan, Jian-hui Yang, Li-na Han, Jing Duan, Ruo-bing Liu, Hesitant Fuzzy Prioritized
Hybrid Average Operator and Its Application to Multiple Attribute Decision Making, In: Bing-Yuan Cao,
Pei-Zhuang Wang, Zeng-Liang Liu, Yu-Bin Zhong eds.; International Conference on Oriental Thinking and
Fuzzy Logic: Celebration of the 50th Anniversary in the era of Complex Systems and Big Data, Advances
in Intelligent Systems and Computing, vol. 443/2016, Springer, 2016. (ISBN 978-3-319-30873-9), pp.
227-234. 2016
http://dx.doi.org/10.1007/978-3-319-30874-6 22
A10-c46 Ronald R Yager, Diversity Measures for Smart Cities, In: Towards Cognitive Cities, Studies in Systems, Decision and Control, vol. 63, Springer, 2016. (ISBN 978-3-319-33797-5) pp. 197-209. 2016
http://dx.doi.org/10.1007/978-3-319-33798-2 10
A10-c45 Gozde Ulutagay, Efendi Nasibov, C × K-Nearest Neighbor Classification with Ordered Weighted
Averaging Distance, In: Mincho Hadjiski, Nikola Kasabov, Dimitar Filev, Vladimir Jotsov eds., Novel
Applications of Intelligent Systems, Studies in Computational Intelligence, vol. 586, Springer, (ISBN 9783-319-14193-0), pp. 105-122. 2016
http://dx.doi.org/10.1007/978-3-319-14194-7 6
2015
A10-c44 Li Zhiwei, Yang Xiyang, To Obtain the OWA Weighting Vector Via Normal Distribution Function,
PROCEEDINGS OF THE 2015 INTERNATIONAL CONFERENCE ON EDUCATION TECHNOLOGY
AND ECONOMIC MANAGEMENT, 39: (Beijing), (ISBN 978-94-6252-122-3), pp. 1478-1481. 2015
WOS: 000371807800377
A10-c43 Ouyang Y, A note on weights vector of ordered weighted averaging aggregation, In: Tang Z, Du J,
Yin S, Li R, He L eds., 12th International Conference on Fuzzy Systems and Knowledge Discovery, FSKD
2015. Institute of Electrical and Electronics Engineers Inc., (ISBN 9781467376822) pp. 971-975. Paper
7382075. 2015
http://dx.doi.org/10.1109/FSKD.2015.7382075
A10-c42 Mikael Collan, Pasi Luukka, Strategic R&D Project Analysis: Keeping It Simple and Smart, In:
Mikael Collan, Mario Fedrizzi, Janusz Kacprzyk eds., Fuzzy Technology: Present Applications and Future
Challenges, Studies in Fuzziness and Soft Computing, vol. 335, Springer, (ISBN 978-3-319-26984-9) pp.
169-191. 2015
http://dx.doi.org/10.1007/978-3-319-26986-3 10
A10-c41 Luqiong Xie, Xuemei Jiang, Wenjun Xu, Qin Wei, Ruifang Li, Zude Zhou, Dynamic Assessment of
Sustainable Manufacturing Capability for CNC Machining Systems in Cloud Manufacturing, In: Shigeki
Umeda, Masaru Nakano, Hajime Mizuyama, Hironori Hibino, Dimitris Kiritsis, Gregor von Cieminski eds.,
Advances in Production Management Systems: Innovative Production Management Towards Sustainable
Growth. (IFIP Advances in Information and Communication Technology, vol. 460, Springer, 2015. (ISBN
978-3-319-22758-0) pp. 396-403. 2015
http://dx.doi.org/10.1007/978-3-319-22759-7_46
A10-c40 Wlodzimierz Ogryczak, Jaroslaw Hurkala, Determining OWA Operator Weights by Maximum Deviation Minimization, In: Pattern Recognition and Machine Intelligence, Lecture Notes in Computer Science,
vol. 9124, Springer, (ISBN 978-3-319-19940-5, pp. 335-344. 2015
http://dx.doi.org/10.1007/978-3-319-19941-2_32
2013
86
A10-c37 Belles-Sampera Jaume, Merigo Jose M, Santolino Miguel, Some New Definitions of Indicators for
the Choquet Integral, ADVANCES IN INTELLIGENT SYSTEMS AND COMPUTING, 228: (Pamplona),
(ISBN 978-3-642-39164-4), pp. 467-476. 2013
http://dx.doi.org/10.1007/978-3-642-39165-1 44
A10-c36 M Moradi, M R Delavar, B Moshiri, SENSITIVITY ANALYSIS OF ORDERED WEIGHTED AVERAGING OPERATOR IN EARTHQUAKE VULNERABILITY ASSESSMENT, H Arefi, M A Sharifi,
P Reinartz, M R Delavar eds., Sensors and Models in Photogrammetry and Remote Sensing, October 5-8,
2013, Tehran, Iran, pp. 277-282. 2013
http://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/
XL-1-W3/277/2013/isprsarchives-XL-1-W3-277-2013.pdf
2011
A10-c35 Jian Wu, Qing-Wei Cao, An OWA Operator Based Approach to Aggregate Group Opinion by Similarity Degree, 2011 Fourth International Conference on Business Intelligence and Financial Engineering,
Wuhan, China, [ISBN: 978-0-7695-4527-1], pp. 665-667. 2011
http://dx.doi.org/10.1109/BIFE.2011.13
A10-c34 Xinwang Liu, Analytical solution for symmetrical OWA operator determination with given medianness
level Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), July 26-28,
2011, Shanghai, China, [ISBN: 978-1-61284-180-9], pp. 77-81. 2011
http://dx.doi.org/10.1109/FSKD.2011.6019523
A10-c33 M Brunelli, M Fedrizzi, M Fedrizzi, OWA-Based Fuzzy m-ary Adjacency Relations in Social Network Analysis, in: Ronald R Yager, Janusz Kacprzyk, Gleb Beliakov eds., Recent Developments in the
Ordered Weighted Averaging Operators: Theory and Practice, Studies in Fuzziness and Soft Computing,
vol. 265/2011, Springer, [ISBN: 978-3-642-17909-9], pp. 255-267. 2011
http://dx.doi.org/10.1007/978-3-642-17910-5_13
A10-c32 Xinwang Liu, A Review of the OWA Determination Methods: Classification and Some Extensions,
in: Ronald R Yager, Janusz Kacprzyk, Gleb Beliakov eds., Recent Developments in the Ordered Weighted
Averaging Operators: Theory and Practice. Studies in Fuzziness and Soft Computing, vol. 265/2011,
Springer, [ISBN 978-3-642-17909-9], pp. 49-90. 2011
http://dx.doi.org/10.1007/978-3-642-17910-5_4
2010
A10-c31 Byeong Seok Ahn, Determining OWA operator weights from ordinal relation on criteria, 2010 IEEE
International Conference on Systems Man and Cybernetics (SMC). October 10-13, 2010, [ISBN 978-14244-6586-6], pp. 3290-3293. 2010
http://dx.doi.org/10.1109/ICSMC.2010.5642320
The programming-based approach is one of the most widely used approaches for the acquisition
of OWA operator weights. Specifically, the MEOWA [1, 2], the minimal variability [A10], the
least-squared OWA (LSOWA) [4] and minimax disparity [5] approaches all fall into this category, showing a common feature that the mathematical programs are formulated subject to the
attitudinal character constraint. (pages 3290-3291)
A10-c30 Gleb Beliakov, Optimization and Aggregation Functions, in: Weldon A Lodwick, Janusz Kacprzyk
eds., Fuzzy Optimization: Recent Advances and Applications, Studies in Fuzziness and Soft Computing
vol. 254/2010, Springer [ISBN 978-3-642-13934-5], pp. 77-108. 2010
http://dx.doi.org/10.1007/978-3-642-13935-2_4
2009
87
A10-c29 X. Liu, On the methods of OWA operator determination with different dimensional instantiations, 6th
International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2009, 14-16 August 2009,
Tianjin, China, Volume 7, [ISBN 978-076953735-1], Article number 5359982, pp. 200-204. 2009
http://dx.doi.org/10.1109/FSKD.2009.312
A10-c28 G.R. Amin; A. Emrouznejad, Determining more realistic OWA weights, 6th International Conference
on Fuzzy Systems and Knowledge Discovery, FSKD 2009, 14-16 August 2009, Tianjin, China, Volume 7,
[ISBN 978-076953735-1], Article number 5359978, pp. 181-185. 2009
http://dx.doi.org/10.1109/FSKD.2009.771
A10-c27 B.S. Ahn, Generation of OWA operator weights based on extreme point approach, 6th International
Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2009, 14-16 August 2009, Tianjin, China,
Volume 7, [ISBN 978-076953735-1], Article number 5359981, pp. 196-199. 2009
http://dx.doi.org/10.1109/FSKD.2009.711
A10-c26 Matteo Brunelli, Michele Fedrizzi, A Fuzzy Approach to Social Network Analysis, Social Network
Analysis and Mining, International Conference on Advances in Social Network Analysis and Mining,
Athens, Greece, July 20-July 22, [ISBN 978-0-7695-3689-7] pp. 225-230. 2009
http://doi.ieeecomputersociety.org/10.1109/ASONAM.2009.72
A10-c25 B. Fonooni; S. Moghadam, Applying induced aggregation operator in designing intelligent monitoring
system for financial market, IEEE Symposium on Computational Intelligence for Financial Engineering,
March 30, 2009 - April 2, 2009, Nashville, TN, [ISBN 978-1-4244-2774-1], pp. 80-84. 2009
http://dx.doi.org/10.1109/CIFER.2009.4937506
A10-c24 Benjamin Fonooni, Seied Javad Mousavi Moghadam, Automated trading based on uncertain OWA
in financial markets, in: Proceedings of the 10th WSEAS international conference on Mathematics and
computers in business and economics, Prague, Czech Republic, pp. 21-25. 2009
2008
A10-c23 Ronald R. Yager, Lexicographically Prioritized Multi-criteria Decisions Using Scoring Function, in:
L. Magdalena, M. Ojeda-Aciego, J.L. Verdegay eds., Proceedings of IPMU’08, June 22-27, 2008, Torremolinos, Spain, pp. 1438-1445. 2008
http://www.gimac.uma.es/ipmu08/proceedings/papers/191-Yager.pdf
A10-c22 K.-M. Björk, Obtaining minimum variability OWA operators under a fuzzy level of orness, ICINCO
2008 - Proceedings of the 5th International Conference on Informatics in Control, Automation and Robotics
ICSO, Volume ICSO, pp. 114-119. 2008
A10-c21 Xinwang Liu; Xiaoguang Yang; Yong Fang, The relationships between two kinds of OWA operator
determination methods, IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2008), 1-6 June
2008, pp. 264-270. 2008
http://dx.doi.org/10.1109/FUZZY.2008.4630375
Apart from maximum entropy OWA operator, Fullér and Majlender [A10] suggested the minimal
variability OWA operator problem in quadratic programming, and proposed an analytical method
of it. Liu [11] gave this OWA operator generating method with the equidifferent OWA operator,
and discussed its properties. (page 264)
A10-c20 B. Fonooni; S. J. Moghadam, Designing financial market intelligent monitoring system based on OWA,
in: Proceedings of the WSEAS international Conference on Applied Computing Conference (Istanbul,
Turkey, May 27 - 30, 2008). M. Demiralp, W. B. Mikhael, A. A. Caballero, N. Abatzoglou, M. N. Tabrizi,
R. Leandre, M. I. Garcia-Planas, and R. S. Choras, Eds. Mathematics And Computers In Science And
Engineering. World Scientific and Engineering Academy and Society (WSEAS), Stevens Point, Wisconsin,
pp. 35-39. 2008
A10-c19 B. Llamazares, J.L. Garcia-Lapresta, Extension of some voting systems to the field of gradual preferences, in: Bustince, Humberto; Herrera, Francisco; Montero, Javier (Eds.) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer Vision Series: Studies in Fuzziness and Soft Computing, Vol. 220,
Springer, [ISBN: 978-3-540-73722-3] 2008, pp. 297-315. 2008
88
http://dx.doi.org/10.1007/978-3-540-73723-0_15
2007
A10-c18 Ronald R. Yager, Enabling agents to perform prioritized multi-criteria aggregation AAAI Spring Symposium, March 26-28, 2007, Stanford, USA, pp. 85-90. 2007
http://www.aaai.org/Papers/Symposia/Spring/2007/SS-07-02/SS07-02-012.pdf
A10-c17 P. Zuccarello, E. De Ves, T. Leon, G. Ayala, J. Domingo, A novel relevance feedback procedure based
on logistic regression and OWA operator for content-based image retrieval system, VISAPP 2007 - 2nd
International Conference on Computer Vision Theory and Applications, 8 - 11 March, 2007, Barcelona,
Spain, Proceedings IU (MTSV/-), pp. 167-172. 2007
A10-c16 Benjamin Fonooni, Rational-Emotional Agent Decision Making Algorithm Design with OWA, 19th
IEEE International Conference on Tools with Artificial Intelligence, October 29-October 31, Paris, France,
2007, pp. 63-66. 2007
http://doi.ieeecomputersociety.org/10.1109/ICTAI.2007.123
A10-c15 Min, Dai; Xu-rui, Zhai; Yun-xiang, Chen, A Note on OWA Operator Based on the Normal Distribution,
International Conference on Management Science and Engineering (ICMSE 2007), pp. 537-542. 2007
http://dx.doi.org/10.1109/ICMSE.2007.4421902
A10-c14 Benjamin Fonooni, Behzad Moshiri and Caro Lucas, Applying Data Fusion in a Rational Decision
Making with Emotional Regulation, in: 50 Years of Artificial Intelligence, Essays Dedicated to the 50th
Anniversary of Artificial Intelligence, Lecture Notes in Computer Science, Volume 4850/2007, Springer,
2007, pp. 320-331. 2007
http://dx.doi.org/10.1007/978-3-540-77296-5_29
A10-c13 M.Zarghaami, R. Ardakanian, R., F. Szidarovszky, Sensitivity analysis of an information fusion tool:
OWA operator in: Belur V. Dasarathy ed., Proceedings of SPIE - The International Society for Optical Engineering 6571, Multisensor, Multisource Information Fusion: Architectures, Algorithms, and Applications
2007, art. no. 65710P, 2007
http://dx.doi.org/10.1117/12.722323
A10-c12 Felix, R., Efficient decision making with interactions between goals, Proceedings of the 2007 IEEE
Symposium on Computational Intelligence in Multicriteria Decision Making, MCDM 2007, April 1-5,
2007, Honolulu, [ISBN 1-4244-0702-8 ], art. no. 4223007, pp. 221-226. 2007
http://dx.doi.org/10.1109/MCDM.2007.369441
A10-c11 M.Zarghaami, R. Ardakanian, R., F. Szidarovszky, Obtaining robust decisions under uncertainty by
sensitivity analysis on OWA operator, Proceedings of the 2007 IEEE Symposium on Computational Intelligence in Multicriteria Decision Making, MCDM 2007, art. no. 4223017, pp. 280-287. 2007
http://dx.doi.org/10.1109/MCDM.2007.369102
2006
A10-c10 Zadrozny S, Kacprzyk J On tuning OWA operators in a flexible querying interface, In: Flexible Query
Answering Systems, 7th International Conference, FQAS 2006, LECTURE NOTES IN COMPUTER SCIENCE, vol. 4027, pp. 97-108. 2006
http://dx.doi.org/10.1007/11766254_9
Fullér and Majlender considered also the variance of an OWA operator defined as:
Pm
i=1 wi
w
−
m
m
i
X
1X 2
1
m
=
wi − 2
var(OW ) =
m
m
m
i=1
i=1
Then they proposed [A10] a class of OWA operators analogous to MEOWA (14) where the variance instead of dispersion is maximized. Also in this case Fullér and Majlender developed analytical formulae for the weight vector W . (page 101)
89
in books
A10-c3 G Beliakov, H Bustince Sola, T Calvo Sánchez, A Practical Guide to Averaging Functions, Studies in
Fuzziness and Soft Computing, vol. 329, Springer, (ISBN 978-3-319-24751-9). 2016
http://dx.doi.org/10.1007/978-3-319-24753-3
A10-c2 Beliakov, G., Pradera, A., Calvo, T., Aggregation Functions: A Guide for Practitioners, Studies in
Fuzziness and Soft Computing, Vol. 221(2007), [ISBN 978-3-540-73720-9], Springer. 2007
http://dx.doi.org/ 10.1007/978-3-540-73721-6_7
Another popular characteristic of weighting vector is weights variance, defined as [A10] (page 79)
A10-c1 Z. Xu, Linguistic Decision Making: Theory and Methods, Springer,[ISBN 978-3-642-29439-6]. 2013
http://www.springer.com/mathematics/applications/book/978-3-642-29439-6
in Ph.D. dissertations
• Olivier Thonnard, A multi-criteria clustering approach to support attack attribution in cyberspace, Télécommunications
et électronique de Paris, France. 2010
https://pastel.archives-ouvertes.fr/pastel-00006003
Fullér and Majlender proposed also in [57] to optimize another popular characteristic of weighting
vector, namely the weights variance, which is defined by (page 82)
[A11] Christer Carlsson and Robert Fullér, A position paper on agenda for soft decision analysis, FUZZY SETS
AND SYSTEMS, 131(2002) 3-11. [Zbl.1010.90029] [MR1920825]. doi 10.1016/S0165-0114(01)00250-0
in journals
A11-c13 Wenfeng Xie, Junhai Ma, Optimization of a Vendor Managed Inventory Supply Chain Based on Complex Fuzzy Control Theory, WSEAS TRANSACTIONS on SYSTEMS 13: pp. 429-439. 2014
http://www.wseas.org/multimedia/journals/systems/2014/e105702-448.pdf
A11-c12 Marle Franck, Gidel Thierry, A multicriteria decisionmaking process for project risk management
method selection, International Journal of Multicriteria Decision Making, 2(2012), number 2, pp. 189-223.
2012
http://dx.doi.org/10.1504/IJMCDM.2012.046948
A11-c11 Mahdi Ghane, Mohammad Jafar Tarokh, Multi-objective design of fuzzy logic controller in supply
chain, Journal of Industrial Engineering International, 8(2012), number 1, pp. 10-17. 2012
http://dx.doi.org/10.1186/2251-712X-8-10
A11-c10 Yohanes Kristianto, Petri Helo, Jianxin (Roger) Jiao, Maqsood Sandhu, Adaptive fuzzy vendor managed inventory control for mitigating the Bullwhip effect in supply chains, EUROPEAN JOURNAL OF
OPERATIONAL RESEARCH, 216(2012), issue 2, pp. 346-355. 2012
http://dx.doi.org/10.1016/j.ejor.2011.07.051
A11-c9 Franck Marle; Julie Le Cardinal, Risk assessment method in project actor choice, INTERNATIONAL
JOURNAL OF PRODUCT DEVELOPMENT, 12(2010), number 1, pp. 21-48. 2010
http://dx.doi.org/10.1504/IJPD.2010.034311
A11-c8 Hakan Tozan, Ozalp Vayvay, A HYBRID FUZZY TIME SERIES AND ANFIS APPROACH TO DEMAND VARIABILITY IN SUPPLY CHAIN NETWORKS, JOURNAL OF NAVAL SCIENCE AND ENGINEERING, 5(2009), pp. 20-34. 2009
www.dho.edu.tr/ENSTITUNet/dergi/MAKALE_AGUSTOS_2009/02_hakan_tozan.pdf
A11-c7 S. Balan, Prem Vrat, Pradeep Kumar, Information distortion in a supply chain and its mitigation using
soft computing approach, OMEGA, 37(2009) 282-299. 2009
http://dx.doi.org/10.1016/j.omega.2007.01.004
90
Carlsson and Fullér [21] sorted out the complexities of bullwhip by using fuzzy numbers in the
bullwhip models. (page 283)
A11-c6 S. Balan, P. Vrat, P. Kumar, Reducing the Bullwhip effect in a supply chain with fuzzy logic approach,
INTERNATIONAL JOURNAL OF INTEGRATED SUPPLY MANAGEMENT, 3 (2007), number 3, pp.
261-282. 2007
http://dx.doi.org/10.1504/IJISM.2007.012630
A11-c5 Neeraj Sharma, S. Balan, Prem Vrat, Pradeep Kumar, Analysis of bullwhip effect in reverse supply
chain, JOURNAL OF ADVANCES IN MANAGEMENT RESEARCH, 3(2006), issue 2, pp 18-33. 2006
http://dx.doi.org/10.1108/97279810680001243
A11-c4 O’Donnell, T., Maguire, L., McIvor, R., Humphreys, P. Minimizing the bullwhip effect in a supply
chain using genetic algorithms, INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, 44 (8),
pp. 1523-1543. 2006
http://dx.doi.org/10.1080/00207540500431347
in proceedings and edited volumes
A11-c2 Hakan Tozan, Ozalp Vayvay, A Hybrid Fuzzy Approach to Bullwhip Effect in Supply Chain Networks,
in: Pengzhong Li ed., Supply Chain Management, InTech, 2011, [ISBN: 978-953-307-184-8], pp. 49-72.
2011
http://www.intechopen.com/download/pdf/pdfs_id/15531
Since pioneer work of Zadeh (1965) ”Fuzzy Sets” in which FL was introduced many studies
have been done related to this brilliant subject. Though studies about FL are extremely high, its
application to SC N and especially to BWE is narrow. The first application of FL approach to
BWE topic; due to our knowledge, appears with the works of Carlsson & Fuller (1999, 2001,
2002, 2004). (page 56)
A11-c1 T O’Donnell, L Maguire, R McIvor, P Humphreys, Using GAs to minimise the bullwhip effect in a
supply chain, 8th Joint Conference on Information Sciences, July 21.-26, 2005, Salt Lake City, USA, pp.
988-991. 2005
[A12] Christer Carlsson, Robert Fullér and Péter Majlender, A possibilistic approach to selecting portfolios with
highest utility score, FUZZY SETS AND SYSTEMS, 131(2002) 13-21. [MR1920826]. doi 10.1016/S01650114(01)00251-2
in journals
2016
A12-c206 Raluca Vernic, Optimal investment with a constraint on ruin for a fuzzy discrete-time insurance risk
model, FUZZY OPTIMIZATION AND DECISION MAKING, 15: (2) pp. 195-217. 2016
http://dx.doi.org/10.1007/s10700-015-9221-9
A12-c205 I-Fei Chen, Ruey-Chyn Tsaur, Fuzzy Portfolio Selection Using a Weighted Function of Possibilistic
Mean and Variance in Business Cycles, INTERNATIONAL JOURNAL OF FUZZY SYSTEMS, 18(2016),
issue 2, pp. 151-159. 2016
http://dx.doi.org/10.1007/s40815-015-0073-9
A12-c204 Nataliia V Tkachenko, Olena V Shabanova, METHODICAL FRAMEWORK DEVELOPMENT
FOR RATING OF NON-STATE PENSION FUNDS BY THEIR INVESTMENT POTENTIAL LEVEL,
ACTUAL PROBLEMS OF ECONOMICS, 176(2016), pp. 450-458 (in Ukrainian). 2016
A12-c203 Abel Rubio, Jose D Bermudez, Enriqueta Vercher, Forecasting portfolio returns using weighted fuzzy
time series, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 75(2016), pp. 1-12. 2016
http://dx.doi.org/10.1016/j.ijar.2016.03.007
91
A12-c202 Oktay Tas, Cengiz Kahraman and Celal Barkan Güran, A Scenario Based Linear Fuzzy Approach
in Portfolio Selection Problem: Application in the ?stanbul Stock Exchange, JOURNAL OF MULTIPLEVALUED LOGIC AND SOFT COMPUTING, 26(2016), number 3-5, pp. 269-294. 2016
A12-c201 Andreas Lundell, Kaj-Mikael Björk, Global optimisation of a portfolio adjustment problem under
credibility measures, INTERNATIONAL JOURNAL OF OPERATIONAL RESEARCH, Volume 25, Issue
4, 2016, Pages 464-474. 2016
http://dx.doi.org/10.1504/IJOR.2016.075292
A12-c200 Ye Wang, Yanju Chen, Yan K Liu, Modeling Portfolio Optimization Problem by Probability-Credibility
Equilibrium Risk Criterion, MATHEMATICAL PROBLEMS IN ENGINEERING (to appear). 2016
http://downloads.hindawi.com/journals/mpe/aip/9461021.pdf
Inuiguchi and Ramik [15] exemplified the advantages and disadvantages of fuzzy mathematical programming approaches in the setting of an optimal portfolio selection problem. When the
returns of assets are taken as trapezoidal fuzzy numbers, a possibilistic approach for selecting
portfolios with the highest utility value was introduced by Carlsson et al. [A12]. Considering
transaction costs, Fang et al. [17] proposed a portfolio rebalancing model based on fuzzy decision
theory. (page 3)
A12-c199 Mikael Collan, Mario Fedrizzi, Pasi Luukka, Possibilistic risk aversion in group decisions: theory
with application in the insurance of giga-investments valued through the fuzzy pay-off method, APPLIED
SOFT COMPUTING (to appear). 2016
http://dx.doi.org/10.1007/s00500-016-2069-2
To determine the possibilistic risk premiums we will use the notions of possibilistic expected value
and possibilistic variance, as introduced by Carlsson and Fullér (2001), Carlsson et al. (2002) and
Fullér and Majlender (2003).
A12-c198 Yong-Jun Liu, Wei-Guo Zhang, Qun Zhang, Credibilistic multi-period portfolio optimization model
with bankruptcy control and affine recourse APPLIED SOFT COMPUTING, Volume 38, pp. 890-906.
2016
http://dx.doi.org10.1016/j.asoc.2015.09.023
Most of literatures were formulated on the basis of probability theory. Though probability theory
is one of the main tools for handling the uncertainty in finance, it cannot describe uncertainty
completely since there exist many non-probabilistic factors in financial markets such as economic,
social, political and people’s psychological factors, etc. Thus, the fuzzy uncertainty associated
with financial markets cannot be neglected. With the widely use of fuzzy set theory in Zadeh
[56], more and more researchers have realized that they could use fuzzy set theory to handle the
fuzziness, vagueness or ambiguity in financial markets such as Alimi et al. [1], Ghaffari-Nasab
et al [16] and Gharakhani and Sadjadi [17]. Actually, fuzzy portfolio selection problem was
researched from 1990s. Based on possibility theory, numerous portfolio selection models had
been proposed, e.g., Carlsson et al. [A12], Deng and Li [12], Tanaka and Guo [47] and Zhang et
al. [58]. (page 891)
2015
A12-c197 Jirakom Sirisrisakulchai, Kittawit Autchariyapanitkul, Napat Harnpornchai, Songsak Sriboonchitta,
Portfolio Optimization of Financial Returns Using Fuzzy Approach with NSGA-II Algorithm, Journal of
Advanced Computational Intelligence and Intelligent Informatics, 19(2015), number 5, pp. 619-623. 2015
https://www.fujipress.jp/jaciii/jc/jacii001900050619/
A12-c196 Zahra Mashayekhi, Hashem Omrani, An integrated multi-objective Markowitz-DEA cross-efficiency
model with fuzzy returns for portfolio selection problem, APPLIED SOFT COMPUTING, 38(2016), pp.
1-9. 2016
http://dx.doi.org/10.1016/j.asoc.2015.09.018
If the asset returns are considered as trapezoidal fuzzy numbers, then the expected value and
variance of the portfolio are computed as follows, respectively [A12]: (page 4)
92
A12-c195 Peng Zhang, An interval mean-average absolute deviation model for multiperiod portfolio selection
with risk control and cardinality constraints, SOFT COMPUTING, 20(2016), number 3, pp. 1203-1212.
2016
http://dx.doi.org/10.1007/s00500-014-1583-3
Though probability theory is a major tool used for analyzing uncertainty in finance, it cannot describe the uncertainty completely since there are many other uncertain factors that differ from the
random ones found in financial markets. Some other techniques can be applied to handle uncertainty of financial markets. Carlsson and Fullér (2001) introduced the notions of lower and upper
possibilistic mean values of a fuzzy number, viewing them as possibility distributions. Carlsson et
al. (2002) introduced a possibilistic approach to select portfolios with highest utility score under
the assumptions that the returns of assets are trapezoidal fuzzy numbers and short sales are not
allowed on all risky assets. (page 1203)
2015
A12-c194 Peng Zhang, Multi-period Possibilistic Mean Semivariance Portfolio Selection with Cardinality Constraints and its Algorithm, JOURNAL OF MATHEMATICAL MODELLING AND ALGORITHMS IN
OPERATIONS RESEARCH, 14: (2) pp. 239-253. 2015
http://dx.doi.org/10.1007/s10852-014-9268-6
Huang [22] proposed mean risk curve portfolio selection models. Zhang et al. [23] proposed the
portfolio selection models based on the lower and upper possibilistic means and possibilistic variances of fuzzy numbers Li et al [24] applied a genetic procedure to solve mean variance skewness
fuzzy portfolio. Carlsson et al. [A12] introduced a possibilistic approach to select portfolios with
highest utility score under the assumption that the returns of assets are trapezoidal fuzzy numbers.
(page 240)
A12-c193 I-Fei Chen, Ruey-Chyn Tsaur, Fuzzy Portfolio Selection Using a Weighted Function of Possibilistic
Mean and Variance in Business Cycles, INTERNATIONAL JOURNAL OF FUZZY SYSTEMS (to appear).
2015
http://dx.doi.org/10.1007/s40815-015-0073-9
A12-c192 Zhongfeng Qin, Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 245:
(2) pp. 480-488. 2015
http://dx.doi.org/10.1016/j.ejor.2015.03.017
In portfolio theory, the security returns are considered as random variables and their characteristics
such as expected value and variance are calculated based on the sample of available historical data.
It remains valid when there are plenty of data such as in the developed financial market. However,
there may be lack of enough t ransaction data in some emerging markets. In the situation, some
researchers regarded security returns as fuzzy variables estimated by experienced experts, and
developed fuzzy portfolio optimization theory. More specifically, fuzzy portfolio optimization has
been studied based on three different methods: fuzzy set theory (Gupta, Mehlawat, & Saxena,
2008), possibility theory (Carlsson, Fullér, & Majlender, 2002; Zhang, Wang, Chen, & Nie, 2007)
and credibility theory (Huang, 2006; Qin, Li, & Ji, 2009). (page 480)
A12-c190 Enriqueta Vercher, Jose D Bermudez, Portfolio optimization using a credibility mean-absolute semideviation model, EXPERT SYSTEMS WITH APPLICATIONS, 42(2015), number 20, pp. 7121-7131.
2015
http://dx.doi.org/10.1016/j.eswa.2015.05.020
A12-c189 Wei Chen, Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem, Physica A: Statistical Mechanics and its Applications, 429(2015), pp. 125-139. 2015
http://dx.doi.org/10.1016/j.physa.2015.02.060
93
All the above literatures assume that the security returns are random variables. However, if there
is not enough historical data, it is more reasonable to assume them as fuzzy variables. Since
Zadeh introduced the fuzzy set theory, many researchers have studied portfolio selection problem
in fuzzy environments, such as Tanaka and Guo [25], Carlsson et al. [A12], Vercher et al. [27],
Smimou et al. [28], Chen et al. [29], Sadjadi et al. [30], Wang et al. [31], Kamdem et al. [32],
Tsaur [33]. Though great progress has been made in fuzzy portfolio selection problems, none of
the above-cited papers incorporate real-world constraints such as transaction costs and cardinality
constraints. (page 126)
In order to use the model (2), it is necessary to estimate the probability distribution of the portfolio
return. It is well-known that the returns of risky assets are in a fuzzy economic environment and
vary from time to time, the future states of returns and risks of risky assets cannot be predicted accurately. Moreover, by using fuzzy approaches, it is better to handle the vagueness and ambiguity
in the investment environment and the investors subjective opinions can be better integrated. Due
to these facts, it is useful and meaningful to discuss the portfolio problem under the assumption
that the returns of the assets are fuzzy numbers. Similar to the possibilistic approach introduced by
Carlsson et al. [A12], and Liu and Zhang [40], we assume that the returns of assets are trapezoidal
fuzzy numbers. (page 128)
A12-c188 Ting Li, Weiguo Zhang, Weijun Xu, A fuzzy portfolio selection model with background risk, Applied
Mathematics and Computation 256(2015), pp. 505-513. 2015
http://dx.doi.org/10.1016/j.amc.2015.01.007
Possibility theory was proposed by Zadeh [7] and was advanced by Dubois and Prade [8]. In
Zadeh’s theory, fuzzy variables are associated with possibility distributions, which is in the similar
way that random variables are associated with probability distribution. Carlsson and Fullér [A12,
B6] introduced the notions of possibilistic mean, possibilistic variance and covariance of fuzzy
numbers. (page 506)
A12-c187 Alireza Nazemi, Behzad Abbasi, Farahnaz Omidi, Solving portfolio selection models with uncertain
returns using an artificial neural network scheme, Applied Intelligence, 42(2015), issue 4, pp. 609-621.
2015
http://dx.doi.org/10.1007/s10489-014-0616-z
A12-c186 Yong-Jun Liu, Wei-Guo Zhang, A multi-period fuzzy portfolio optimization model with minimum
transaction lots, European Journal of Operational Research, 24(2015), issue 3, pp. 933-941. 2015
http://dx.doi.org/10.1016/j.ejor.2014.10.061
With the wide use of fuzzy set theory in Zadeh (1965), more and more researchers have realized
that they could use the fuzzy set theory to handle the vagueness and ambiguity, see for example,
Tanaka and Guo (1999), Carlsson, Fullér, and Majlender (2002), Fang et al. (2006), Vercher et al.
(2007), Zhang, Wang, Chen, and Nie (2007), Zhang, Zhang, and Xiao (2009), Zhang et al. (2010),
Barak, Abessi, and Modarres (2013), and Liu and Zhang (2013). (page 934)
A12-c185 Ruey-Chyn Tsaur, Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions,
International Journal of Systems Science, 46(2015), Issue 3, pp. 438-450. 2015
http://dx.doi.org/10.1080/00207721.2013.784820
A12-c184 Ziqiang Zeng, Ehsan Nasri, Abdol Chini, Robert Ries, Jiuping Xu, A multiple objective decision
making model for energy generation portfolio under fuzzy uncertainty: Case study of large scale investorowned utilities in Florida, RENEWABLE ENERGY, 75(2015), pp. 224-242. 2015
http://dx.doi.org/10.1016/j.renene.2014.09.030
A12-c183 Jose M Brotons, Antonio Terceno, M Gloria Barbera-Marine, A new index for bond management in
an uncertain environment FUZZY SETS AND SYSTEMS, 266(2015), pp. 144-156. 2015
http://dx.doi.org/10.1016/j.fss.2014.08.002
One reasonable function that is commonly employed by financial theorists [23] assigns a risky
portfolio P with risky rate of return rP an expected rate of return E(rP )and a variance of the rate
of return σ 2 (rP ) the utility score U (P ) = E(rP ) − 0.005 · A · σ 2 (rP ) where A is an index of the
94
DM’s risk aversion. Carlsson et al. [24], i n a fuzzy environment, uses E() as a measure of return
and σ 2 () as a measure of risk. (page 145)
A12-c182 Thanh T Nguyen, Lee Gordon-Brown, Abbas Khosravi, Douglas Creighton, Saeid Nahavandi, Fuzzy
Portfolio Allocation Models through a New Risk Measure and Fuzzy Sharpe Ratio, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 23: (3) pp. 656-676. 2015
http://dx.doi.org/10.1109/TFUZZ.2014.2321614
Chen and Huang [3] considered the uncertainty of future returns and risk and presented them
in triangular fuzzy numbers and solved the optimal asset allocation by a fuzzy optimization. The
portfolio solutions obtained were argued to be more reasonable and suitable in the imprecise financial environment. Hasuike et al. [4] modeled uncertain expected returns as fuzzy random variables
and proposed several random fuzzy nonlinear portfolio selection models. An efficient solving approach involving parametric convex programming problem is constructed to find a global optimal
solution for portfolio optimizations. The proposed method was found to be more flexible and
adaptable compared with the models of Carlsson et al. [A12] and Vercher et al. [6]. (page 656)
2014
A12-c181 Peng Zhang, Wei-Guo Zhang, Multiperiod mean absolute deviation fuzzy portfolio selection model
with risk control and cardinality constraints, FUZZY SETS AND SYSTEMS, 255(2014), pp. 74-91. 2014
http://dx.doi.org/10.1016/j.fss.2014.07.018
Carlsson et al. [A12] introduced a possibilistic approach to selecting portfolios with highest utility
score under the assumption that the returns of assets are trapezoidal fuzzy numbers. (page 76)
A12-c180 Gholamreza Taghizadegan, Zahra Alipour Darvish, Abdollah Yavaran Bakhshayesh, Portfolio Optimization of Equity Mutual Funds in Tehran Stock Exchange (TSE) With Fuzzy Set, MANAGEMENT
AND ADMINISTRATIVE SCIENCES REVIEW,, 3(2014), number 4, pp. 484-494. 2014
http://absronline.org/journals/index.php/masr/article/view/208/229
A12-c179 Adel Azar, Hossein Sayyadi Tooranloo, Ali Rajabzadeh, Laya Olfat, A Model for Assessing Agility
Drivers with Possibility Theory, Applied mathematics in Engineering, Management and Technology, June
2014: (1119) p. 1134. 2014
http://amiemt.megig.ir/test/sp2/136.pdf
A12-c178 Wei Chen, An artificial bee colony algorithm for uncertain portfolio selection, The Scientific World
Journal, 2014: Paper 578182. 2014
http://downloads.hindawi.com/journals/tswj/aip/578182.pdf
A12-c177 Takashi Hasuike, Hideki Katagiri, Risk-controlled multiobjective portfolio selection problem using a
principle of compromise, Mathematical Problems in Engineering (to appear). 2014
http://downloads.hindawi.com/journals/mpe/aip/232375.pdf
As a nonprobabilistic approach, many researchers proposed fuzzy-based portfolio selection problems using the fuzzy theory (Bilbao-Terol et al. [4], Carlsson et al. [A12], Duan and Stahlecker
[6], Huang [13, 14], Inuiguchi and Tanino [16], Tanaka et al. [24, 25], Watada [26]). (page 2)
A12-c176 Wei Chen, Hui Ma, Yiping Yang, Mengrong Sun, Application of artificial bee colony algorithm to
portfolio adjustment problem with transaction costs, Journal of Applied Mathematics. Paper 192868. 2014
http://dx.doi.org/10.1155/2014/192868
Carlsson et al. [A12] introduced a possibilistic approach to the selection of portfolios with highest
utility score. (page 1)
A12-c175 Gupta P, Mittal G, Mehlawat MK, A multicriteria optimization model of portfolio rebalancing with
transaction costs in fuzzy environment, Memetic Computing 6: (1) pp. 61-74. 2014
http://dx.doi.org/10.1007/s12293-012-0102-2
95
A12-c174 M.K. Mehlawat and P. Gupta, Credibility-based fuzzy mathematical programming model for portfolio
selection under uncertainty, International Journal of Information Technology & Decision Making, Volume
13, Issue 1, January 2014, Pages 101-135. 2014
http://dx.doi.org/10.1142/S0219622014500059
A12-c173 Zhang Wei-Guo, Liu Yong-Jun, Xu Wei-Jun, A new fuzzy programming approach for multi-period
portfolio optimization with return demand and risk control, Fuzzy Sets and Systems, 247(2014), pp. 107126. 2014
http://dx.doi.org/10.1016/j.fss.2013.09.002
A12-c172 Mukesh Kumar Mehlawat, Pankaj Gupta, Fuzzy Chance-Constrained Multiobjective Portfolio Selection Model, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 22(2014), issue 3, pp. 653-671. 2014
http://dx.doi.org/10.1109/TFUZZ.2013.2272479
2013
A12-c171 Arnold F Shapiro, Fuzzy post-retirement financial concepts: an exploratory study, METRON, 71(2013),
issue 3, pp 261-278. 2013
http://dx.doi.org/10.1007/s40300-013-0028-6
These fuzzy concepts present two basic problems. First, they impede the communication between
the individual and his or her financial advisor. Zadeh [47], Ribeiro [32], Parra et al. [2], Carlsson
et al. [A12], Sadiq and Khan [33], and Shapiro [37] provide insights into this issue. (page 261)
A12-c170 M Shahmohammdi, L Emami, Y Zare Mehrjerdi, A Hybrid Intelligent Algorithm for Portfolio Selection using Fuzzy Mean-Variance-Skewness, ?International Journal of Industrial Engineering & Production
Management, 23(2013), number 4, pp. 447-458. 2013
A12-c169 Shu-Ping Wan, Jiu-Ying Dong, Possibility Method for Triangular Intuitionistic Fuzzy Multi-attribute
Group Decision Making with Incomplete Weight Information, International Journal of Computational Intelligence Systems (to appear). 2013
http://dx.doi.org/10.1080/18756891.2013.857150
A12-c168 Liu Yong-Jun, Zhang Wei-Guo, Fuzzy portfolio optimization model under real constraints, Insurance:
Mathematics and Economics, 53(2013), number 3, pp. 704-711. 2013
http://dx.doi.org/10.1016/j.insmatheco.2013.09.005
A12-c167 Zhang Xili, Zhang Weiguo, Xiao Weilin, Multi-period portfolio optimization under possibility measures, Economic Modelling 35(2013), pp. 401-408. 2013
http://dx.doi.org/10.1016/j.econmod.2013.07.023
Carlsson et al. (2002) and Zhang et al. (2009a) introduced a possibilistic approach for selecting portfolios with the highest utility value under the assumption that the returns of assets are
trapezoidal fuzzy numbers. (page 401)
A12-c166 Jiandong H, A fuzzy portfolio selection model with cardinality constraints based on differential evolution algorithm, International Journal of Applied Mathematics and Statistics, 39(2013), number 9, pp.
130-137. 2013
Scopus: 84881574858
A12-c165 QIN ZHONGFENG, WANG DAVID Z W, LI XIANG, MEAN-SEMIVARIANCE MODELS FOR
PORTFOLIO OPTIMIZATION PROBLEM WITH MIXED UNCERTAINTY OF FUZZINESS AND RANDOMNESS, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21(2013),
supp 01, pp. 127-139. 2013
http://dx.doi.org/10.1142/S0218488513400102
A12-c164 Anna Darmani, Payam Hanafizadeh, Business Process Portfolio Selection in Re-engineering Projects,
Business Process Management Journal, 16(2013), number 9. Paper 17094367. 2013
A12-c163 Yong-Jun Liu, Wei-Guo Zhang, Pu Zhang, A multi-period portfolio selection optimization model by
using interval analysis, ECONOMIC MODELLING, 33(2013), pp. 113-119. 2013
http://dx.doi.org/10.1016/j.econmod.2013.03.006
96
Carlsson et al. (2002) considered portfolio selection problems under possibility distributions and
presented an algorithm for finding an exact optimal solution to these problems. (page 113)
A12-c162 Shu-Ping Wan, Deng-Feng Li, Zhen-Feng Rui, Possibility mean, variance and covariance of triangular intuitionistic fuzzy numbers, JOURNAL OF INTELLIGENT AND FUZZY SYSTEMS, 24(2013),
number 4, pp. 847-858. 2013
http://dx.doi.org/10.3233/IFS-2012-0603
A12-c161 Takashi Hasuike, Hideki Katagiri, Robust-based interactive portfolio selection problems with an
uncertainty set of returns, FUZZY OPTIMIZATION AND DECISION MAKING, 12 (2013), number 3,
pp. 263-288. 2013
http://dx.doi.org/10.1007/s10700-013-9157-x
As a nonprobabilistic approach, many researchers have proposed fuzzy-based portfolio selection
problems using the fuzzy theory, for instance, possibilistic portfolio selection problems (Carlsson
et al. 2002; Guo and Tanaka 1998; Inuiguchi and Ramik 2000; Inuiguchi and Tanino 2000;
Li and Xu 2007; Tanaka and Guo 1999; Tanaka et al. 2000), credibilistic portfolio selection
problems (Huang 2009), fuzzy chance-constrained portfolio selection problems (Huang 2006),
fuzzy compromise programming (Bilbao-Terol et al. 2006), portfolio selection problems using
fuzzy goal approaches (Watada 1997), fuzzy random portfolio selection problems (Katagiri et al.
2005), random fuzzy portfolio selection problems (Hasuike et al. 2009; Huang 2007), etc. (page
264)
A12-c160 Irina Georgescu, A new notion of possibilistic covariance, NEW MATHEMATICS AND NATURAL
COMPUTATION, 9(2013), number 1, pp. 1-11. 2013
http://dx.doi.org/10.1142/S1793005713500014
A12-c159 Tsaur R-C, Fuzzy portfolio model with different investor risk attitudes, European Journal of Operational Research, 227(2013), number 2, pp. 385-390. 2013
http://dx.doi.org/10.1016/j.ejor.2012.10.036
Carlsson et al. (2002) proved that feasible solutions form a convex polytope that contains all
optional solutions for portfolio selection problems. (page 385)
A12-c158 Chen W, Sheng Y, A possibilistic adjusting model for portfolio selection with transaction costs,
Information (Japan), 16(2013), number 1A, pp. 39-52. 2013
Scopus: 84873343281
A12-c157 Pankaj Gupta, Masahiro Inuiguchi, Mukesh Kumar Mehlawat, Garima Mittal, Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints, INFORMATION SCIENCES, 229(2013),
pp. 1-17. 2013
http://dx.doi.org/10.1016/j.ins.2012.12.011
A12-c156 Jun Li, Jiuping Xu, Multi-objective portfolio selection model with fuzzy random returns and a compromise approach-based genetic algorithm, INFORMATION SCIENCES, 220(2013), pp. 507-521. 2013
http://dx.doi.org/10.1016/j.ins.2012.07.005
A12-c155 Mohsen Gharakhani, Seyed Jafar Sadjadi, A fuzzy compromise programming approach for the BlackLitterman portfolio selection model, DECISION SCIENCE LETTERS, 2(2013), pp. 11-22. 2013
http://dx.doi.org/10.5267/j.dsl.2012.12.001
According to Lai et al. (2002), Wang and Zhu (2002), and Giove et al. (2006) linear interval
programming model has been used for portfolio selection. Carlsson et al. (2002) introduced a
possibilistic approach for selecting portfolios with the highest utility value assuming assets returns
as trapezoidal fuzzy numbers. (page 13)
A12-c154 Shu-Ping Wan, Deng-Feng Li, Zhen-Feng Rui, Possibility mean, variance and covariance of triangular intuitionistic fuzzy numbers, JOURNAL OF INTELLIGENT AND FUZZY SYSTEMS, 24(2013),
number 4, pp. 847-858. 2013
http://dx.doi.org/10.3233/IFS-2012-0603
2012
97
A12-c153 Yong-Jun Liu, Wei-Guo Zhang, Wei-Jun Xu, Fuzzy multi-period portfolio selection optimization
models using multiple criteria, Automatica, 48(2012), number 12, pp. 3042-3053. 2012
http://dx.doi.org/10.1016/j.automatica.2012.08.036
Numerous researchers have studied fuzzy portfolio selection problems (see for example Carlsson,
Fullér, & Majlender, 2001; Fang, Lai, & Wang, 2006; Giove, Funari, & Nardelli, 2006; Inuiguchi
& Tanino, 2000; León, Liern, & Vercher, 2002; Sadjadi, Seyedhosseini, & Hassanlou, 2011;
Watada, 1997; Zhang, Liu, & Xu, 2012; Zhang, Xiao, & Xu, 2010; Zhang, Zhang, & Xu, 2010).
(page 3043)
A12-c152 I. Georgescu, Expected utility operators and possibilistic risk aversion, SOFT COMPUTING, Volume
16, Issue 10, September 2012, Pages 1671-1680. 2012
http://dx.doi.org/10.1007/s00500-012-0851-3
A12-c151 Yang L, Chen W, Application of PSO algorithm to portfolio optimization problem with fuzzy returns,
INTERNATIONAL REVIEW ON COMPUTERS AND SOFTWARE, 7(2012), number 2, pp. 855-861.
2012
Scopus: 84864373982
A12-c150 Jules Sadefo Kamdem, Christian Deffo Tassak, Louis Aime Fono, Moments and semi-moments for
fuzzy portfolios selection, Insurance: Mathematics and Economics, 51(2012), number 3, pp. 517-530. 2012
http://dx.doi.org/10.1016/j.insmatheco.2012.07.003
In the one approach, some scholars have proposed to use imprecise probability, possibility, etc.
to deal with uncertainty in portfolio selection since 1990’s. For example, some authors such
as Tanaka and Guo [22] quantified mean and variance of a portfolio through fuzzy probability
and possibility distributions, Carlsson et al. [A14]-[A12] used their own definitions of mean and
variance of fuzzy numbers. (page 518)
A12-c149 Pankaj Gupta, Garima Mittal, Mukesh Kumar Mehlawat, Multiobjective expected value model for
portfolio selection in fuzzy environment, OPTIMIZATION LETTERS (to appear). 2012
http://dx.doi.org/10.1007/s11590-012-0521-5
A12-c148 X Huang, L Qiao, A risk index model for multi-period uncertain portfolio selection, INFORMATION
SCIENCES, Volume 217, December, 2012 Pages 108-116. 2012
http://dx.doi.org/10.1016/j.ins.2012.06.017
Later on, many scholars studied how to use the mean-variance framework to select the portfolio
in this situation by using fuzzy set theory, and different versions of fuzzy mean-variance models
have been developed, e.g. possibilistic models by Carlsson et al. [A12], Gupta et al. [10], Zhang
et al. [27], and credibilistic models by Huang [11, 12], Qin et al. [21], and Li et al. [17], etc.
Recently, Bilbao-Terol et al. [1] has used goal programming and fuzzy technology to select a
socially responsible portfolios.
A12-c147 Seyed Mohammad Mirnoori, Abdollah Shariati, Fuzzy portfolio optimization using Chen and Huang
model: Evidence from Iranian mutual funds, AFRICAN JOURNAL OF BUSINESS MANAGEMENT,
6(2012), number 22, pp. 6608-6616. 2012
http://dx.doi.org/10.5897/AJBM12.303
A12-c146 Xiaoxia Huang, A risk index model for portfolio selection with returns subject to experts’ estimations,
FUZZY OPTIMIZATION AND DECISION MAKING, Volume 11, Issue 4, December 2012, Pages 451463. 2012
http://dx.doi.org/10.1007/s10700-012-9125-x
For example, based on possibility measure, Watada (1997), Tanaka and Guo (1999), Carlsson et al.
(2002), Bilbao-Terol et al. (2006), Lacagnina and Pecorella (2006) extended the mean-variance
idea to solve the portfolio selection problems in different ways. Based on credibility measure,
Huang (2007, 2008), Qin et al. (2009), Li et al. (2010), and Zhang et al. (2010) proposed a
spectrum of credibilistic mean-variance portfolio selection models. (page 452)
98
A12-c145 Xiaoxia Huang, Mean-variance models for portfolio selection subject to experts’ estimations, EXPERT SYSTEMS WITH APPLICATIONS, 39(2012), issue 5, pp. 5887-5893. 2012
http://dx.doi.org/10.1016/j.eswa.2011.11.119
Much work has been done on extending the meanvariance selection idea to fuzzy environment in
different ways. For example Tanaka, Guo, and Türksen (2000) quantified mean and variance of a
portfolio through fuzzy probability. Carlsson, Fullér, and Majlender (2002) used their definition
of mean and variance of fuzzy numbers (Carlsson & Fullér, 2001) to find the optimum portfolio.
(page 5887)
A12-c144 Yanju Chen, Yankui Liu, Xiaoli Wu, A new risk criterion in fuzzy environment and its application,
APPLIED MATHEMATICAL MODELLING, 36(2012), number 7, pp. 3007-3028. 2012
http://dx.doi.org/10.1016/j.apm.2011.09.081
Carlsson et al. [A12] introduced a possibilistic approach for selecting portfolios with the highest
utility value under the assumption that the returns of assets are trapezoidal fuzzy numbers; (page
3008)
A12-c143 Xiang Li, Biying Shou, Zhongfeng Qin, An expected regret minimization portfolio selection model,
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 218(2012), number 2, pp. 484-492. 2012
http://dx.doi.org/10.1016/j.ejor.2011.11.015
Within the framework of the possibility theory, Tanaka and Guo (1999) first proposed a centerspread model on the assumption that securities returns are exponential fuzzy variables. Inuiguchi
and Ramik (2000) proposed a necessity maximization model and a chance-constrained programming model, Carlsson et al. (2002) proposed a meanvariance model, Zhang et al. (2009, 2011)
presented an extended meanvariance model based on interval-valued possibilistic mean and variance. (page 485)
A12-c142 J D Bermúdeza, J V Segurab, E Vercher, A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection, FUZZY SETS AND SYSTEMS , 188(2012), number 1, pp. 16-26. 2012
http://dx.doi.org/10.1016/j.fss.2011.05.013
2011
A12-c141 Brotons J M, Terceno A, Return risk map in a fuzzy environment, FUZZY ECONOMIC REVIEW,
16(2011), issue 2, pp. 33-57. 2011
Scopus: 84858065828
A12-c140 M. Jasemi, A. M. Kimiagari, A. Memariani, A conceptual model for portfolio management sensitive to mass psychology of market, INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING
INTERNATIONAL: THEORY, APPLICATION AND PRACTICE, 18(2011), number 1, pp. 1-15. 2011
Scopus: 82955240899
A12-c139 ZHAO Li-hu, YANG Yong, ZHANG Zai-sheng, Fuzzy Portfolio Selection Model Based on Investor’s
Preference, Journal of UESTC (Social Sciences Edition), 13(2011), number 3, pp. 58-61 (in Chinese). 2011
http://www.xb.uestc.edu.cn/social/public/uploadfiles/UESTC20110312.pdf
A12-c138 Rupak Bhattacharyya, Samarjit Kar, Possibilistic mean- variance- skewness portfolio selection models, INTERNATIONAL JOURNAL OF OPERATIONS RESEARCH, 8(2011), number 3, pp. 44-56. 2011
http://www.orstw.org.tw/IJOR/vol8no3/5-Vol_8,%20No.%203,%20pp.44-56.pdf
A12-c137 Wei-Guo Zhang, Xili Zhang, Yunxia Chen, Portfolio adjusting optimization with added assets and
transaction costs based on credibility measures, INSURANCE: MATHEMATICS AND ECONOMICS
49(2011), number 3, pp. 353-360. 2011
http://dx.doi.org/10.1016/j.insmatheco.2011.05.008
A12-c136 Irina Georgescu; Jani Kinnunen, Credibility measures in portfolio analysis: From possibilistic to
probabilistic models, JOURNAL OF APPLIED OPERATIONAL RESEARCH, 3(2011), number 2, pp.
91-102.
http://www.tadbir.ca/jaor/archive/v3/n2/jaorv3n2p91.pdf
99
A12-c135 S. A. Farzad, Technology portfolio modeling in hybrid environment, AFRICAN JOURNAL OF
BUSINESS MANAGEMENT, 5(2011), number 5, pp. 4051-4058. 2011
http://www.academicjournals.org/ajbm/PDF/pdf2011/4June/Farzad.pdf
Because of this vagueness and complicacy, predicting future returns through the method of historical data is not feasible. In order to confront this problem, researchers have suggested applying
Fuzzy sets theory (Zade, 1965, 2005). But even in that case, there has also been some problems
in risk calculation which is rooted in uncertainty, furthermore a lot of models have been proposed
around the issue of portfolio that among them Watada (1997), Carlsson et al. (2002) and Huang’s
model (2007a) can be referred. (page 4052)
A12-c134 M. B. Aryanezhad, H. Malekly, M. Karimi-Nasab, A fuzzy random multi-objective approach for
portfolio selection, JOURNAL OF INDUSTRIAL ENGINEERING INTERNATIONAL , 7(2011), number
13, pp. 12-21. 2011
http://www.sid.ir/en/VEWSSID/J_pdf/117320111302.pdf
A12-c133 Wei Chen, Yiping Yang, Hui Ma, Fuzzy Portfolio Selection Problem with Different Borrowing and
Lending Rates, MATHEMATICAL PROBLEMS IN ENGINEERING, vol. 2011, pp. 1-15. Paper 263240.
2011
http://dx.doi.org/10.1155/2011/263240
Carlsson et al. [A12] introduced a possibilistic approach to selecting portfolios with highest utility
score. Fang et al. [20] proposed a linear programming model for portfolio rebalancing with
transaction costs, in which portfolio liquidity was also considered. (page 2)
A12-c132 Irina Georgescu, Jani Kinnunen, Possibilistic risk aversion with many parameters, PROCEDIA
COMPUTER SCIENCE 4(2011), pp. 1735-1744. 2011
http://dx.doi.org/10.1016/j.procs.2011.04.188
A12-c131 Irina Georgescu; Jani Kinnunen, Multidimensional possibilistic risk aversion, MATHEMATICAL
AND COMPUTER MODELLING, 54(2011), issues 1-2, pp. 689-696. 2011
http://dx.doi.org/10.1016/j.mcm.2011.03.011
A12-c130 Takashi Hasuike; Hideki Katagiri, Strict and efficient solution methods for robust programming problems with ellipsoidal distributions under fuzziness, INTERNATIONAL JOURNAL OF KNOWLEDGE
ENGINEERING AND SOFT DATA PARADIGMS, 3(2011), number 1, pp. 57-68. 2011
http://inderscience.metapress.com/link.asp?id=0172643566800205
A12-c129 Xiaoxia Huang, Mean-risk model for uncertain portfolio selection FUZZY OPTIMIZATION AND
DECISION MAKING, 10(2011), number 1, pp. 71-89. 2011
http://dx.doi.org/10.1007/s10700-010-9094-x
Regarding that security returns are fuzzy, some researchers such as Watada (1997), Carlsson et al.
(2002), Lacagnina and Pecorella (2006) and Zhang et al. (2007) employed possibility measure to
study fuzzy portfolio selection problems, while other scholars such as Huang (2007), etc. Qin et
al. (2009), Li et al. (2009b, 2010) used credibility measure to help select fuzzy portfolios. (page
72)
A12-c128 Xiaoxia Huang, Minimax mean-variance models for fuzzy portfolio selection, SOFT COMPUTING,
Volume 15, Issue 2, pp. 251-260. 2011
http://dx.doi.org/10.1007/s00500-010-0654-3
A12-c127 Irina Georgescu, A possibilistic approach to risk aversion, SOFT COMPUTING, 15(2011), pp. 795801. 2011
http://dx.doi.org/10.1007/s00500-010-0634-7
A12-c126 Xili Zhang, Wei-Guo Zhang, Wei-Jun Xu An optimization model of the portfolio adjusting problem
with fuzzy return and a SMO algorithm, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), issue 4,
pp. 3069-3074. 2011
http://dx.doi.org/10.1016/j.eswa.2010.08.097
100
Carlsson et al. (2002) and Zhang et al. (2009) introduced possibilistic approaches to portfolio
selection problem under the assumption that the returns of assets are trapezoidal fuzzy numbers.
Trapezoidal possibilistic distribution is only considered because it can easily be generalized to the
case of possibility distribution of type LR. (page 3070)
2010
A12-c125 Xue Deng, Junfeng Zhao, Lihong Yang, Rongjun Li, Possibilistic mean-variance utility to portfolio
selection for bounded assets, INTERNATIONAL JOURNAL OF DIGITAL CONTENT TECHNOLOGY
AND ITS APPLICATIONS, 4(2010) number 6, pp. 150-160. 2010
http://www.aicit.org/jdcta/ppl/18%20-%20JDCTA4-460058.pdf
A12-c124 Weijun Xu, Weidong Xu, Hongyi Li, Weiguo Zhang, Uncertainty portfolio model in cross currency markets, INTERNATIONAL JOURNAL OF UNCERTAINTY, FUZZINESS AND KNOWLEDGEBASED SYSTEMS, 18(2010), Issue 6, pp. 759-777. 2010
http://dx.doi.org/10.1142/S0218488510006787
A12-c123 Guohua Chen, Fuzzy Data Decision Support in Portfolio Selection: a Possibilistic Safety-first Model,
COMPUTER AND INFORMATION SCIENCE 3(2010), number 4, pp. 116-124. 2010
http://www.ccsenet.org/journal/index.php/cis/article/view/8102/6121
Tanaka et al(2000) formulate fuzzy decision problems based on probability events. Carlsson et
al(2002) studied a portfolio selection model in which the rate of return of securities follows the
possibility distribution. Enriqueta et al(2007) presented a fuzzy downside risk approach for managing portfolio problems in the framework of risk-return trade-off using interval-valued expectations. (page 117)
A12-c122 Fei Bao, Panpan Zhu, Peibiao Zhao, Portfolio Selection Problems Based on Fuzzy Interval Numbers
Under the Minimax Rules, INTERNATIONAL JOURNAL OF MATHEMATICAL ANALYSIS, 4(2010),
number 44, pp. 2143-2166. 2010
A12-c121 Zdeněk Zmeškal, Generalised soft binomial American real option pricing model (fuzzy-stochastic
approach), EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 207(2010), vol. 2, pp. 1096-1103.
2010
http://dx.doi.org/10.1016/j.ejor.2010.05.045
The second approach is based on assumption that input data (parameters, distribution functions)
is possible to introduce only vaguely. A survey of vaguely formulated problems in finance and
accounting decision-making is in Siegel et al. (1995), and financial engineering in Riberio et al.
(1999). Other financial applications examples, except option valuation models, are Lai and Hwang
(1993), Inuiguchi and Ramik (2000), Tanaka et al. (2000), Cherubini and Lunga (2001), Carlsson
et al. (2002), Zmeskal (2005), Koissi and Shapiro (2006), Xu and Kaymak (2008). (page 1097)
A12-c120 Wei-Guo Zhang, Xi-Li Zhang, Wei-Jun Xu, A risk tolerance model for portfolio adjusting problem with transaction costs based on possibilistic moments, INSURANCE: MATHEMATICS AND ECONOMICS, 46(2010), issue 3, pp. 493-499. 2010
http://dx.doi.org/10.1016/j.insmatheco.2010.01.007
It is well known that the future states of returns and risks about risky assets are hard to predict
accurately. In many important cases, the estimation of the possibility distributions of return rates
on assets may be easier than the probability distributions. Moreover, by using fuzzy approaches, it
is better to handle the vagueness and ambiguity in the investment environment and the investors’
subjective opinions can be better integrated. Hence, it is useful and meaningful to discuss the
portfolio adjusting problem under the assumption that the returns of the assets are fuzzy numbers.
Similar to the possibilistic approach introduced by Carlsson et al. (2002), we assume that the
returns of assets are trapezoidal fuzzy numbers in the following discussion. (pages 494-495)
A12-c119 Xili Zhang, Wei-Guo Zhang, Ruichu Cai, Portfolio adjusting optimization under credibility measures,
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 234(2010), pp. 1458-1465. 2010
http://dx.doi.org/10.1016/j.cam.2010.02.022
101
A12-c118 W.-G. Zhang, W.-L. Xiao, W.-J. Xu, A possibilistic portfolio adjusting model with new added assets,
ECONOMIC MODELLING, 27(2010), Number 1, pp. 208-213. 2010
http://dx.doi.org/10.1016/j.econmod.2009.08.008
2009
A12-c117 T. Hasuike, H. Ishii, Portfolio selection problems using the scenario model with fuzzy returns, ASIA
PACIFIC MANAGEMENT REVIEW, 14(2009), Issue 3, pp. 335-347. 2009
http://apmr.management.ncku.edu.tw/comm/updown/DW0908122664.pdf
Carlsson (2002) has proposed a portfolio selection problem using the possibility mean value. In
this paper, we assume the following cases: (a) Since the main objective is to minimize the total
variance and the investor considers that she or he manages to minimize it as small as possible
even if the aspiration level becomes smaller. (b) On the other hand, it is clear that the investor
also considers that she or he never fails to earn the total return more than the goal in the variance
constraint.(page 340)
A12-c116 Wei Chen, Weighted portfolio selection models based on possibility theory, FUZZY INFORMATION
AND ENGINEERING, 1(2009), pp. 115-127. 2009
http://dx.doi.org/10.1007/s12543-009-0010-4
A12-c115 Mohamed Dia, A Portfolio Selection Methodology Based on Data Envelopment Analysis, INFOR:
INFORMATION SYSTEMS AND OPERATIONAL RESEARCH, 47(82009), Number 1/2, pp. 71-79.
2009
http://dx.doi.org/10.3138/infor.47.1.71
A12-c114 Guohua Chen, Xiaolian Liao, Shouyang Wang, A cutting plane algorithm for MV portfolio selection
model, APPLIED MATHEMATICS AND COMPUTATION, Volume 215, Issue 4, 15 October 2009, pp.
1456-1462. 2009
http://dx.doi.org/10.1016/j.amc.2009.06.040
A12-c113 C. Quek, K. C. Yow, Philip Y. K. Cheng, C. C. Tan, Investment portfolio balancing: application of
a generic self-organizing fuzzy neural network (GenSoFNN), INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE & MANAGEMENT, Volume 16 Issue 1-2, Pages 147-164. 2009
http://dx.doi.org/10.1002/isaf.298
Thereafter, there are many others who developed a refined portfolio selection system based on
Markowitz’s model: Jones’ (2001) ’Digital portfolio theory’ extends the portfolio selection model
by employing digital signal-processing techniques, Carlsson et al. (2002) use a possibilistic approach and Yang (2006) extends the mean-variance model by means of incorporating genetic
algorithm (GA) techniques to establish a more accurate estimation of the model parameters. (page
148)
A12-c112 Takashi Hasuike and Hiroaki Ishii, Robust Portfolio Selection Problems Including Uncertainty Factors, IAENG INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS, 38(2009), article number 9.
2009
http://www.iaeng.org/IJAM/issues_v38/issue_3/IJAM_38_3_09.pdf
A12-c111 Zhong Wan, YaLin Wang, Penalty Algorithm Based on Conjugate Gradient Method for Solving Portfolio Management Problem, JOURNAL OF INEQUALITIES AND APPLICATIONS, 2009(2009), Article
ID 970723, 16 pages. 2009
http://dx.doi.org/10.1155/2009/970723
A12-c110 Xiaoxia Huang, A review of credibilistic portfolio selection, FUZZY OPTIMIZATION AND DECISION MAKING, 8(2009), pp. 263-281. 2009
http://dx.doi.org/10.1007/s10700-009-9064-3
A12-c109 Xiang Li, Yang Zhang, Hau-San Wong, Zhongfeng Qin, A hybrid intelligent algorithm for portfolio
selection problem with fuzzy returns, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 233(2009), pp. 264-278. 2009
http://dx.doi.org/10.1016/j.cam.2009.07.019
102
A12-c108 Wei Chen, Shaohua Tan, On the possibilistic mean value and variance of multiplication of fuzzy
numbers, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 232(2009), pp. 327334. 2009
http://dx.doi.org/10.1016/j.cam.2009.06.016
A12-c107 Takashi Hasuike, Hideki Katagiri, Hiroaki Ishii, Portfolio selection problems with random fuzzy
variable returns, FUZZY SETS AND SYSTEMS, 160(2009), Issue 18, pp. 2579-2596. 2009
http://dx.doi.org/10.1016/j.fss.2008.11.010
Then, it is similar to the optimal portfolio for Carlsson et al. model. This means that our model
and Carlsson et al. model mainly consider maximizing the total pröt, while Vercher et al. model
considers minimizing the downside risk of the investment, measured by the mean-semi-absolute
deviation. (page 2592)
Furthermore, in the case of comparing our model with Carlsson et al. model, each average return
is nearly equal, but variance of these 100 samples for our model is lower than that of Carlsson et
al. model. (page 2593)
Table 9 obviously shows that our proposed model earns much higher profits than Carlsson et al.
model and Vercher et al. model. Then, from Table 8, the optimal portfolio of our proposed model
is well-decentralized compared to previous standard fuzzy models. (page 2594)
A12-c106 T. Hasuike, H. Ishii, Safety first models of portfolio selection problems considering the multi-scenario
including fuzzy returns, INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING, INFORMATION AND CONTROL, 5(2009), pp. 1463-1474. 2009
A12-c105 Wei-Guo Zhang and Wei-Lin Xiao, On weighted lower and upper possibilistic means and variances of fuzzy numbers and its application in decision, KNOWLEDGE AND INFORMATION SYSTEMS,
18(2009), pp. 311-330. 2009
http://dx.doi.org/10.1007/s10115-008-0133-7
A12-c104 Wei-Guo Zhang, Xi-Li Zhang, Wei-Lin Xiao, Portfolio selection under possibilistic mean-variance
utility and a SMO algorithm, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 197(2009), pp.
693-700. 2009
http://dx.doi.org/10.1016/j.ejor.2008.07.011
Carlsson et al. [A12] introduced a possibilistic approach to select portfolios with highest utility
score under the assumptions that the returns of assets are trapezoidal fuzzy numbers and short sales
are not allowed on all risky assets. Carlsson et al. [A12] also presented an algorithm of complexity
O(n3 ) for finding an exact optimal solution to the n-asset portfolio selection problem. According
to the algorithm, the optimal portfolio consists of 3 assets at most. Clearly, this algorithm cannot
be used to solve the problem with the lower and upper bounds constraints on holdings of assets.
In order to obtain the optimal solution of this problem, a new algorithm is needed. (page 693)
In the next section, we consider a portfolio selection problem with n risky assets. Let rj be the
return rate of asset j and let xj be the proportion invested in asset j, j = 1, . . . , n. Carlsson et
al. [A12] introduced a possibilistic approach to portfolio selection problem with highest utility
score on the assumption that the returns of assets are trapezoidal fuzzy numbers. Trapezoidal
possibilistic distribution is only considered because it can easily be generalized to the case of
possibility distribution of type LR or triangle. The portfolio selection problem with possibility
distributions can be formulated as follows [A12]:
X
X
X
n
n
n
max U
ri xi = M̄
ri xi − 0.005 × A × Var
ri xi
i=1
s.t.
X
i=1
xi = 1,
xi ≥ 0, i = 1, . . . , n
where A is the index of the investor’s risk aversion. (pages 694-695)
103
i=1
Carlsson et al. [A12] pointed out the fact that an exact optimal solution to the problem (2) can be
obtained as a convex combination of at most 3 assets. It means that the optimal portfolio consists
of 3 assets at most. Clearly, the algorithm proposed by [A12] cannot be used to solve the problem
(4) because the optimal solution to the problem (4) must consist of n assets, provided di > 0 for all
i. Inspired by the efficiency of SMO used in SVM, we now present a SMO algorithm for finding
an optimal solution to the problem (4). (page 696)
In this paper, we have considered the portfolio selection problem for bounded assets based on
the weighted average of possibilistic means and possibilistic variance on the assumption that each
investor’s utility is the mean-variance type function. We have proposed the parametric quadratic
programming model for portfolio selection problem, which can be regarded as a natural extension
of Carlsson et al. [A12]. Because the algorithm [A12] fails to solve the portfolio selection model
for bounded assets, we have also presented a SMO algorithm special for finding an exact optimal
solution to these problems. (page 700)
A12-c103 P. Jana, T.K. Roy, S.K. Mazumder, Multi-objective possibilistic model for portfolio selection with
transaction cost, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 228(2009), pp.
188-196. 2009
http://dx.doi.org/10.1016/j.cam.2008.09.008
In 1987 Dubois and Prade [11] defined an interval valued expectation of fuzzy numbers, viewing
them as consonant random sets. In this paper we use crisp possibilistic mean and variance of
continuous possibility distributions [A12], which are consistent with the extension principle. (page
191)
A12-c102 Liang-Hsuan Chen, Lindsay Huang, Portfolio optimization of equity mutual funds with fuzzy return
rates and risks, EXPERT SYSTEMS WITH APPLICATIONS, 36(2009), pp. 3720-3727. 2009
http://dx.doi.org/10.1016/j.eswa.2008.02.027
Carlsson, Fullér, and Majlender (2002) assumed that each investor can assign a welfare or utility
score to computing investment portfolios based on the expected return and risk of those portfolios.
(page 3721)
A12-c101 Wei-Guo Zhang, Wei-Lin Xiao, Ying-Luo Wang, A fuzzy portfolio selection method based on possibilistic mean and variance, SOFT COMPUTING, 13(2009), pp. 627-633. 2009
http://dx.doi.org/10.1007/s00500-008-0335-7
Carlsson et al. (2002) and Zhang (2007) introduced possibilistic approaches to select portfolios
under the assumption that the returns of assets are trapezoidal fuzzy numbers. Zhang and Wang
(2005) discussed the portfolio selection problem when returns of assets are symmetric triangular
fuzzy numbers. Vasant (2006), Bhattacharya and Vasant (2007) researched fuzzy decision making problems using S-curve membership functions. In the following section, we propose a new
possibilistic mean-variance model to portfolio se lection when the return rates obey the general
LR-type possibility distributions, which can be regarded as extensions of previous approaches
such as Markowitz’s model (4), Tanaka’s model (Tanaka et al. 2000) etc. (page 629)
2008
A12-c100 Xiaoxia Huang, Mean-Entropy Models for Fuzzy Portfolio Selection, IEEE TRANSACTIONS ON
FUZZY SYSTEMS, 16(2008) pp. 1096-1101. 2008
http://dx.doi.org/10.1109/TFUZZ.2008.924200
Thus, in many situations, prediction about security returns contains much subjectivity. In this context, it is reasonable to use fuzzy variables to describe security returns so that statistical data and
experts’ judgements can be reflected. In fact, with the introduction and development of fuzzy set
theory, scholars have begun to handle fuzziness of portfolios in recent decades. Many researchers
have extended Markowitz’s mean-variance idea in the fuzzy environment in different ways, such
as Carlsson et al. [A12], Parra et al. [28], Tanaka et al. [33], Watada [34], etc. (page 1096)
104
A12-c99 Enriqueta Vercher, Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 217(2008) 381-393. 2008
http://dx.doi.org/10.1016/j.cam.2007.02.017
Dubois and Prade [4] introduce the mean interval of a fuzzy number as a closed interval bounded
by the expectations calculated from its lower and upper probability mean values. Alternatively,
Carlsson and Fullér define the interval-valued possibilistic mean of a fuzzy number, which has
been used for selecting portfolios [A12]. (pages 382-383)
A12-c98 Xiaoxia Huang, Mean-semivariance models for fuzzy portfolio selection, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol. 217, pp. 1-8. 2008
http://dx.doi.org/10.1016/j.cam.2007.06.009
Carlsson et al. [A12] used their own dénitions of mean and variance of fuzzy numbers [A14],
and found the optimum portfolio by maximizing utility. Bilbao-Terol et al. formulated a fuzzy
compromise programming problem [4]. (page 2)
A12-c97 Xiaoxia Huang, Expected model for portfolio selection with random fuzzy returns, INTERNATIONAL
JOURNAL OF GENERAL SYSTEMS, Volume 37, Issue 3 June 2008, pp. 319-328. 2008
http://dx.doi.org/10.1080/03081070601176422
A12-c96 Xiaoxia Huang, Risk curve and fuzzy portfolio selection, COMPUTERS AND MATHEMATICS
WITH APPLICATIONS, 55(2008) 1102-1112. 2008
http://dx.doi.org/10.1016/j.camwa.2007.06.019
Carlsson et al. [A12] found the optimum portfolio by use of their own dénition of mean and variance of fuzzy numbers [A14]. Bilbao-Terol et al. formulated a fuzzy compromise programming
problem [4]. In particular, Huang [25] quantified portfolio return and risk by the expected value
and variance based on credibility measure, and proposed two new fuzzy mean-variance models
for portfolio selection with fuzzy returns. In addition, Huang [22] presented two types of fuzzy
chance-constrained models to find optimal portfolio. However, so far, there is no research on
fuzzy portfolio selection taking semivariance as risk measure. For the similar reasons discussed in
stochastic portfolio selection, when the membership functions of fuzzy returns are asymmetric, the
fuzzy variance may also become a deficient risk measure because it also eliminates both low and
high return extremes. Since semivariance is a direct, clear, comparatively simple and very popular
measure to gauge downside risk, in this paper, we will extend stochastic mean-semivariance idea
to fuzzy environment. (page 1102)
A12-c95 Pankaj Gupta, Mukesh Kumar Mehlawat, Anand Saxena, Asset portfolio optimization using fuzzy
mathematical programming, INFORMATION SCIENCES, 178(2008), pp. 1734-1755. 2008
http://dx.doi.org/10.1016/j.ins.2007.10.025
Carlsson et al. [A12] introduced a possibilistic approach for selecting portfolios with the highest
utility value under the assumption that the returns of assets are trapezoidal fuzzy numbers. Wang et
al. [33] and Zhang and Wang [37] discussed the general weighted possibilistic portfolio selection
problems. Lacagnina and Pecorella [14] developed a multistage stochastic soft constraints fuzzy
program with recourse in order to capture both uncertainty and imprecision as well as to solve a
portfolio management problem. (page 1735)
A12-c94 Yao Shaowen; Lan Zhang, Fuzzy environment, safety standards based on the credibility of the portfolio
model, STATISTICS AND DECISION, 21(2008), pp. 23-25 (in Chinese). 2008
http://www.cqvip.com/qk/95927x/2008021/28676226.html
A12-c93 YAO Shao-wen, Portfolio Selection Model Based on Information Entropy Risk Measure in Fuzzy Environment, JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY (SOCIAL SCIENCES EDITION),
10(2008), number 6, pp. 59-61 (in Chinese). 2008
http://d.wanfangdata.com.cn/Periodical_bjlgdxxb-shkxb200806014.aspx
2007
105
A12-c92 CHEN Wei; ZHANG Run-tong; YANG Ling, A Fuzzy Portfolio Selection Decision Methodology
under Borrowing Constraint, JOURNAL OF BEIJING JIAOTONG UNIVERSITY SOCIAL SCIENCES
EDITION, 6(2007), number 1, pp. 67-70 (in Chinese). 2007
http://www.cqvip.com/qk/87426a/2007001/24080096.html
A12-c91 A Chun-xiang; LIU San-yang, A Hybrid Intelligent Algorithm Approach to Selecting Portfolios Based
on Credibility Distribution, MATHEMATICS IN PRACTICE AND THEORY, 37(2007), number 11, pp (in
Chinese). 2007
http://d.wanfangdata.com.cn/Periodical_sxdsjyrs200711003.aspx
A12-c90 Xiaoxia Huang, A new perspective for optimal portfolio selection with random fuzzy returns, INFORMATION SCIENCES, 177 (23), pp. 5404-5414. 2007
http://dx.doi.org/10.1016/j.ins.2007.06.003
Since the security market is so complex, in many situations security returns cannot always be accurately predicted from historical data. They are beset with ambiguity and vagueness. To deal with
this problem, researchers have made use of fuzzy set theory [45,46]. Assuming that the returns are
fuzzy, a great deal of work has been dedicated to extrapolating traditional mean-variance models:
for example, Watada [43], Tanaka and Guo [40,41], Parra et al. [37], Carlsson et al. [A12], Zhang
and Nie [47], Amelia, Blanca, Mar and Maria [3], Lacagnina and Pecorella [25], etc. (page 5405)
A12-c89 Zhang, W.-G., Wang, Y.-L., Notes on possibilistic variances of fuzzy numbers, APPLIED MATHEMATICS LETTERS, 20 (11), pp. 1167-1173. 2007
http://dx.doi.org/10.1016/j.aml.2007.03.002
Zhang and Nie [5] presented the notions of lower and upper possibilistic variances and covariances of fuzzy numbers based on [3]. Furthermore, Carlsson et al. [A12] and Zhang et al. [7,8]
introduced their applications to portfolio selection problems under the assumption that the returns
of assets are fuzzy numbers. (page 1167)
A12-c88 Xiaoxia Huang, Portfolio selection with fuzzy returns, JOURNAL OF INTELLIGENT AND FUZZY
SYSYTEMS, 18 (4), pp. 383-390. 2007
By giving possibility degrees, they proposed a fuzzy probability and identied two possibility upper and lower- distributions to security returns. Carlsson et al. [A12] modelled the rates of return
on securities by possibility distribution, and further found the optimum portfolio by maximizing
utility based on the expected return and variance of the portfolio. (page 383)
A12-c87 Xiaoxia Huang, Two new models for portfolio selection with stochastic returns taking fuzzy information, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 180 (1): 396-405 JUL 1 2007
http://dx.doi.org/10.1016/j.ejor.2006.04.010
In the former direction, for example, we have mean-lower-partial- moments model [7], meanabsolute deviation model [24], maximizing probability model [27], and different types of meanvariance models [1,4,9,28] and minimax models [2,5,6]; in the latter direction, we have fuzzy goal
programming model [22], admissible efficient portfolio selection model [29], possibility approach
model with highest utility score [A12], upper and lower exponential possibility distribution based
model [25], and model with fuzzy probabilities [26]. (pages 396-397)
A12-c86 Zhang, W.-G., Wang, Y.-L., Chen, Z.-P., Nie, Z.-K., Possibilistic mean-variance models and efficient
frontiers for portfolio selection problem, INFORMATION SCIENCES, 177 (13), pp. 2787-2801. 2007
http://dx.doi.org/10.1016/j.ins.2007.01.030
Ida [14] investigated portfolio selection problem with interval and fuzzy coeffcients, two kinds of
effcient solutions are introduced: possibly effcient solution as an optimistic solution, necessarily
effcient solution as a pessimistic solution. Carlsson et al [A12] introduced a possibilistic approach
for selecting portfolios with the highest utility value under the assumption that the returns of assets
are trapezoidal fuzzy numbers. (page 2778)
106
A12-c85 Zhang, W.-G., Possibilistic mean-standard deviation models to portfolio selection for bounded assets,
APPLIED MATHEMATICS AND COMPUTATION, 189 (2), pp. 1614-1623. 2007
http://dx.doi.org/10.1016/j.amc.2006.12.080
Carlsson et al. [A12] introduced a possibilistic approach to selecting portfolios with highest utility
score under the assumption that the returns of assets are trapezoidal fuzzy numbers. Zhang and
Wang [26] and Zhang et al. [27] discussed the portfolio selection problem based on the (crisp)
possibilistic mean and variance when short sales are not allowed on all risky assets. In this paper,
we will discuss the portfolio selection problem for bounded assets based on the lower and upper
possibilistic means and variances of fuzzy numbers. (page 1615)
A12-c84 Smimou, K., Bector, C.R., Jacoby, G., A subjective assessment of approximate probabilities with a
portfolio application, RESEARCH IN INTERNATIONAL BUSINESS AND FINANCE, 21 (2), pp. 134160. 2007
http://dx.doi.org/10.1016/j.ribaf.2005.12.002
A recognition of the important role of uncertainty in dealing with problems of organized complexity began another stage that is characterized by the emergence of several new theories (fuzzy set
theory, possibility theory, and rough set theory) of uncertainty, different from probability theory,
which is capable of capturing only one of several types of uncertainty (Zadeh (1968, 1984, 1986),
Carlsson et al. (2002), Bezdek (1994), Ralescu (1995), Schmeidler (1989)). We now combine
fuzzy sets and fuzzy probabilities results in continuous spaces as follows. (page 148)
A12-c83 Vercher E, Bermudez JD, Segura JV, Fuzzy portfolio optimization under downside risk measures,
FUZZY SETS AND SYSTEMS, 158 (7): 769-782 APR 1 2007
http://dx.doi.org/10.1016/j.fss.2006.10.026
We shall illustrate the above results by a simple example from [A12] with three assets whose
returns are the following trapezoidal fuzzy numbers: (page 774)
A12-c82 Lin PC, Chen JS, FuzzyTree crossover for multi-valued stock valuation, INFORMATION SCIENCES,
177 (5): 1193-1203 MAR 1 2007
http://dx.doi.org/10.1016/j.ins.2006.08.017
The various soft computing technologies do provide alternative solutions to nancial problems. For
exam- ple, fuzzy logic is used as a possibility distribution of portfolios [A12,17,19], or for the
credit analysis of loans [5,8]. Neural networks are used to predict nancial distress [2,3,6]. (page
1194)
2006
A12-c81 Guohua Chen, Shou Chen, Yong Fang, Shouyang Wang, A Possibilistic Mean VaR Model for Portfolio
Selection, ADVANCED MODELING AND OPTIMIZATION, Volume 8, Number 1, pp. 99-107. 2006
http://www.ici.ro/camo/journal/vol8/v8a8.pdf
By using the fuzzy decision principle, Ostermark [11] proposed a dynamic portfolio management
model. Watada [14] presented another type of portfolio selection model based on the fuzzy decision principle. The model is directly related to the mean-variance model, where the goal rate for an
expected return and the corresponding risk described by logistic membership functions. Tanaka et
al [13] give a special formulation of fuzzy decision problems by the probability events. Carlsson
et al [A12] studied the portfolio selection model in which the rate of return of security follows
the possibility distribution. This paper is organized as follows. In Section 2, we introduce briefly
the mean downside-risk framework and present a mean VaR portfolio selection model with transaction costs. In Section 3, we introduce briefly the possibility theory and propose a possibilistic
mean VaR portfolio selection model. (page 100)
A12-c80 Xiaoxia Huang, Fuzzy chance-constrained portfolio selection, APPLIED MATHEMATICS AND
COMPUTATION, 177 (2): 500-507 JUN 15 2006
http://dx.doi.org/10.1016/j.amc.2005.11.027
107
With the introduction of fuzzy set theory by Zadeh in 1965 [32], scholars began to realize that
they could employ fuzzy set theory to manage portfolio in another type of uncertain environment
called fuzzy environment. For example, Tanaka and Guo [27], Tanaka et al. [28], Parra et al. [24]
and Carlsson et al. [A12] replaced probability distributions of returns of (page 500)
2005
A12-c79 Zdenek Zmeskal, Value at risk methodology of international index portfolio under soft conditions
(fuzzy-stochastic approach), INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS, 14(2005) 263275. 2005
http://dx.doi.org/10.1016/j.irfa.2004.06.011
Hybrid fuzzy-stochastic methodology has been studied and explained previously (see, e.g., Carlsson et al., 2002; Dubois & Prade, 1980; Kacprzyk & Fedrizzi, 1988; Kruse & Meyer, 1987; Liu
& Kao, 2002; Luhandjula, 1996; Puri & Ralescu, 1986; Sakawa et al., 2003; Viertl, 1996; Wang
& Qiao, 1993; Wu, 2003; Yoshida, 2003; Zmeskal, 2001). (page 268)
in proceedings and edited volumes
2015
A12-c65 M V Petrova, E S Volkova, Fuzzy programming methods to selecting portfolios, In: 2015 XVIII
International Conference on Soft Computing and Measurements (SCM), (ISBN 978-1-4673-6960-2) pp.
264-266. 2015
http://dx.doi.org/10.1109/SCM.2015.7190478
2014
A12-c64 Leandro Maciel, Fernando Gomide, Rosangela Ballini, Minimum Variance Fuzzy Possibilistic Portfolio, XVII SEMEAD Seminarios em Administracao. Sao Paulo, Brasil, October 29-31, 2014, pp. 1-14,
ISSN: 2177-3866. 2014
http://semead6.tempsite.ws/17semead/resultado/trabalhosPDF/976.pdf
A possibilistic approach to select portfolios was suggested by (Carlsson, Fullér, & Majlender,
2002) with highest utility score under assumptions that the returns of assets are trapezoidal fuzzy
numbers and short sales are not allowed on all risky assets. In (Zhang, Zhang, & Xiao, 2009) was
dealt with the same problem but proposed a sequential minimal optimization algorithm to obtain
the optimal portfolio. (pages 1-2)
A12-c63 Zhongfeng Qin, Lei Xu, Mean-Variance Adjusting Model for Portfolio Selection Problem with Fuzzy
Random Returns, In: Proceedings of the Seventh International Joint Conference on Computational Sciences
and Optimization. IEEE, [ISBN 978-1-4799-5371-4, pp. 83-87. 2014
http://dx.doi.org/10.1109/CSO.2014.147
2013
A12-c62 Meng-rong Sun, Wei Chen, An artificial bee colony algorithm for fuzzy portfolio model with concave transaction costs, 2013 International Conference on Management Science and Engineering (ICMSE),
[ISBN 978-1-4799-0473-0 ], pp. 400-405. 2013
http://dx.doi.org/10.1109/ICMSE.2013.6586312
A12-c61 Cheng Sri, Wei Cren, OPF: A novel framework for fuzzy portfolio selection, In: Proceedings of the
2013 International Conference on Management Science and Engineering (ICMSE), IEEE, [ISBN 978-14799-0473-0 ], pp. 1739-1744. 2013
http://dx.doi.org/10.1109/ICMSE.2013.6586501
108
A12-c60 Rupak Bhattacharyya, POSSIBILISTIC SHARPE RATIO BASED NOVICE PORTFOLIO SELECTION MODELS, in: Rupak Bhattacharyya and Arup Kr. Bhaumik eds., Computer Science & Information
Technology, National Conference on Advancement of Computing in Engineering Research (ACER 13),
MArch 22-23, 2013, Krishnagar, West Bengal, INDIA, [ISBN 978-1-921987-11-3], pp. 33-45. 2013
http://dx.doi.org/10.5121/csit.2013.3204
Ida [33] investigates portfolio selection problem with interval and fuzzy coefficients, two kinds of
efficient solutions are introduced: possibly efficient solution as an optimistic solution, necessity
efficient solution as a pessimistic solution. Carlsson et al. [A12] introduce a possibilistic approach
for selecting portfolios with the highest utility value under the assumption that the returns of assets
are trapezoidal fuzzy numbers. (page 34)
2012
A12-c59 Enriqueta Vercher, José D Bermúdez, Fuzzy Portfolio Selection Models: A Numerical Study, in:
Financial Decision Making Using Computational Intelligence, Springer Optimization and Its Applications
Ser, [ISBN 978-1-4614-3773-4], pp. 253-280. 2012
http://dx.doi.org/10.1007/978-1-4614-3773-4_10
A12-c58 Carlos Cruz, Ricardo C Silva, José Luis Verdegay Solving Real-World Fuzzy Quadratic Programming
Problems by a Parametric Method 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, July 9-13, 2012, Catania, Italy, Communications in Computer and Information Science, vol. 299, Springer, [ISBN: 978-3-642-31718-7], pp.
102-111. 2012
http://dx.doi.org/0.1007/978-3-642-31718-7_11
A12-c57 You Surong, Analysis of expected utility toward fuzzy random wealth and its application in portfolio
selection, 9th International Conference on Fuzzy Systems and Knowledge Discovery, May 29-31, 2012,
Chongqing, China, [ISBN 978-1-4673-0025-4], pp. 433-437. 2012
http://dx.doi.org/10.1109/FSKD.2012.6233875
A12-c56 I Georgescu, J Kinnunen, A Mixed Portfolio Selection Problem, 9th International Conference on
Distributed Computing and Artificial Intelligence, March 28-30, 2012, Salamanca, Spain, Advances in
Intelligent and Soft Computing, vol. 151/2012, Springer, [ISBN: 978-3-642-28764-0], pp. 95-102. 2012
http://dx.doi.org/10.1007/978-3-642-28765-7_13
A12-c55 I Georgescu, J Kinnunen, A Generalized 3-Component Portfolio Selection Model, 11th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (AIKED ’12),
February 22-24, 2012, Cambridge, England, [ISBN: 978-1-61804-068-8], pp. 142-147. 2012
http://www.wseas.us/e-library/conferences/2012/CambridgeUK/AIKED/AIKED-22.pdf
2011
A12-c54 Xiaoxia Huang, Mean-Risk Model for Hybrid Portfolio Selection with Fuzziness and Randomness,
5th International Conference on Convergence and Hybrid Information Technology, September 22-24, 2011,
Daejeon, Korea, Lecture Notes in Computer Science, vol. 6935/2011, Springer, [ISBN: 978-3-642-240812], pp. 221-228. 2011
http://dx.doi.org/10.1007/978-3-642-24082-9_27
Therefore, many scholars began to use fuzzy variables to reflect the experts’ knowledge in the prediction of security returns and studied fuzzy portfolio selection problem. For example, Carlsson et
al [A12], Bilbao-Terol et al [1] and Huang [4] extended mean-variance idea to fuzzy environment.
(page 221)
109
A12-c53 Surong You, Qiao Lei, Analysis of Expected Utility toward Fuzzy Wealth and Applications in Portfolio
Selection, Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), July 2628, 2011, Shanghai, China, [ISBN: 978-1-61284-180-9], pp. 791-795. 2011
http://dx.doi.org/10.1109/FSKD.2011.6019760
There also exists the problem of how to define the expected utility and select an optimal portfolio from expected utility maximization. To the mean value of a fuzzy number with application in financial analysis, Carlsson ([A12]) applied possibilistic mean value and variance to solve
Markowitz meanvariance portfolio selection model under the assumption that the returns of assets
were modeled by possibility distribution. (page 791)
A12-c52 Takashi Hasuike, Hideki Katagiri, A Robust Portfolio Selection Problem based on a Confidence Interval with Investor’s Subjectivity, 2011 IEEE International Conference on Fuzzy Systems, June 27-30, 2011,
Taipei, Taiwan, [ISBN: 978-1-4244-7316-8], pp. 531-536. 2011
http://dx.doi.org/10.1109/FUZZY.2011.6007371
Until now, there are some basic researches under various uncertainty conditions with respect to
portfolio selection problems (Bilbao-Terol et al. [4], Carlsson et al. [5], Guo and Tanaka [10],
Hasuike et al. [11], Huang [12, 13], Inuiguchi et al. [14, 15], Katagiri et al. [17, 18], Tanaka et
al. [23, 24], Watada [25]). However, there are few models considering the confidential interval
with investor’s subjectivity. Furthermore, there are no researches which are analytically extended
and explicitly solved these types of portfolio selection problems. Therefore, we develop the exact
solution algorithm for the proposed robust portfolio selection problem. (page 531)
A12-c51 Irina Georgescu, Jani Kinnunen, Multidimensional risk aversion with mixed parameters, In: 6th
IEEE International Symposium on Applied Computational Intelligence and Informatics, May 19-21, 2011,
Timisoara, Romania, [ ISBN: 978-1-4244-9108-7], pp. 63-66. 2011
http://dx.doi.org/10.1109/SACI.2011.5872974
A12-c50 Irina Georgescu, Mixed risk aversion: Probabilistic and possibilistic aspects, 2011 IEEE 9th International Symposium on Applied Machine Intelligence and Informatics (SAMI), January 27-29, 2011,
Smolenice, Slovakia, [ISBN: 978-1-4244-7429-5], pp. 279-283. Paper 11883948. 2011
http://dx.doi.org/10.1109/SAMI.2011.5738889
2010
A12-c49 B.R. Petreska; T.D. Kolemisevska-Gugulovska, A Fuzzy Rate-of-Return Based Model for Portfolio
Selection and Risk Estimation, 2010 IEEE International Conference on Systems, Man and Cybernetics,
SMC 2010, October 10-13, 2010, Istanbul, Turkey, [ISBN 978-142446588-0], pp. 1871-1877. 2010
http://dx.doi.org/10.1109/ICSMC.2010.5642278
A12-c48 Irina Georgescu, A possibilistic Pratt theorem, 8th International Symposium on Intelligent Systems
and Informatics (SISY), 10-11 September 2010, Subotica, Serbia, [ISBN 978-1-4244-7394-6], pp. 193196. 2010
http://dx.doi.org/10.1109/SISY.2010.5647299
A12-c47 Irina Georgescu, Jani Kinnunen, Multidimensional Possibilistic Risk Aversion, 11th International
Symposium on Computational Intelligence and Informatics (CINTI), November 18-20, 2010, Budapest,
Hungary, [ISBN 978-1-4244-9279-4], pp. 163-168. 2010
http://dx.doi.org/10.1109/CINTI.2010.5672253
A12-c46 Ying-yu He, Portfolio selection model with transaction costs based on fuzzy information, 2nd IEEE
International Conference on Information and Financial Engineering (ICIFE), 17-19 Sept. 2010, Chongqing,
China, [ISBN 978-1-4244-6927-7], pp. 148-152. 2010
http://dx.doi.org/10.1109/ICIFE.2010.5609270
Lacagnina and Pecorella [10] developed a multistage stochastic soft constraints fuzzy program
with recourse in order to capture both uncertainty and imprecision as well as to solve a portfolio
management problem. In Tanaka and Guo [17], Tanaka et al. [18] the possibility theory is applied
110
to handle uncertainty and solve portfolio optimization problem. Carlsson et al. [A12 ] introduced
a possibilistic approach for selection portfolio with highest utility value under the assumption that
the returns of assets are trapezoidal fuzzy numbers. (page 148)
A12-c45 R C Silva, J L Verdegay, A Yamakami, A parametric convex programming approach applied to portfolio selection problems with fuzzy costs, 2010 IEEE International Conference on Fuzzy Systems. Barcelona,
Spain, July 18-25, 2010, [ ISBN 978-1-4244-6919-2], pp. 1-6. 2010
http://dx.doi.org/10.1109/FUZZY.2010.5584441
The risk investment analysis, first introduced by Markowitz [13], is an important research field
in the modern finance. However, vagueness, approximate values and lack of precision are very
frequent in that context, and that convex programming problems have shown to be extremely
useful to solve a variety of portfolio models. In the following we will present a general solution
approach for fuzzy convex programming problems that, if needed, can be easily particularized to
solve more specific portfolio models ([12], [16], [A12]). In any case, it is important to emphasize
that the aim of this work is not to solve portfolio models. It was considered only for the sake of
illustrating the proposed fuzzy approach, which in fact is the main goal of this contribution. (page
2)
A12-c44 Ruo-ning Xu, Xiao-yan Zhai, Fuzzy Portfolio Model with Transaction Cost Based on Downside Risk
Measure, in: Bing-yuan Cao, Guo-jun Wang, Si-zong Guo, Shui-li Chen eds., Fuzzy Information and
Engineering 2010, Advances in Intelligent and Soft Computing, vol. 78/2010, Springer, [ISBN 978-3-64214879-8], pp. 377-384. 2010
http://www.springerlink.com/content/086l476q345x1573/
A12-c43 Irina Georgescu; Jani Kinnunen, Credibility measures in portfolio analysis, in: Mikael Collan ed.,
Proceedings of the 2nd International Conference on Applied Operational Research - ICAOR’10, Lecture
Notes in Management Science, vol. 2/2010, August 25-27, 2010 Turku, Finland, [ISBN: 978-952-12-24140], pp. 6-18. 2010
A12-c42 Takashi Hasuike and Hiroaki Ishii, Mathematical Approaches for Fuzzy Portfolio Selection Problems
with Normal Mixture Distributions, in: Weldon A. Lodwick and Janusz Kacprzyk eds., Fuzzy Optimization:
Recent Advances and Applications, Studies in Fuzziness and Soft Computing, vol. 254/2010, Springer,
[ISBN 978-3-642-13934-5], pp. 407-423. 2010
http://dx.doi.org/10.1007/978-3-642-13935-2_19
Until now, there is a body of research under various uncertainty conditions with respect to portfolio
selection problems (Bilbao-Terol and Perez-Gladish [2], Carlsson et al. [3], Guo and Tanaka
[6], Huang [10, 11], Inuiguchi et al. [12, 13], Katagiri et al. [14, 15], Tanaka et al. [24, 25],
Watada [26]). We also proposed some portfolio models with both randomness and fuzziness [7, 8,
9]. However, there are few models considering both normal mixture distribution and ambiguity,
simultaneously. Furthermore, there are no studies which are analytically extended and solved
these types of portfolio selection problems. In this chapter, we propose more extensional portfolio
selection models including the general random distribution with fuzzy factors and develop the
efficient solution method. (page 408)
A12-c41 Xiaoxia Huang, Mean-Variance Models for International Portfolio Selection with Uncertain Exchange
Rates and Security Returns, 2010 International Conference on Information Science and Applications (ICISA),
21-23 April 2010, Seoul, South Korea, [ISBN 978-1-4244-5941-4], pp.1-7. 2010
http://dx.doi.org/10.1109/ICISA.2010.5480377
When handling the uncertainty of security returns, traditionally, security returns were assumed to
be random. Since the security market is complex, it is found that future security returns are hard to
be always well reflected by the historical data. With the introduction and development of fuzzy set
theory, scholars began to use fuzzy set theory and credibility theory to manage domestic portfolios
with returns containing fuzzy uncertainty. In the area of domestic fuzzy portfolio selection, Carlsson et al. [4], Bilbao-Terol et al. [2], Gupta, Mehlawat and Saxena [12], etc. proposed different
possibilistic mean-variance models. (page 2)
111
A12-c40 José Manuel Brotons, Bond Management: An Application to the European Market, International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU
2010), June 28 - July 2, 2010, Dortmund, Germany, in: E. Hüllermeier, R. Kruse, and F. Hoffmann (Eds.):
IPMU 2010, Part II, Communications in Computer and Information Science, vol. 81(2010), [ISBN 978-3642-14057-0], pp. 316-323. 2010
http://dx.doi.org/10.1007/978-3-642-14058-7_32
2009
A12-c39 J M Brotons, Return risk map in a fuzzy environment, 4th International Conference on Intelligent
Systems and Knowledge Engineering (ISKE 2009), November 27-28, 2009, Hasselt, Belgium, [ISBN:
978-981-4295-05-5], pp. 106-111. 2009
A12-c36 Y. Zhang, X. Li, H. Wong, and L. Tan, Fuzzy multi-objective portfolio selection model with transaction
costs, in: Proceedings of the 18th international Conference on Fuzzy Systems Jeju Island, Korea, August
20 - 24, 2009, IEEE Press, Piscataway, NJ, [ISBN 978-1-4244-3596-8], pp. 273-278. 2009
A12-c38 Takashi Hasuike and Hiroaki Ishii, A Type-2 Fuzzy Portfolio Selection Problem Considering Possibility Measure and Crisp Possibilistic Mean Value, in: J. P. Carvalho, D. Dubois, U. Kaymak and J. M. C.
Sousa eds., Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and
2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009,
[ISBN 978-989-95079-6-8], pp. 1120-1124. 2009
www.eusflat.org/publications/proceedings/IFSA-EUSFLAT_2009/
pdf/tema_1120.pdf
A12-c37 Hasuike Takashi and Katagiri Hideki, Strict Solution Method for Linear Programming Problem with
Ellipsoidal Distributions under Fuzziness. In: 5th International Workshop on Computational Intelligence &
Applications IEEE SMC Hiroshima Chapter (WCIA 2009), Hiroshima, Japan, November 10-11, 2009, pp.
59-64. 2009
http://eprints.lib.okayama-u.ac.jp/19638/1/IWCIA2009_A1201.pdf
A12-c36 T. Hasuike; H.Katagiri, H. Ishii, Multiobjective random fuzzy portfolio selection problems based on
CAPM, Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics , Oct.
11-14, 2009, San Antonio, TX USA [ISBN 978-1-4244-2793-2 ], art. no. 5346239, pp. 1316-1321. 2009
http://dx.doi.org/10.1109/ICSMC.2009.5346239
Until now, there are some basic researches under various uncertainty conditions with respect to
portfolio selection problems (Bilbao-Terol et al. [2], Carlsson et al. [A12], Guo and Tanaka [6],
Huang [9, 10], Inuiguchi et al. [11, 12], Katagiri et al. [13, 14], Tanaka et al. [27], Watada [28]).
We also proposed some portfolio models with both randomness and fuzziness [7, 8]. However,
there are few models considering both general random distributions and fuzziness, simultaneously.
Furthermore, there are no researches which are analytically extended and solved these types of
portfolio selection problems. (pages 1316-1317)
A12-c35 Ruo-ning Xu and Xiao-yan Zhai, Fuzzy Model for Portfolio Selection with Transaction Cost, in:
Bingyuan Cao, Tai-Fu Li, Cheng-Yi Zhang eds., Fuzzy Information and Engineering Volume 2, Advances
in Soft Computing, vol. 62/2009, [ISBN 978-3-642-03663-7], pp. 1365-1372. 2009
http://dx.doi.org/10.1007/978-3-642-03664-4_145
A12-c34 W. Chen; S. Tan, Fuzzy portfolio selection problem under uncertain exit time, IEEE International
Conference on Fuzzy Systems, art. no. 5277181, pp. 550-554. 2009
http://dx.doi.org/10.1109/FUZZY.2009.5277181
A12-c33 T. Hasuike; H. Ishii, A portfolio selection problem with type-2 fuzzy return based on possibility
measure and interval programming, IEEE International Conference on Fuzzy Systems, art. no. 5277134,
pp. 267-272. 2009
http://dx.doi.org/10.1109/FUZZY.2009.5277134
112
In order to compare our proposed models with other models for portfolio selection problems, let
us consider a numerical example based on the data of securities on the Tokyo Stock Exchange.
In this paper, we compare our proposed model (11) based on the optimistic satisfaction index in
Section 3 with Carlsson et al. model [2] and Vercher et al. model [26]. These problems are
formulated as the following form: (page 271)
A12-c32 Wei Chen; Ling Yang; Fasheng Xu, PSO-based possibilistc mean-variance model with transaction
costs, 2009 Chinese Control and Decision Conference, CCDC 2009, 17-19 June, 2009, Guilin, China, art.
no. 5195275, pp. 5993-5997. 2009
http://dx.doi.org/10.1109/CCDC.2009.5195275
Tanaka and Guo [8,9] proposed two kinds of portfolio selection models based on fuzzy probabilities and exponential possibility distributions, respectively. Carlsson and Fullér [A14] introduced
the notions of lower and upper possibilistic mean values of a fuzzy number, then proposed a possibilistic approach to selecting portfolios with highest utility score in [A12]. Huang [12] defined
semivariance of fuzzy variables and proposed mean-semivariance models for fuzzy portfolio selection. Chen [13] discuss the portfolio selection problem with investing constraints based on the
p ossibilistic theory. Moreover, Zhang [14] discussed the portfolio selection problem based on the
lower, upper possibilistic means and possibilistic variances. (page 5993)
A12-c30 Wei Chen, Two Possibilistic Mean-Variance Models for Portfolio Selection, in: Bingyuan Cao, Tai-Fu
Li, Cheng-Yi Zhang eds., Fuzzy Information and Engineering Volume 2, Advances in Soft Computing, vol.
62/2009, [ISBN 978-3-642-03663-7], pp. 1035-1044. 2009
http://dx.doi.org/10.1007/978-3-642-03664-4_111
A12-c29 Z. Zmeškal, D. Dluhosova, Multiple attribute evaluation of company financial level applying soft
methodology (fuzzy approach), Risk Management Conference 2009, Venice, June 22-24, 2009, pp. 1-9.
2009
http://www.finanzafirenze.org/IRMC/files/
A12-c28 Ying Liu; Fang-Fang Hao, The K-T conditions for portfolio selection problem in fuzzy decision system, 2009 International Conference on Machine Learning and Cybernetics, Volume 2, 12-15 July 2009, pp.
860-865. 2009
http://dx.doi.org/10.1109/ICMLC.2009.5212386
A12-c27 Yong Fang, Ruiwen Xue, Shouyang Wang, A Portfolio Optimization Model with Fuzzy Liquidity
Constrains, International Joint Conference on Computational Sciences and Optimization, vol. 1, pp. 472476. 2009
http://doi.ieeecomputersociety.org/10.1109/CSO.2009.362
A12-c26 Ruo-ning Xu, Xiao-yan Zhai, A Portfolio Selection Problem with Fuzzy Return Rate, in: Fuzzy
Information and Engineering, Advances in Soft Computing series, vol. 54/2009, Springer, [ISBN 978-3540-88913-7], pp. 520-525. 2009
http://dx.doi.org/10.1007/978-3-540-88914-4_64
A12-c25 B. Liu, Machine Scheduling Problem, in: Theory and Practice of Uncertain Programming, Studies in
Fuzziness and Soft Computing series, vol. 239/2009, pp. 167-177. 2009
http://dx.doi.org/10.1007/978-3-540-89484-1_12
2008
A12-c24 G H Chen, S Chen, Y Fang, S Y Wang, A possibilistic mean variance portfolio selection model, 2nd
International Conference on Management Science and Engineering Management, November 3-8, 2008,
Chongqing, China, [ISBN: 978-1-84626-002-5], pp. 365-372. 2008
A12-c23 G H Chen, X L Luo, A Possibilistic Mean Absolute Deviation Portfolio Selection Model, 3rd Annual
Conference on Fuzzy Information and Engineering, December 5-10, 2008, Haikou, China, [ISBN: 978-3540-88913-7], pp. 386-396. 2008
113
A12-c22 T. Hasuike, H. Ishii, Robust programming problems based on the mean-variance model including
uncertainty factors, AIP Conference Proceedings, IAENG TRANSACTIONS ON ENGINEERING TECHNOLOGIES VOLUME I: Special Edition of the International MultiConference of Engineers and Computer
Scientists 2008, vol. 1089, pp. 224-235. 2008
http://dx.doi.org/10.1063/1.3078129
A12-c21 Takashi Hasuike and Hiroaki Ishii, Portfolio Selection Problems with Normal Mixture Distributions
Including Fuzziness, Fourth International Workshop on Computational Intelligence & Applications IEEE
SMC Hiroshima Chapter, Hiroshima, Japan, December 10-11, 2008, pp. 65-70. 2008
http://eprints.lib.okayama-u.ac.jp/14796/1/IWCIA10-07-PS080003.pdf
Until now, there are some basic researches under various uncertainty conditions with respect to
portfolio selection problems (Bilbao-Terol and Perez-Gladish [2], Carlsson et al. [A12], Guo and
Tanaka [6], Huang [10, 11], Inuiguchi et al. [12, 13], Katagiri et al. [14, 15], Tanaka et al. [23, 24],
Watada [25]). We also proposed some portfolio models with both randomness and fuzziness [7, 8,
9]. However, there are few models considering both normal mixture distribution and ambiguity,
simultaneously. Furthermore, there are no researches which are analytically extended and solved
these types of portfolio selection problems. (page 65)
A12-c20 W. Chen, A possibilistic portfolio model with borrowing and bounded constraints and its application,
Chinese Control and Decision Conference, CCDC 2008, Yantai, China, July 2-4, 2008, art. no. 4597424,
pp. 804-808. 2008
http://dx.doi.org/10.1109/CCDC.2008.4597424
Carlsson [A12] introduced a possibilistic approach to selecting portfolios with highest utility score
under the assumption that the returns of assets are trapezoidal fuzzy numbers. (page 804)
A12-c19 Takashi Hasuike and Hiroaki Ishii, Robust Mean-Variance Portfolio Selection Problem Including
Fuzzy Factors, Proceedings of the International MultiConference of Engineers and Computer Scientists
2008 Vol II, IMECS 2008, 19-21 March, 2008, Hong Kong, pp. 1865-1870. 2008
http://www.iaeng.org/publication/IMECS2008/IMECS2008_pp1865-1870.pdf
2007
A12-c18 J. Zhang and W. Tang and C. Wang and R. Zhao, Fuzzy Dynamic Portfolio Selection for Survival, in:
Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues, Lecture Notes in Computer Science, vol. 4681, Springer, pp. 34-45. 2007
http://dx.doi.org/10.1007/978-3-540-74171-8_5
With the introduction of fuzzy set theory by Zadeh [18] in 1965, researchers began to realize that
they could employ fuzzy set theory to manage portfolio in another type of uncertain environment
called fuzzy environment. Since then a lot of researchers began to study the portfolio selection
problem, such as Carlsson et al [A12], Inuiguchi and Tanino [5], Léon et al [6] and Tanaka and
Guo [15]. (page 34)
A12-c17 Silva, Ricardo C.; Verdegay, Jose L.; Yamakami, Akebo, Two-phase method to solve fuzzy quadratic
programming problems, IEEE International Fuzzy Systems Conference (FUZZ-IEEE 2007), 23-26 July
2007, pp.1-6. 2007
http://dx.doi.org/10.1109/FUZZY.2007.4295501
Provided that the risk investment analysis, first introduced by Markowitz [5], is an important research field in the modem finance, that vagueness, approximate values and lack of precision are
very frequent in that context, and that quadratic programming problems have shown to be extremely useful to solve a variety of portfolio models, in the following we will present a general
solution approach for fuzzy quadratic programming problems that, if needed, can be easily particularized to solve more specific portfolio models ([6], [7], [A12]. In any case it is important
to quote that the aim of this work is not to solve portfolio models, that here are only considered
for the sake of ilustratingthe fuzzy quadratic programming problems solution approach presented,
which in fact is the goal and main aim of this contribution. (page 2)
114
A12-c16 Wei Chen, Runtong Zhang, Wei-Guo Zhang and Yong-Ming Cai, A Fuzzy Portfolio Selection Methodology Under Investing Constraints, in: B.-Y. Cao, ed., Fuzzy Information and Engineering, Proceedings of
the Second International Conference of Fuzzy Information and Engineering (ICFIE), Dalian, China, Advances in Soft Computing Series, Vol. 40, Springer, [ISBN 978-3-540-71440-8] pp. 564-572 . 2007
http://dx.doi.org/10.1007/978-3-540-71441-5_61
A12-c15 Po-Chang Ko, Ping-Chen Lin, Yao-Te Tsai, A Nonlinear Stock Valuation Using a Hybrid Model of
Genetic Algorithm and Cubic Spline, In: Proceedings of the Second International Conference on Innovative
Computing, Information and Control, 2007 (ICICIC ’07), September 5-7, 2007, Kumamoto, Japan, pp. 1-4.
2007
http://dx.doi.org/10.1109/ICICIC.2007.58
There are several computational intelligence (CI) technologies do give alternative solutions to
financial issues. For instance, artificial neural network [7] and evolutionary computation (GA,
PSO) [8] are used to predict financial distress. Fuzzy logic is used as a possibility distribution of
portfolios [A12]. Genetic programming is applied to option hedging [10] and foreign exchange
market forecasting [11]. However, fewer studies had used CI techniques for stock valuation. (page
1)
A12-c14 Takashi Hasuike, Hiroaki Ishii, Portfolio Selection Problems Considering Fuzzy Returns of Future
Scenarios, In: Proceedings of the Second International Conference on Innovative Computing, Information
and Control, 2007 (ICICIC ’07), September 5-7, 2007, Kumamoto, Japan, pp. 1-4. 2007
http://dx.doi.org/10.1109/ICICIC.2007.457
These mathematical programming problems with probabilities and possibilities are called stochastic programming problems and fuzzy programming problems, and there are some basic researches
considering them with respect to portfolio selection problems (Bilbao-Terol [2], Carlsson [A12],
Guo [4], Inuiguchi [5], Katagiri [6,7], Tanaka [13], Watada [14]). However, there are few models considering the scenario with fuzzy future returns and multi-objective programming problem.
Therefore in this paper, we proposed multi-objective fuzzy portfolio selection problems maximizing the total profits and develop the efficient solution method to find the global optimal solution of
such nonlinear programming problems. (page 1)
A12-c13 Lan, Yuping; Lv, Xuanli; Zhang, Weiguo A Linear Programming Model of Fuzzy Portfolio Selection
Problem, IEEE International Conference on Control and Automation, (ICCA 2007), May 30 2007-June 1
2007, Guangzhou, China, [ISBN: 978-1-4244-0818-4], pp. 3116-3118. 2007
http://dx.doi.org/10.1109/ICCA.2007.4376935
Carlsson [A12] introduced a possibilistic approach to selecting portfolios with highest utility
score. In this paper, we consider the portfolio selection problem based on the possibilistic mean
and variance under the assumption that the returns of assets are fuzzy numbers. (page 3116)
A12-c12 Bermudez, J.D.; Segura, J.V.; Vercher, E.; A fuzzy ranking strategy for portfolio selection applied to
the Spanish stock market, Fuzzy Systems Conference (FUZZ-IEEE 2007), 23-26 July 2007, London, UK,
pp. 787-790. 2007
http://dx.doi.org/10.1109/FUZZY.2007.4295466
Some fuzzy approaches to the portfolio selection problem have also been considered (see, for
instance, Carlsson et al. [A12], Leon et al. [12], Tanaka and Guo [17] and Watada [23]).
A12-c11 Zhang WG, Chen QQ, Lan HL, A portfolio selection method based on possibility theory, LECTURE
NOTES IN COMPUTER SCIENCE, vol 4041/2006, pp. 367-374. 2006
http://dx.doi.org/10.1007/11775096_34
Carlsson [A12] introduced a possibilistic approach to selecting portfolios with highest utility
score. (page 368)
A12-c10 Chen YJ, Liu YK, Chen JF, Fuzzy portfolio selection problems based on credibility theory, LECTURE
NOTES IN ARTIFICIAL INTELLIGENCE, vol. 3930(2006), pp. 377-386. 2006
115
http://dx.doi.org/10.1007/11739685_40
On the other hand, based on possibility theory [4] [18], a lot of researchers such as Carlsson, Fullér
and Majlender [A12], Inuiguchi and Tanino [6], Tanaka, Guo and Türksen [16] and León, Liern
and Vercher [8] have devoted their efforts to the fuzzy portfolio selection problem. (page 377)
A12-c9 Xiaoxia Huang, Credibility based fuzzy portfolio selection, IEEE International Conference on Fuzzy
Systems, July 16-21, Vancouver, Canada, art. no. 1681709, pp. 159-163. 2006
http://dx.doi.org/10.1109/FUZZY.2006.1681709
However, in real world, people can not always have access to precise and enough information
about security returns. In such situation, it is expected that fuzzy set theory can help solve the
problem. Many scholars such as Watada [34], Tanaka and Guo [30], Tanaka, Guo and Türksen
[31], Parra et al [27] and Carlsson et al [A12] have employed possibility measure to describe
security returns and extended Markowitz’s mean-variance modelling idea in different ways. Different from those researches in fuzzy portfolio selection, this paper will discuss portfolio selection
problem based on credibility measure.(page 159)
A12-c8 Chen, Y.-J., Liu, Y.-K. Portfolio selection in fuzzy environment, 2005 International Conference on
Machine Learning and Cybernetics, ICMLC 2005, 18 - 21 August 2005, Guangzhou, China, pp. 26942699. 2005
http://dx.doi.org/10.1109/ICMLC.2005.1527400
Since the development of possibility theory [4][18], a lot of researchers used possibility theory to
portfolio selection problem, such as Carlsson, Fullér and Majlender [A12], Inuiguchi and Tanino
[6], Tanaka, Guo and Türksen [16] and Len, Liern and Vercher [8]. It is well known that an
investor will decide the investment proportion to each investment type according to the return rate
of each investment type. But the investor cannot know the return rate well in the decision-making
stage. In order to estimate the return rate, the investor will take experts’ knowledge into account.
A fuzzy variable can reflect the experts’ knowledge easily. So it is reasonable to treat the return
rate of the investment type as a fuzzy variable. (page 2694)
A12-c7 Zhang, J.-P., Li, S.-M., Portfolio selection with quadratic utility function under fuzzy environment,
International Conference on Machine Learning and Cybernetics, ICMLC 2005, 18 - 21 August 2005,
Guangzhou, China, pp. 2529-2533. 2005
http://dx.doi.org/10.1109/ICMLC.2005.1527369
A12-c6 Z. Zmeskal, Soft Approach to Company Financial Level Multiple Attribute Evaluation, 21st International Conference on Mathematical Methods in Economics, September 10-12, 2003, Prague, Czech Republic, [ISBN: 978-80-213-1046-9], pp. 273-280. 2003
ISI:000261161100045
in books
A12-c3 Xiaoxia Huang, Portfolio Analysis: From Probabilistic to Credibilistic and Uncertain Approaches,
Studies in Fuzziness and Soft Computing, vol. 250/2010, Springer, [ISBN 978-3-642-11213-3]. 2010
http://dx.doi.org/10.1007/978-3-642-11214-0
A12-c2 Fang Yong, Lai Kin Keung, Wang Shouyang, Fuzzy Portfolio Optimization: Theory and Methods,
Lecture Notes in Economics and Mathematical Systems, vol. 609/2008, Springer, Berlin; Heidelberg,
[ISBN 978-3-540-77925-4 ], pp. 131-141. 2008
http://dx.doi.org/10.1007/978-3-540-77926-1
Carlsson, Fullér and Majlender (2002) assume that (i) each investor can assign a welfare, or utility,
score to competing investment portfolios on the expected return and risk of the portfolios; (ii)
the rates of return on securities are modelled by possibility distributions rather than probability
distributions. (page 10)
116
In traditional portfolio selection models, uncertainty is regarded as randomness. The probability
theory is very useful to deal with observable random events. Though often applied to deal with
uncertainty, the probabilistic approaches only partly capture the reality. In reality, although many
events are characterized as fuzzy by probabilistic approaches, they are not random events. Carlsson, Fullér and Majlender (2002) have found cases where assignment of probabilities is based
on very rough, subjective estimates and then the subsequent calculations are carried out with a
precision of two decimal points. The routine use of probabilities is not a good choice is shown.
The choice of the utility theory, which builds on a decision maker’s relative preferences for artificial lotteries, is a way to anchor portfolio selection in the von Neumann-Morgenstern axiomatic
utility theory. Carlsson, Fullér and Majlender showed that using the utility theory has proved to
be problematic: (i) utility measures cannot be validated inter-subjectively, (ii) the consistency of
utility measures cannot be validated across events or contexts for the same subject, (iii) utility
measures show discontinuities in empirical tests (as shown by Tversky), which should not happen
with rational decision makers if the axiomatic foundation is correct, and (iv) utility measures are
artificial and intuitive and, thus, hard to use. As the combination of probability assessments with
the utility theory has these well-known limitations, Tanaka and Guo (1999) have explored the use
of the possibility theory as a substituting conceptual framework. Carlsson, Fullér and Majlender
assume that (i) each investor can assign a welfare, or utility, score to competing investment portfolios based on the expected return and risk of the portfolios; and (ii) the rates of return on securities
are modeled by possibility distributions rather than probability distributions. They presented an
algorithm of complexity O(n3 ) for finding an exact optimal solution (in the sense of utility scores)
to the n-asset portfolio selection problem under possibility distributions. (page 131)
A12-c1 B. Liu, Uncertainty Theory, Series: Studies in Fuzziness and Soft Computing , Vol. 154, Springer,
[ISBN: 978-3-540-73164-1]. 2007
in Ph.D. dissertations
• Takashi Hasuike, Studies on Mathematical Methods for Asset Allocation Problems with Randomness and
Fuzziness, Graduate School of Information Science and Technology Osaka University, Japan. 2009
http://ir.library.osaka-u.ac.jp/metadb/up/LIBCLK003/f_2008-23046h.pdf
Consequently, problem (3.8) is a fuzzy optimization problem for portfolio selection problems and
is solved by using results of previous studies on fuzzy portfolio selection models (For example,
Carlsson et al. [A14, A12] and Vercher et al. [117]). Furthermore, we formally introduce the
following mean-variance model: (page 23)
[A13] Robert Fullér and Péter Majlender, An analytic approach for obtaining maximal entropy OWA operator weights, FUZZY SETS AND SYSTEMS, 124(2001) 53-57. [Zbl.0989.03057]. doi 10.1016/S01650114(01)00007-0
in journals
2016
A13-c220 Elvis Hernandez, Claudio M Rocco, Jose E Ramirez-Marquez, Node Ranking for Network TopologyBased Cascade Models: An Ordered Weighted Averaging Operators? Approach RELIABILITY ENGINEERING & SYSTEM SAFETY (to appear). 2016
http://dx.doi.org/10.1016/j.ress.2016.06.014
A13-c219 Emad A Mohammed, Christopher T Naugler, Behrouz H Far, Breast Tumor Classification Using a
New OWA Operator, EXPERT SYSTEMS WITH APPLICATIONS (to appear). 2016
http://dx.doi.org/10.1016/j.eswa.2016.05.037
Maximal entropy OWA weight vector (Fullér and Majlender, 2001) is one of the first methods
for obtaining the weight vector of an OWA, which selects the weight vector that maximizes the
117
entropy of the OWA operator; as it is based on the solution of a constrained optimization problem
that requires computational efforts to find the optimal weight. An extension of this method was
proposed to obtain minimal variability (Fullér and Majlender, 2003) OWA weighting vector for
any level of optimism.
A13-c218 Yung-Tsan Jou, Kang-Hung Yang, Ming-Li Liao, Cheng-Shih Liaw, Multi-criteria failure mode effects and criticality analysis method: a comparative case study on aircraft braking system, INTERNATIONAL JOURNAL OF RELIABILITY AND SAFETY, 10: (1) pp. 1-21. 2016
http://dx.doi.org/10.1504/IJRS.2016.076338
A13-c217 Dug Hun Hong, A Note on Properties of the Continuous Weighted OWA Operator, APPLIED MATHEMATICAL SCIENCES, 10: (31) pp. 1537-1547. 2016
http://dx.doi.org/10.12988/ams.2016.6271
A13-c216 Bobo Zhao, Tao Tang, Bin Ning, Wei Zheng, Hybrid Decision-making Method for Emergency Response System of Unattended Train Operation Metro, PROMET-TRAFFIC & TRANSPORTATION,
http://dx.doi.org/10.7307/ptt.v28i2.1760
The OWA operator uses different decision criteria such as maximax (optimistic), maximin (pessimistic), etc., which express the decision maker’s degree of optimism [27]. The OWA operator
weights are measured by two important parameters, called dispersion (or entropy) and orness [17].
The dispersion can be interpreted as the entropy of the probability distribution and the orness measures the degree to which the aggregation is like an or operation, and can be viewed as a measure
of optimism of a decision maker [28]. There were many methods of determining OWA operator
weights for decision making in a valid way. Fullér and Majlender [29] introduced a method of
minimizing the variance of OWA operator weights under a given level of orness. (page 107)
A13-c215 Di Bona G, Forcina A, Petrillo A, De Felice F, Silvestri A, A-IFM reliability allocation model based
on multicriteria approach, INTERNATIONAL JOURNAL OF QUALITY & RELIABILITY MANAGEMENT, 33: (5) pp. 676-698. 2016
http://dx.doi.org/10.1108/IJQRM-05-2015-0082
A13-c214 Ronald R Yager, Naif Alajlan, Some Issues on the OWA Aggregation with Importance Weighted
Arguments, KNOWLEDGE-BASED SYSTEMS, 100(2016), pp. 89-96. 2016
http://dx.doi.org/10.1016/j.knosys.2016.02.009
A13-c214 Ameri Fateme, Zoej Mohammad Javad Valadan, Mokhtarzade Mehdi, Multi-Criteria, Graph-Based
Road Centerline Vectorization Using Ordered Weighted Averaging Operators, PHOTOGRAMMETRIC
ENGINEERING AND REMOTE SENSING, 82: (2) pp. 107-120. 2016
http://dx.doi.org/10.14358/PERS.82.2.107
A13-c213 Bobo Zhao, Tao Tang, Bin Ning, Applying Hybrid Decision-Making Method Based on Fuzzy AHPWOWA Operator for Emergency Alternative Evaluation of Unattended Train Operation Metro System,
MATHEMATICAL PROBLEMS IN ENGINEERING, 2016(2016), Paper 4105079. 12 p. 2016
http://dx.doi.org/10.1155/2016/4105079
A13-c212 Vluymans, S.; Sanchez Tarrago, D.; Saeys, Y.; Cornelis, C.; Herrera, F., Fuzzy Multi-Instance Classifiers, IEEE Transactions on Fuzzy Systems (to appear). 2016
http://dx.doi.org/10.1109/TFUZZ.2016.2516582
A13-c211 Ankit Gupta, Shruti Kohli, An MCDM approach towards handling outliers in web data: a case study
using OWA operators, ARTIFICIAL INTELLIGENCE REVIEW, Volume 46, Issue 1, 1 June 2016, Pages
59-82. 2016
http://dx.doi.org/10.1007/s10462-015-9456-4
A13-c210 Gurbinder Kaur, Joydip Dhar, Rangan Kumar Guha, Minimal variability OWA operator combining
ANFIS and fuzzy c-means for forecasting BSE index, MATHEMATICS AND COMPUTERS IN SIMULATION, 122(2016), pp. 69-80. 2016
http://dx.doi.org/10.1016/j.matcom.2015.12.001
118
The OWA first introduced by Yager [35], has gained much interest among researchers. In recent years, many related studies have been conducted. Fuller and Majlender [A13] use Lagrange
multipliers to solve constrained optimization problem and determine the optimal weighing vector.
(page 70)
A13-c209 Bin Zhu, Zeshui Xu, Ren Zhang, Mei Hong, Hesitant analytic hierarchy process, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 250(2016), pp. 602-614. 2016
http://dx.doi.org/10.1016/j.ejor.2015.09.063
2015
A13-c209 Meng Fanyong, Chen Xiaohong, Zhang Qiang, Some uncertain generalized Shapley aggregation operators for multi-attribute group decision making, JOURNAL OF INTELLIGENT & FUZZY SYSTEMS,
29: (4) pp. 1251-1263. 2015
http://dx.doi.org/10.3233/IFS-131069
A13-c208 G Tohidi, M Khodadadi, The OWA Weights of Improved Minimax Disparity Model, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 30: (7) pp. 781-797. 2015
http://dx.doi.org/10.1002/int.21711
A13-c207 Gianpaolo Di Bona, Antonio Forcina, Alessandro Silvestri, Critical Flow Method: A New Reliability Allocation Approach for a Thermonuclear System, QUALITY AND RELIABILITY ENGINEERING
INTERNATIONAL (to appear). 2015
http://dx.doi.org/10.1002/qre.1899
A13-c206 Chung-Ho Su, Kai-Chong Hsaio, Developing and Evaluating Gamifying Learning System by Using Flow-Based Model, EURASIA JOURNAL OF MATHEMATICS, SCIENCE AND TECHNOLOGY
EDUCATION, 11: (6) pp. 1283-1306. 2015
http://dx.doi.org/10.12973/eurasia.2015.1386a
Fullér & Majlender (2001) proposed a new OWA step based on a maximum entropy; it is a simplified step, based on the original OWA, in which the weight can be calculated by using only
situational variable α, number of attributes n, and the importance ordering factor. Their step is
defined as (page 1289)
A13-c205 Hongping Wang, Hongming Mo, Re han Sadiq, Yong Hu, Yong Deng, Ordered visibility graph
weighted averaging aggregation operator: a methodology based on network analysis, COMPUTERS AND
INDUSTRIAL ENGINEERING, 88(2015), pp. 181-190. 2015
http://dx.doi.org/10.1016/j.cie.2015.06.021
The weights were referred to as the maximum entropy weights. In other words, the maximum
entropy method determines a special type of OWA operators with maximum entropy of the OWA
weights for a given level of orness. The method of Lagrange multipliers was used by Fuller and
Majlender (2001) to solve O’Hagan’s procedure analytically. (page 182)
For this application, the results are compared with the approach proposed by Fuller and Majlender
(2001). The main calculation processes are introduced in Section 2.1. Here, we let n be 18. The
corresponding weights are computed and shown in Table 4 (page 187)
A13-c204 Singh A, Kishor A, Pal N, Stancu OWA Operator, IEEE TRANSACTIONS ON FUZZY SYSTEMS,
23(2015), number 4, pp. 1306-1313. 2015
http://dx.doi.org/10.1109/TFUZZ.2014.2336696
A13-c203 Ayhan Mentes, Emre Ozen, A hybrid risk analysis method for a yacht fuel system safety, SAFETY
SCIENCE, 79(2015), pp. 94-104. 2015
http://dx.doi.org/10.1016/j.ssci.2015.05.010
An important issue in the theory of OWA operators is determination of associated weights. Fuller
and Majlender (2001) used the method of Lagrange multipliers to transfer Yager’s OWA equation
to derive a polynomial equation, which can determine the optimal weighting vector under maximal
entropy. By their method, the associated weighting vector is obtained by (pages 97-98)
119
A13-c202 Mikael Collan, Mario Fedrizzi, Pasi Luukka, New closeness coefficients for fuzzy similarity based
fuzzy TOPSIS: An approach combining fuzzy entropy and multi-distance, Advances in Fuzzy Systems (to
appear). 2015
http://www.hindawi.com/journals/afs/aip/251646/
The above constrained optimization problem can be solved by using different methods. Here an
analytical solution introduced by Fullér and Majlender [21] is used. Below this weighting scheme
is presented: (page 8)
A13-c201 Manish Aggarwal, On Learning of Weights through Preferences, INFORMATION SCIENCES,
321(2015), pp. 90-102. 2015
http://dx.doi.org/10.1016/j.ins.2015.05.034
A13-c200 Ayhan Mentes, Hakan Akyildiz, Murat Yetkin, Nagihan Turkoglu, A FSA based fuzzy DEMATEL approach for risk assessment of cargo ships at coasts and open seas of Turkey, SAFETY SCIENCE,
79(2015), pp. 1-10. 2015
http://dx.doi.org/10.1016/j.ssci.2015.05.004
Different types of aggregation operators can be seen in the literature for aggregating information
(Yager et al., 2011). One of the most common aggregation methods is the ordered weighted
averaging (OWA) which was first introduced by Yager (1988). It is an important aggregation
operator within the class of weighted aggregation methods. The technique gets optimal weights
of the attributes based on the ranks of these weighting vectors (Chang et al., 2012). One important
issue in the theory of OWA operators is the determination of the associated weights (Fuller and
Majlender, 2001). (page 4)
A13-c199 Kuei-Hu Chang, A novel efficient approach for supplier selection problem using the OWA-based
ranking technique, JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING (to appear).
2015
http://dx.doi.org/10.1080/21681015.2015.1045563
A13-c198 Ligang Zhou, Peng Wu, Chenyi Fu, Huayou Chen, Jinpei Liu, Generalized exponential multiple
averaging operator and its application to group decision making, JOURNAL OF INTELLIGENT AND
FUZZY SYSTEMS (to appear). 2015
http://dx.doi.org/10.3233/IFS-151606
A13-c197 Erhan Bozdag, Umut Asan, Ayberk Soyer, Seyda Serdarasan, Risk Prioritization in Failure Mode and
Effects Analysis Using Interval Type-2 Fuzzy Sets, EXPERT SYSTEMS WITH APPLICATIONS, 42: (8)
pp. 4000-40015. 2015
http://dx.doi.org/10.1016/j.eswa.2015.01.015
The weights used in Eq. 14 are derived by the method suggested by Fuller and Majlender (2001)
who use Lagrange multipliers to formulate a polynomial equation and then determine the optimal
weighting vector by solving a constrained optimization problem. The weight vector for single
numerical values is obtained as follows: (page 4008)
Different from Fuller and Majlenders (2001) original approach, in this study, interval data is used
to calculate the optimum weights. The new weighting procedure applied here can be summarized
as follows. Experts provide endpoints of an interval for the situation parameter (0 ≤ γ ≤ 1).
Once the optimum weight intervals are calculated for each expert, these individual weights are
aggregated into group weights in form of IT2 FNs by using IMA method (see Step 3). (page
4009)
The weights were then derived by using Fuller and Majlender’s (2001) method and aggregated
over the experts into group weights using the IT2 fuzzistics method IMA. (page 4011)
A13-c196 Jianwei Gao, Ming Li, Huihui Liu, Generalized ordered weighted utility proportional averaginghyperbolic absolute risk aversion operators and their applications to group decision-making, Applied Mathematics and Computation, 252(2015), pp. 114-132. 2015
http://dx.doi.org/10.1016/j.amc.2014.12.009
120
A13-c195 Jianwei Gao, Ming Li, Huihui Liu, Generalized ordered weighted utility averaging-Hyperbolic Absolute Risk Aversion operators and their applications to group decision-making, European Journal of Operational Research, 243(2015), number 1, pp. 258-270. 2015
http://dx.doi.org/10.1016/j.ejor.2014.11.039
A13-c194 Ligang Zhou, Zhifu Tao, Huayou Chen, Jinpei Liu, Generalized ordered weighted logarithmic harmonic averaging operators and their applications to group decision making, SOFT COMPUTING, 19: (3),
pp. 715-730. 2015
http://dx.doi.org/10.1007/s00500-014-1295-8
Another crucial issue of applying the OWA operator for multiple attribute decision making is
the determination of the associated weights. A number of approaches have been developed for
obtaining the OWA operator weights (Ahn 2006; Amin and Emrouznejad 2006; Emrouznejad and
Amin 2010; Filev and Yager 1998; Fuller and Majlender 2001; Wang et al. 2007; Wang and Parkan
2005, 2007; Xu 2004b, 2005, 2006a; Yager 1993, 1996, 2007, 2009a,b). In Dujmovi (1974),
Dujmovic’ introduced the measure of orness for the power mean under the disjunction degree,
which results in the orness concept independently in the case of the OWA operator proposed by
Yager (1988). Filev and Yager (1998) brought forward a learning method based on observed
data and an exponential smoothing method, which produced the exponential OWA operator and
the operator weights with orness measure. Fuller and Majlender (2001) developed an analytic
approach for obtaining maximal entropy OWA operator weights for a given level of orness. Wang
and Parkan (2005) proposed a minimax disparity approach for obtaining OWA operator weights
for a given level of orness. Moreover, Wang and Parkan (2007) presented a preemptive goal
programming method for aggregating OWA operator weights in group decision making. Wang
et al. (2007) proposed two new models for determining the OWA operator weights, called the
least-squares method (LSM) and the chi-square (χ2 ) method (CSM), with a given level of orness.
(page 716)
2014
A13-c194 Liao Huchang, Xu Zeshui, Xu Jiuping, An approach to hesitant fuzzy multi-stage multi-criterion
decision making KYBERNETES, 43: (9-10) pp. 1447-1468. 2014
http://dx.doi.org/10.1108/K-11-2013-0246
A13-c193 Ali Emrouznejad, Marianna Marra, Ordered Weighted Averaging Operators 1988-2014: A CitationBased Literature Survey, International Journal of Intelligent Systems, 29(2014), number 11, pp. 994-1014.
2014
http://dx.doi.org/10.1002/int.21673
A13-c192 Dongping Chen, Xuening Chu, Xiwu Sun, Yupeng Li, A new product service system concept evaluation approach based on Information Axiom in a fuzzy-stochastic environment, International Journal of
Computer Integrated Manufacturing (to appear). 2014
http://dx.doi.org/10.1080/0951192X.2014.961550
A13-c191 Solairaju A, Robinson P John, Kumar S Rethina, An analytic approach for interval valued intuitionistic fuzzy MAGDM using maximal entropy OWA weights, INTERNATIONAL JOURNAL OF APPLIED
SCIENCE AND ENGINEERING RESEARCH, 3(2014), number 1, pp. 220-231. 2014
http://dx.doi.org/10.6088/ijaser.030100022
A13-c190 L Gu, J Zhong, C Wang, Z Ni, Y Zhang, Trust Model in Cloud Computing Environment Based on
Fuzzy Theory, INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL,
9: (5) pp. 570-583. 2014
http://univagora.ro/jour/index.php/ijccc/article/view/1276
A13-c189 Hu-Chen Liu, Jian-Xin You, Xiao-Yue You, Evaluating the risk of healthcare failure modes using
interval 2-tuple hybrid weighted distance measure, Computers & Industrial Engineering, 78(2014), pp.
249-258. 2014
http://dx.doi.org/10.1016/j.cie.2014.07.018
121
A13-c188 Hu-Chen Liu, Long Liu, Ping Li, Failure mode and effects analysis using intuitionistic fuzzy hybrid
weighted Euclidean distance operator, International Journal of Systems Science, 45(2014), number 10, pp.
2012-2030. 2014
http://dx.doi.org/10.1080/00207721.2012.760669
The OWA weighing calculation methods in both methods are different. The OWA-based FMEA
used the method of Lagrange multipliers (Fullér and Malender 2001) to determine OWA weights.
Although the weighting calculation method can reflect the aggregate situation during the aggregation process, it is hard to determine the situation parameter in practice and the authors did not
give a general guideline for practitioners in terms of choosing an appropriate situation parameter.
In the proposed FMEA model, the ordered weights for the risk factors were derived by the normal
distribution-based method (Xu 2005), which can relieve the influence of unfair arguments on the
decision results by weighting these arguments with small values.
A13-c187 Ligang ZHOU, Huayou CHEN, Generalized Ordered Weighted Proportional Averaging Operator and
Its Application to Group Decision Making, INFORMATICA, 25(2014), pp. 327-360. 2014
http://www.mii.lt/informatica/htm/INFO1014.htm
A13-c186 Meng F, Cheng H, Zhang Q, Induced Atanassov’s interval-valued intuitionistic fuzzy hybrid Choquet
integral operators and their application in decision making, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 7: (3) pp. 524-542. 2014
http://dx.doi.org/10.1080/18756891.2013.865402
A13-c185 Jeong Jin Su, Garcia-Moruno Lorenzo, Hernandez-Blanco Julio, Jaraiz-Cabanillas Francisco Javier,
An operational method to supporting siting decisions for sustainable rural second home planning in ecotourism sites, Land Use Policy, 41(2014), pp. 550-560. 2014
http://dx.doi.org/10.1016/j.landusepol.2014.04.012
A13-c184 A Solairaju, P John Robinson, S Rethinakumar, Interval Valued Intuitionistic Fuzzy MAGDM Problems with OWA Entropy Weights, International Journal of Mathematics Trends and Technology, 9: (2) pp.
152-158. (2014)
http://dx.doi.org/10.14445/22315373/IJMTT-V9P518
A13-c183 Hu-Chen Liu, Jian-Xin You, Yi-Zeng Chen, Xiao-Jun Fan, Site selection in municipal solid waste
management with extended VIKOR method under fuzzy environment, Environmental Earth Sciences, 72(2014),
number 10, pp. 4179-4189. 2014
http://dx.doi.org/10.1007/s12665-014-3314-6
Fullér and Majlender (2001) used the method of Lagrange multipliers to solve this constrained optimization problem and derive a polynomial equation, which can determine the optimal weighting
vector under maximal entropy. By the method, the associated weights can be obtained using the
following equations:
A13-c182 Kaihong Guo, Quantifiers Induced by Subjective Expected Value of Sample Information, IEEE
TRANSACTIONS ON CYBERNETICS (to appear). 2014
http://dx.doi.org/10.1109/TCYB.2013.2295316
O’Hagan [27] presented a maximum entropy approach, which involved a constrained nonlinear
optimization problem. This resulting OWA operator is called the maximum entropy OWA (MEOWA) operator, and has been widely cited in followup studies on this aspect. Filev and Yager [12]
explored the analytic properties of the MEOWA operator, and Fullér and Majlender [A13] showed
that this maximum entropy model could be transformed into a polynomial equation that could be
solved analytically.
A13-c181 Peng Juan-juan, Wang Jian-qiang, Zhang Hong-yu, Sun Teng, Chen Xiao-hong, OWA aggregation
over a continuous fuzzy argument with applications in fuzzy multi-criteria decision-making, Journal of
Intelligent and Fuzzy Systems, 27(2014), number 3, pp. 1407-1417. 2014
http://dx.doi.org/10.3233/IFS-131107
122
A13-c180 K. Guo, Quantifiers Induced by Subjective Expected Value of Sample Information, IEEE Transactions on Cybernetics (to appear). 2014
http://dx.doi.org/10.1109/TCYB.2013.2295316
A13-c179 Jun Hang, Jianzhong Zhang, Ming Cheng, Fault diagnosis of wind turbine based on multi-sensors
information fusion technology, IET Renewable Power Generation, 8(2014), number 3, pp. 289-298. 2014
http://dx.doi.org/10.1049/iet-rpg.2013.0123
A13-c178 Zooho Kim, Vijay P Singh, Assessment of Environmental Flow Requirements by Entropy-Based
Multi-Criteria Decision, Water Resources Management, Volume 28, Issue 2, January 2014, Pages 459-474.
2014
http://dx.doi.org/10.1007/s11269-013-0493-y
Fullér and Majlender (2001) determined the optimal weighting vector using the method of Lagrange multipliers. Once, w1 , wn are computed using Eqs. (12) and (13), then the other weights
are obtained from Eq. (14): (page 465)
A13-c177 Sang Xiuzhi, Liu Xinwang, An analytic approach to obtain the least square deviation OWA operator
weights, Fuzzy Sets and Systems, Volume 240, 1 April 2014, Pages 103-116. 2014
http://dx.doi.org/10.1016/j.fss.2013.08.007
O’Hagan [27] first determined OWA operator weights and suggested a maximum entropy method.
Fullér and Majlender [A13] transformed the maximum entropy model into a polynomial equation which can be solved analytically. They also suggested [A10] the minimal variability OWA
operator problem in quadratic programming, and proposed an analytic solution. (page 103)
A13-c176 A Kishor, A Singh, N Pal, Orness Measure of OWA Operators: A New Approach, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 22: (4) pp. 1039-1045. 2014
http://dx.doi.org/10.1109/TFUZZ.2013.2282299
2013
A13-c175 Liu Hu-Chen, Wu Jing, Li Ping, Assessment of health-care waste disposal methods using a VIKORbased fuzzy multi-criteria decision making method, WASTE MANAGEMENT (to appear). 2013
http://dx.doi.org/10.1016/j.wasman.2013.08.006
A13-c174 Sang X, Liu X, Aggregating metasearch engine results based on maximal entropy OWA operator,
Journal of Southeast University (English Edition), 29(2013), number 2, pp. 139-144. 2013
http://dx.doi.org/10.3969/j.issn.1003-7985.2013.02.006
A13-c173 S. Charles and L. Arockiam, Fuzzy Weighted Gaussian Mixture Model for Feature Reduction, International Journal of Computer Applications, 64(2013), number 18, pp. 9-15. 2013
http://cirworld.com/index.php/ijct/article/view/1170/0
A13-c172 Feng-Mei Ma, Ya-Jun Guo, Determination of the Attitudinal Character by Self-Evaluation for the
Maximum Entropy OWA Approach, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 28(2013),
number 11, pp. 1089-1098. 2013
http://dx.doi.org/10.1002/int.21618
A13-c171 Gu X, Xu Z, Tu H, Liu X, Time effectiveness in trust services under cloud environment, Wuhan
Daxue Xuebao (Xinxi Kexue Ban)/Geomatics and Information Science of Wuhan University, 38: (5) 626630. 2013
Scopus: 84878369102
A13-c170 Xiao-wen Qi, Chang-yong Liang, Junling Zhang, Some generalized dependent aggregation operators with interval-valued intuitionistic fuzzy information and their application to exploitation investment
evaluation, JOURNAL OF APPLIED MATHEMATICS, 2013(2013). Paper 705159. 2013
http://downloads.hindawi.com/journals/jam/aip/705159.pdf
A13-c169 M. Rahmanimanesh and S. Jalili, ADAPTIVE ORDERED WEIGHTED AVERAGING FOR ANOMALY
DETECTION IN CLUSTER-BASED MOBILE AD HOC NETWORKS, Iranian Journal of Fuzzy Systems,
10(2013), number 2, pp. 83-109. 2013
123
http://www.sid.ir/en/VEWSSID/J_pdf/90820130206.pdf
A13-c168 Ming Li Liao, Yung Tsan Jou, Cheng Shih Liaw, Amalgamated Criticality Analysis Methodology,
ADVANCED MATERIALS RESEARCH, 679(2013), pp. 101-106. 2013
http://dx.doi.org/10.4028/www.scientific.net/AMR.679.101
A13-c167 Hu-Chen Liu, Ling-Xiang Mao, Zhi-Ying Zhang, Ping Li, Induced aggregation operators in the
VIKOR method and its application in material selection, APPLIED MATHEMATICAL MODELLING,
37(2013), issue 9, pp. 6325-6338. 2013
http://dx.doi.org/10.1016/j.apm.2013.01.026
A13-c166 Jibin Lan; Qing Sun; Qingmei Chen; Zhongxing Wang, Group decision making based on induced
uncertain linguistic OWA operators, DECISION SUPPORT SYSTEMS, 55(2013), number 1, pp. 296-303.
2013
http://dx.doi.org/10.1016/j.dss.2013.01.030
A13-c165 Chang K-H, A general integrated soft set and the ordered weighted averaging approach for a supplier selection problem under incomplete information, ICIC Express Letters, Part B: Applications 4(2013),
number 2, pp. 395-400. 2013
Scopus: 84875333033
A13-c164 Luukka P, Kurama O, Similarity classifier with ordered weighted averaging operators, EXPERT
SYSTEMS WITH APPLICATIONS, 40(2013), number 4, pp. 995-1002. 2013
http://dx.doi.org/10.1016/j.eswa.2012.08.014
There are many possibilities how to solve this optimization problem. One of them, is to use the
method of Lagrange multipliers. In 2001 Fullér and Majlender introduced the analytical solution
to the above mentioned problem. They presented the following results:
···
Basically for obtaining the weights in a case, where n ≥ 3, the first step should be determining
the first weight. After that, one can calculate the last weight of the weighting vector and then
other weights. Moreover if w1 = wn , then the dispersion will be disp(W) = ln n, which is the
optimal solution to this problem for α = 0.5 (Fullér & Majlender, 2001). This was one method
of obtaining OWA operator weights which we are further examining in our similarity classifier.
(page 996)
A13-c163 Ligang Zhou, Huayou Chen, Jinpei Liu, Generalized Multiple Averaging Operators and their Applications to Group Decision Making, GROUP DECISION AND NEGOTIATION, 22(2013), number 2, pp.
331-358. 2013
http://dx.doi.org/10.1007/s10726-011-9267-1
2012
A13-c163 Ching-Hsue Cheng, Liang-Ying Wei, Jing-Wei Liu, Tai-Liang Chen, OWA-based ANFIS model for
TAIEX forecasting, ECONOMIC MODELLING, 30(2012), pp. 442-448. 2012
http://dx.doi.org/10.1016/j.econmod.2012.09.047
2.1.2. Fuller and Majlender’s OWA
Fuller and Majlender (2001) transform Yager’s OWA equation to a polynomial equation by using Lagrange multipliers. According to their approach, the associated weighting vector can be
obtained by Eq. (5)-(7) (page 443)
Besides, in practical stock markets, investors usually make their short-term decisions based on
recent stock information, such as recent periods of stock prices and technical analysis reports.
Therefore, the investors are influenced by recent stock price fluctuations to make investment decisions, and the recent different periods of prices influence their decisions to different degrees. To
deal with the condition above, the OWA operator is proposed to produce one aggregate value for
forecasting the future prices with different weights to meet the variations of influence degrees. Additionally, we argue that applying OWA in forecasting models can improve forecasting accuracy,
because the literature (Fuller and Majlender, 2001) has shown that weighted-based technologies
are superior methods to enhance the performances of time series models. (page 445)
124
A13-c162 Zhou L, Chen H, Liu J, Generalized logarithmic proportional averaging operators and their applications to group decision making, Knowledge-Based Systems, 36(2012), pp. 268-279. 2012
http://dx.doi.org/10.1016/j.knosys.2012.07.006
A13-c161 Feng-Mei Ma, Ya-Jun Guo, Ping-Tao Yi, Cluster-reliability-induced OWA operators, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 27(2012), number 9, pp. 823-836. 2012
http://dx.doi.org/10.1002/int.21549
A13-c160 Rasim M Alguliev, Ramiz M Aliguliyev, Fadai S Ganjaliyev, Aggregating Edge Weights in Social
Networks on the Web Extracted from Multiple Sources with Different Importance Degrees, JOURNAL OF
INTELLIGENT LEARNING SYSTEMS AND APPLICATIONS, 2012(2012), number 4, pp. 154-158.
2012
http://dx.doi.org/10.4236/jilsa.2012.42015
At this point, the edge weights of the resultant network could be calculated, except the values
for the unknown coefficients in formula (2) have to be found. Several approaches have been
proposed to identify weight vectors for OWA operators. We use the one presented in [A13]. The
authors present an analytical approach to determine the weight vector, achieved by transforming
the following mathematical programming problem into a polynomial equation using the Lagrange
multipliers method: (page 155)
A13-c159 G Yari, A R Chaji, Maximum Bayesian entropy method for determining ordered weighted averaging
operator weights, COMPUTERS & INDUSTRIAL ENGINEERING, 63(2012), number 1, pp. 338-342.
2012
http://dx.doi.org/10.1016/j.cie.2012.03.010
A13-c158 Feng-Mei Ma, Ya-Jun Guo, Xiang Shan, Analysis of the impact of attitudinal character on the multicriteria decision making with OWA operators, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 27(2012), number 5, pp. 502-518. 2012
http://dx.doi.org/10.1002/int.21533
A13-c157 Dug Hun Hong, The relationship between the maximum entropy and minimax ratio RIM quantifier
problems, FUZZY SETS AND SYSTEMS, 202(2012), pp. 110-117. 2012
http://dx.doi.org/10.1016/j.fss.2012.01.014
A13-c156 Chang K -H, Chang Y -C, Wen T -C, Cheng C -H, An innovative approach integrating 2-tuple and
lowga operators in process failure mode and effects analysis, INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING, INFORMATION AND CONTROL, 8(2012), number 1B, pp. 747-761. 2012
Scopus: 84856948976
A13-c155 Sultan Al-Yahyai, Yassine Charabi, Adel Gastli, Abdullah Al-Badi, Wind farm land suitability indexing using multi-criteria analysis, RENEWABLE ENERGY, 44(2012), pp. 80-87. 2012
http://dx.doi.org/10.1016/j.renene.2012.01.004
A13-c154 Xinwang Liu, Models to determine parameterized ordered weighted averaging operators using optimization criteria, INFORMATION SCIENCES, 190(2012), pp. 27-55. 2012
http://dx.doi.org/10.1016/j.ins.2011.12.007
Fullér and Majlender [A13] transformed the maximum entropy model into a polynomial equation
model, which could be solved analytically. (page 28)
A13-c153 Chang K -H, Chang Y -C, Wen T -C, Cheng C -H, An innovative approach integrating 2-tuple and
lowga operators in process failure mode and effects analysis International Journal of Innovative Computing,
Information and Control, 8(2012), issue 1B, pp. 747-761. 2012
Scopus: 84856948976
A13-c152 Guiwu Wei, Xiaofei Zhao, Some dependent aggregation operators with 2-tuple linguistic information
and their application to multiple attribute group decision making, EXPERT SYSTEMS WITH APPLICATIONS, 39(2012), issue 5, pp. 5881-5886. 2012
http://dx.doi.org/10.1016/j.eswa.2011.11.120
125
A13-c151 Ligang Zhou, Huayou Chen, Jinpei Liu, Generalized weighted exponential proportional aggregation
operators and their applications to group decision making, APPLIED MATHEMATICAL MODELLING,
36(2012), number 9, pp. 4365-4384. 2012
http://dx.doi.org/10.1016/j.apm.2011.11.063
A13-c150 Li-Gang Zhou; Hua-You Chen; José M. Merigó; Anna M. Gil-Lafuente, Uncertain generalized aggregation operators, EXPERT SYSTEMS WITH APPLICATIONS, 39 (2012), pp. 1105-1117. 2012
http://dx.doi.org/10.1016/j.eswa.2011.07.110
In order to apply the aggregation operator, most crucial issue is to determine its weights. In
O’Hagan (1988), O’Hagan developed a procedure to generate the OWA weights that have a predefined degree of orness and maximize the entropy of the OWA weights. And in Fullér and
Majlender (2001), Fullér and Majlender applied the maximum entropy model to solve O’Hagan’s
procedure analytically. (page 1105)
A13-c149 Xinwang Liu, Shui Yu, On the Stress Function-Based OWA Determination Method With Optimization Criteria, IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS,
42(2012), number 1, pp. 246-257. 2012
http://dx.doi.org/10.1109/TSMCB.2011.2162233
2011
A13-c148 LIANG Cheng, LUO Jia-wei, LI Ren-fa, New representation for characteristic sequence of RNA secondary structure and analysis of similarity/dissimilarity, APPLICATION RESEARCH OF COMPUTERS,
28(2011), number 3, pp. 969-979 (in Chinese). 2011
http://dx.doi.org/10.3969/j.issn.1001-3695.2011.03.050
A13-c147 Fei He, New Web service selection model with QoS constraints, APPLICATION RESEARCH OF
COMPUTERS, 28(2011), number 3, pp. 976-979 (in Chinese). 2011
http://dx.doi.org/10.3969/j.issn.1001-3695.2011.03.052
A13-c146 Yanbing Gong, A combination approach for obtaining the minimize disparity OWA operator weights,
FUZZY OPTIMIZATION AND DECISION MAKING, 10(2011), number 4, pp. 311-321. 2011
http://dx.doi.org/10.1007/s10700-011-9107-4
Filev and Yager (1995, 1998) suggested a learning approach using observed data and an exponential smoothing method. The resulting OWA operators are called exponential OWA operators.
Fullér and Majlender (2001) showed that the maximum entropy model could be transformed into
a polynomial equation which can be solved analytically. (page 312)
A13-c145 Dug Hun Hong, The relationship between the minimum variance and minimax disparity rim quantifier problems, FUZZY SETS AND SYSTEMS, 181(2011), number 1, pp. 50-57. 2011
http://dx.doi.org/10.1016/j.fss.2011.05.014
A13-c144 Feng-Mei Ma, Ya-Jun Guo, Density-Induced Ordered Weighted Averaging Operators, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 26(2011), issue 9, pp. 866-886. 2011
http://dx.doi.org/10.1002/int.20500
A13-c143 KH Chang, CH Cheng, Evaluating the risk of failure using the fuzzy OWA and DEMATEL method,
JOURNAL OF INTELLIGENT MANUFACTURING, 22(2011), number 2, pp. 113-129. 2011
http://dx.doi.org/10.1007/s10845-009-0266-x
A13-c142 Ya N. Imamverdiev, S. A. Derakshande, Fuzzy OWA Model for Information Security Risk Management, AUTOMATIC CONTROL AND COMPUTER SCIENCES 45(2011), number 1, pp. 20-28. 2011
http://dx.doi.org/10.3103/S0146411611010056
A13-c141 Cheng-Shih Liaw, Yung-Chia Chang, Kuei-Hu Chang, Thing-Yuan Chang, ME-OWA based DEMATEL reliability apportionment method, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), number
8, pp. 9713-9723. 2011
http://dx.doi.org/10.1016/j.eswa.2011.02.029
126
Fuller and Majlender (2001) used the method of Lagrange multipliers on Yager’s OWA equation
to derive a polynomial equation which can determine the optimal weighting vector under the
maximal entropy. By their method, the associated weighting vector is easily obtained by Eqs.
(7)-(9): (pages 9714-9715)
A13-c140 Byeong Seok Ahn, Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 212(2011),
pp. 552-559. 2011
http://dx.doi.org/10.1016/j.ejor.2011.02.017
The resulting weights are called the maximum entropy OWA (MEOWA) weights for a specified
value of attitudinal character, and their analytic solution and properties can be found in Filev and
Yager (1995) and Fuller and Majlender (2001). (page 554)
A13-c139 T. Gao, R. Jin, T. Xu, L. Wang, Energy-efficient hierarchical routing for wireless sensor networks,
AD HOC & SENSOR WIRELESS NETWORKS, 11(2011), pp. 35-72. 2011
A13-c138 Dug Hun Hong, On proving the extended minimax disparity OWA problem, FUZZY SETS AND
SYSTEMS, 168(2011), issue 1, pp. 35-46. 2011
http://dx.doi.org/10.1016/j.fss.2010.08.008
Fullér and Majlender [A13, A10] showed that the maximum entropy model could be transformed
into a polynomial equation that could be solved analytically and suggested a minimum variance
approach to obtain the minimal variability OWA weights. (page 36)
A13-c137 Xiaoyong Li, Feng Zhou, Xudong Yang, A multi-dimensional trust evaluation model for large-scale
P2P computing, JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING, 71(2011), issue 6, 837847. 2011
http://dx.doi.org/10.1016/j.jpdc.2011.01.007
Fuller proposed two ways to obtain it. The first approach is to use a kind of learning mechanism
using some sample data, and the second approach is to try to give some semantics or meaning to
the weights [A13]. (page 842)
2010
A13-c137 X. Liu, The relationships between two variability and orness optimization problems for OWA operator
with RIM quantifier extensions, INTERNATIONAL JOURNAL OF UNCERTAINTY, FUZZINESS AND
KNOWLEDGE-BASED SYSTEMS, 18: (5) 515-538. 2010
http://dx.doi.org/10.1142/S0218488510006684
Hagan [12] suggested a problem of constraint nonlinear programming with a maximum entropy
procedure, the resulting OWA operator was called the MEOWA (Maximum Entropy OWA) operator. Filev and Yager [13] further analyzed the properties of the MEOWA operator, and proposed
a method to generate MEOWA weighting vector by an immediate parameter. Fullér and Majlender [A13] transformed the maximum entropy model into a polynomial equation, which can be
solved in an analytical way. Liu and Chen [15] proposed the general forms of the maximum entropy weighting vector by a parametric geometric approach. The analytical solution methods and
aggregation properties were discussed. (page 516)
A13-c136 Byeong Seok Ahn, Parameterized OWA operator weights: An extreme point approach, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 51(2010), pp. 820-831. 2010
http://dx.doi.org/10.1016/j.ijar.2010.05.002
A13-c135 Byeong Seok Ahn, A priori identification of preferred alternatives of OWA operators by relational
analysis of arguments, INFORMATION SCIENCES, 180(2010), Issue 23, pp. 4572-4581. 2010
http://dx.doi.org/10.1016/j.ins.2010.08.010
A13-c134 J.-W. Liu; C.-H. Cheng; Y.H. Chen; S.-F. Huang, OWA based PCA information fusion method
for classification problem, INTERNATIONAL JOURNAL OF INFORMATION AND MANAGEMENT
SCIENCES, 21(2010), Issue 2, pp. 209-225. 2010
127
A13-c133 Chang, Liang; Shi, Zhong-Zhi; Chen, Li-Min; Niu, Wen-Jia, Family of extended dynamic description
logics, Ruan Jian Xue Bao (Journal of Software). Vol. 21, no. 1, pp. 1-13. 2010
A13-c132 R. A. Nasibova; E. N. Nasibov, Linear Aggregation with Weighted Ranking, AUTOMATIC CONTROL AND COMPUTER SCIENCES, 44(2010), Number 2, pp. 96-102. 2010
http://dx.doi.org/10.3103/S0146411610020057
A13-c131 Li-Gang Zhou and Hua-you Chen, Generalized ordered weighted logarithm aggregation operators
and their applications to group decision making, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 25(2010), issue 7, pp. 683-707. 2010
http://dx.doi.org/10.1002/int.20419
A13-c130 Victor M Vergara, Shan Xia, Minimization of uncertainty for ordered weighted average, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS 25(2010), pp. 581-595. 2010
http://dx.doi.org/10.1002/int.20422
There are several methods that find the OWA weights. [3,9-12] Yager [3] proposed finding weights
that maximizes their entropy (also known as weights dispersion). Later, Fuller and Majlender
[A13] found an analytical solution to Yager’s theory based on Lagrange multipliers. In addition, these two authors proposed minimizing the variance of weights [A10] instead of maximizing
their entropy. The goal of these methods is to maximize similarity. Maximizing the entropy or
minimizing the variance of the weights {w1 , w2 , . . . , wn } makes each weight wi more similar in
magnitude tot he others. (page 582)
A13-c129 Yao-Hsien Chen, Ching-Hsue Cheng, Jing-Wei Liu, Intelligent preference selection model based on
NRE for evaluating student learning achievement, COMPUTERS & EDUCATION, 54(2010), pp. 916-926.
2010
http://dx.doi.org/10.1016/j.compedu.2009.09.020
This step computes the aggregate values of the test-score examples and typical score examples,
for different orders of evaluation items by using the OWA operator. First, according to the
Fullér and Majlenders’ equation introduced P
in Section 3, we can obtain a set of OWA weights
n
Wα {w1 , w2 , . . . , wn }, where 0 ≤ w1 ≤ 1, i=1 wi = 1 and α ∈ [0, 1]. Second, to compute
the aggregate values, we multiply the values of the evaluation items, which are permuted by all
possible orders, by the corresponding OWA weights, and then sum up these multiplication values.
(page 920)
A13-c128 A. Emrouznejad, G.R. Amin, Improving minimax disparity model to determine the OWA operator
weights, INFORMATION SCIENCES, 180(2010) 1477-1485. 2010
http://dx.doi.org/10.1016/j.ins.2009.11.043
A13-c127 Xiao-Yong Li, Xiao-Lin Gui, Cognitive Model of Dynamic Trust Forecasting, JOURNAL OF SOFTWARE, 21(2010), number 1, pp. 163-176 (in Chinese). 2010
http://dx.doi.org/10.3724/SP.J.1001.2010.03558
A13-c126 Kuei-Hu Chang, Ta-Chun Wen, A novel efficient approach for DFMEA combining 2-tuple and the
OWA operator, EXPERT SYSTEMS WITH APPLICATIONS, Volume 37, Issue 3, 15 March 2010, pp.
2362-2370. 2010
http://dx.doi.org/10.1016/j.eswa.2009.07.026
A13-c125 Jing-Wei Liu, Ching-Hsue Cheng, Yao-Hsien Chen, Tai-Liang Chen, OWA rough set model for forecasting the revenues growth rate of the electronic industry, EXPERT SYSTEMS WITH APPLICATIONS,
37(2010), pp. 610-617. 2010
http://dx.doi.org/10.1016/j.eswa.2009.06.020
Fullér and Majlender (2001) proposed a new method by using Lagrange multipliers to improve
the problem in Eq. (5) and got the following: (page 611)
A13-c124 Pan Yuhou; Yao Shuang; Guo Yajun, Comprehensive Multi-index Group Evaluation Method for
Scheme of Oilfield Development Adjustment and Its Application, TECHNOLOGY ECONOMICS, 29(2010),
number 3, pp. 31-34 (in Chinese). 2010
128
http://d.wanfangdata.com.cn/Periodical_jsjj201003007.aspx
2009
A13-c123 Yung-Chia Chang, Kuie-Hu Chang, Cheng-Shih Liaw, Innovative reliability allocation using the
maximal entropy ordered weighted averaging method, COMPUTERS & INDUSTRIAL ENGINEERING,
57(2009), Issue 4, pp. 1274-1281. 2009
http://dx.doi.org/10.1016/j.cie.2009.06.007
Additionally, Fuller and Majlender (2001) used Lagrange multipliers on Yager’s OWA equation
to derive a polynomial equation, which determines the optimal weighting vector under maximal
entropy (ME-OWA operator). The proposed approach thus determines the optimal weighting
vector under maximal entropy, and the OWA operator ascertains the optimal reliability allocation
rating after an aggregation process. This method is both a simple and effective approach that can
efficiently resolve the shortcomings of the FOO technique and average weighting allocation. (page
1275)
A13-c122 S. Zadrozny, J. Kacprzyk, Issues in the practical use of the OWA operators in fuzzy querying, JOURNAL OF INTELLIGENT INFORMATION SYSTEMS, 33(2009), No. 3, pp. 307-325. 2009
http://dx.doi.org/10.1007/s10844-008-0068-1
A13-c121 Yu Yi, Thomas Fober, Eyke Hüllermeier, Fuzzy Operator Trees for Modeling Rating Functions, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE AND APPLICATIONS, 8(2009),
pp. 423-428. 2009
http://dx.doi.org/10.1142/S1469026809002679
The issue of model selection and parameter estimation has been addressed, though, for simpler
types of decision models, especially for models using a single aggregation operator. For example,
the problem of fitting parameters on the basis of exemplary outputs has been studied for weighted
mean and OWA operators, [7,29] the WOWA (weighted OWA) operator, [30] the Choquet integral,
[18,31] and the Sugeno integral. [14] Besides, attempts have been made to identify the parameters
of such models using other types of information, such as the so-called ”orness” or degree of
disjunction [A10, A13] as well as preferences and order relations. (page 426)
A13-c120 E. Cables Pérez, M.Teresa Lamata, OWA weights determination by means of linear functions,
MATHWARE & SOFT COMPUTING, 16(2009), 107-122. 2009
http://ic.ugr.es/Mathware/index.php/Mathware/article/view/398/pdf-16-2-art1-final
A13-c119 Kuei-Hu Chang, Evaluate the orderings of risk for failure problems using a more general RPN
methodology, MICROELECTRONICS RELIABILITY, Volume 49, Issue 12, pp. 1586-1596. 2009
http://dx.doi.org/10.1016/j.microrel.2009.07.057
A13-c118 Jian Wu, Bo-Liang Sun, Chang-Yong Liang, Shan-Lin Yang, A linear programming model for determining ordered weighted averaging operator weights with maximal Yager’s entropy, COMPUTERS &
INDUSTRIAL ENGINEERING, Volume 57, Issue 3, pp. 742-747. 2009
http://dx.doi.org/10.1016/j.cie.2009.02.001
A13-c117 Byeong Seok Ahn, Some remarks on the LSOWA approach for obtaining OWA operator weights,
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Volume 24 Issue 12, Pages 1265-1279.
2009
http://dx.doi.org/10.1002/int.20384
A13-c116 R.R. Yager, On the dispersion measure of OWA operators, INFORMATION SCIENCES, 179(2009),
pp. 3908-3919. 2009
http://dx.doi.org/10.1016/j.ins.2009.07.015
A13-c115 Badredine Arfi, Probing the Democratic Peace Argument Using Linguistic Fuzzy Logic, INTERNATIONAL INTERACTIONS: EMPIRICAL AND THEORETICAL RESEARCH IN INTERNATIONAL
RELATIONS, 35(2009), pp. 30-57. 2009
http://dx.doi.org/10.1080/03050620902743838
129
A13-c114 S. Yao, Y.-J. Guo, P.-T. Yi, Multi-variable induced ordered weighted averaging operator and its
application, Dongbei Daxue Xuebao/Journal of Northeastern University, 30(2009), pp. 298-301. 2009
A13-c113 F. Szidarovszky, M. Zarghami, Combining fuzzy quantifiers and neat operators for soft computing,
IRANIAN JOURNAL OF FUZZY SYSTEMS, 6(2009), pp. 15-25. 2009
A13-c112 B.S. Ahn, H. Park, An efficient pruning method for decision alternatives of OWA operators, IEEE
Transactions on Fuzzy Systems, 16 (2009), pp. 1542-1549. 2009
http://dx.doi.org/10.1109/TFUZZ.2008.2005012
A13-c111 Ching-Hsue Cheng, Jia-Wen Wang, Ming-Chang Wua, OWA-weighted based clustering method for
classification problem, EXPERT SYSTEMS WITH APPLICATIONS, 36(2009), pp. 4988-4995. 2009
http://dx.doi.org/10.1016/j.eswa.2008.06.013
2.1.2. Fullér and Majlender’s OWA
Fullér and Majlender (2001) transform Yager’s OWA equation to a polynomial equation by using Lagrange multipliers. According to their approach, the associated weighting vector can be
obtained by (5)-(7).
A13-c110 YAO Shuang; GUO Ya-jun; YI Ping-tao, Multi-variable Induced Ordered Weighted Averaging Operator and Its Application, JOURNAL OF NORTHEASTERN UNIVERSITY(NATURAL SCIENCE),
30(2009), number 2, pp. (in Chinese). 2009
http://d.wanfangdata.com.cn/Periodical_dbdxxb200902037.aspx
2008
A13-c109 LU Zhen-bang; ZHOU Li-hua, Probabilistic Fuzzy Cognitive Maps Based on Ordered Weighted
Averaging Operators COMPUTER SCIENCE, 35(2008), number 12, pp. 187-189 (in Chinese). 2008
http://d.wanfangdata.com.cn/Periodical_jsjkx200812049.aspx
A13-c108 ZHOU Rong-xi, LIU Shan-cun, QIU Wan-hua, Survey of applications of entropy in decision analysis,
CONTROL AND DECISION, 23(2008), number 4, pp. 361-366 (in Chinese), 2008
http://d.wanfangdata.com.cn/Periodical_kzyjc200804001.aspx
A13-c107 XU Jian-Rong; ZOU Rong-Xi, A model of weight variables for obtaining an MEOWA operator based
on the constraint of interval orness measure, JOURNAL OF BEIJING UNIVERSITY OF CHEMICAL
TECHNOLOGY (NATURAL SCIENCE EDITION), 35(2008), number 3, pp. 100-103 (in Chinese). 2008
http://d.wanfangdata.com.cn/Periodical_bjhgdxxb200803023.aspx
A13-c106 Robert I. John, Shang-Ming Zhou, Jonathan M. Garibaldi and Francisco Chiclana, Automated Group
Decision Support Systems Under Uncertainty: Trends and Future Research, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE RESEARCH, 4(2008), pp. 357-371. 2008
http://www.cci.dmu.ac.uk/preprintPDF/Franciscov4i4p5.pdf
A13-c150 K. -H. Chang; C. -H. Cheng; Y. -C. Chang, Reliability assessment of an aircraft propulsion system
using IFS and OWA tree, ENGINEERING OPTIMIZATION, 40(2008) 907-921. 2008
http://dx.doi.org/10.1080/03052150802132914
A13-c149 Konstantinos Anagnostopoulos, Haris Doukas, John Psarras, A linguistic multicriteria analysis system combining fuzzy sets theory, ideal and anti-ideal points for location site selection, EXPERT SYSTEMS
WITH APPLICATIONS, 35 (2008) pp. 2041-2048. 2008
http://dx.doi.org/10.1016/j.eswa.2007.08.074
In this paper we use a special class of OWA operators which have maximum entropy for a given
level of orness (O’Hagan, 1988). The weighing vector of an OWA operator with maximum entropy
is calculated applying the results of Fullér and Majlender (2001). (page 2044)
130
A13-c148 Ali Emrouznejad, MP-OWA: The most preferred OWA operator, KNOWLEDGE-BASED SYSTEMS, 21(2008), Issue 8, pp. 847-851. 2008
http://dx.doi.org/10.1016/j.knosys.2008.03.057
However to apply the OWA operator for decision making, a very crucial issue is to determine its
weights. O’Hagan [16] suggested a maximum entropy method as the rst approach to determine
OWA operator weights in which he formulated the OWA operator weight problem to a constrained
nonlinear optimization model with a predéned degree of orness. Fullér and Majlender [A13] transformed the maximum entropy method into a polynomial equation that can be solved analytically.
A13-c147 Lopez V, Montero J, Garmendia L, Resconi G, Specification and computing states in fuzzy algorithms, INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED
SYSTEMS, vol. 16(2008), pp. 306-331. 2008
http://dx.doi.org/10.1142/S0218488508005303
A13-c146 Zhou, R.-X., Liu, S.-C., Qiu, W.-H., Survey of applications of entropy in decision analysis, CONTROL AND DECISION, Volume 23, Issue 4, April 2008, Pages 361-366. 2008
A13-c145 Xinwang Liu, A general model of parameterized OWA aggregation with given orness level INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, vol. 48, pp. 598-627. 2008
http://dx.doi.org/10.1016/j.ijar.2007.11.003
Filev and Yager [12] further proposed a method to generate MEOWA weight vector by an immediate parameter. Fullér and Majlender [A13] transformed the maximum entropy model into a
polynomial equation, which can be solved analytically. (page 599)
A13-c144 Xinwang Liu and Da Qingli, On the properties of regular increasing monotone (RIM) quantifiers
with maximum entropy, INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, Volume 37, Issue 2,
pp. 167-179. 2008
http://dx.doi.org/10.1080/03081070701192675
A13-c143 Byeong Seok Ahn, Some Quantier Functions From Weighting Functions With Constant Value of Orness, IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, PART B: CYBERNETICS,
38: (2) 540-546. 2008
http://dx.doi.org/10.1109/TSMCB.2007.912743
A13-c142 Xinwang Liu and Shilian Han, Orness and parameterized RIM quantifier aggregation with OWA
operators: A summary, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, Volume 48,
Issue 1, Pages 77-97. 2008
http://dx.doi.org/10.1016/j.ijar.2007.05.006
A13-c141 B.S. Ahn, Preference relation approach for obtaining OWA operators weights, INTERNATIONAL
JOURNAL OF APPROXIMATE REASONING, 47 (2), pp. 166-178. 2008
http://dx.doi.org/10.1016/j.ijar.2007.04.001
The resulting weights are called maximum entropy OWA (MEOWA) weights for a given degree
of orness and analytic forms and property for these weights are further investigated by several
researchers [25,A13]. (page 167)
A13-c140 B.S. Ahn, H. Park, Least-squared ordered weighted averaging operator weights, INTERNATIONAL
JOURNAL OF INTELLIGENT SYSTEMS, 23(1), pp. 33-49. 2008
http://dx.doi.org/10.1002/int.20257
2007
A13-c139 D.H. Hong and K.T. Kim, A note on the maximum entropy weighting function problem, JOURNAL
OF APPLIED MATHEMATICS AND COMPUTING, 23(2007), No. 1-2, pp. 547-552. 2007
http://www.mathnet.or.kr/mathnet/thesis_file/DHHong0613F.pdf
131
A13-c138 Zhenbang Lv and Lihua Zhou, Advanced Fuzzy Cognitive Maps Based on OWA Aggregation, INTERNATIONAL JOURNAL OF COMPUTATIONAL COGNITION, 5(2007) pp. 31-34. 2007
http://www.yangsky.com/ijcc/pdf/ijcc524.pdf
A13-c137 Xinwang Liu, Hongwei Lou, On the equivalence of some approaches to the OWA operator and RIM
quantier determination, FUZZY SETS AND SYSTEMS, vol. 159, pp. 1673-1688. 2007
http://dx.doi.org/10.1016/j.fss.2007.12.024
Filev and Yager [2] further analyzed the properties of ME-OWA operators, and proposed a method
for obtaining weights as a function of one parameter. Recently, Fullér and Majlender [A13] proposed an analytical solution by transforming the problem into a polynomial equation. (page 1677)
A13-c136 X. Liu, Some OWA operator weights determination methods with RIM quantifier, JOURNAL OF
SOUTHEAST UNIVERSITY (ENGLISH EDITION), vol. 23 (SUPPL.), pp. 76-82. 2007
A13-c135 Z.-B. Lu, L.-H. Zhou, Hybrid fuzzy cognitive maps, JOURNAL OF XIDIAN UNIVERSITY (NATURAL SCIENCE), 34 (5), pp. 779-783 (in Chinese). 2007
A13-c134 B.S. Ahn, The OWA aggregation with uncertain descriptions on weights and input arguments, IEEE
TRANSACTIONS ON FUZZY SYSTEMS, 15 (6), pp. 1130-1134. 2007
http://dx.doi.org/10.1109/TFUZZ.2007.895945
A13-c133 L. Zhenbang, Z. Lihua, A hybrid fuzzy cognitive model based on weighted OWA operators and
single-antecedent rules, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 22 (11), pp. 11891196. 2007
http://dx.doi.org/10.1002/int.20243
A13-c132 Sadiq, R., Tesfamariam, S., Probability density functions based weights for ordered weighted averaging (OWA) operators: An example of water quality indices, EUROPEAN JOURNAL OF OPERATIONAL
RESEARCH, 182 (3), pp. 1350-1368. 2007
http://dx.doi.org/10.1016/j.ejor.2006.09.041
A13-c131 Llamazares, B., Choosing OWA operator weights in the field of Social Choice, INFORMATION
SCIENCES, 177 (21), pp. 4745-4756. 2007
http://dx.doi.org/10.1016/j.ins.2007.05.015
In the field of OWA operators, one of the first approaches, suggested by O’Hagan [18], lies in
selecting the vector that maximizes the entropy of the OWA weights for a given level of orness.
This methodology has also been used by Fullér and Majlender [A13]. (page 4745)
A13-c130 Wang YM, Luo Y, Liu XW, Two new models for determining OWA operator weights COMPUTERS
& INDUSTRIAL ENGINEERING 52 (2): 203-209 MAR 2007
http://dx.doi.org/10.1016/j.cie.2006.12.002
Fullér and Majlender (2001) showed that the maximum entropy model could be transformed into
a polynomial equation that can be solved analytically. (page 203)
A13-c129 Yeh DY, Cheng CH, Yio HW, Empirical research of the principal component analysis and ordered
weighted averaging integrated evaluation model on software projects CYBERNETICS AND SYSTEMS,
38 (3): 289-303 2007
http://dx.doi.org/10.1080/01969720601187347
A13-c128 Wang YM, Parkan C, A preemptive goal programming method for aggregating OWA operator weights
in group decision making INFORMATION SCIENCES, 177 (8): 1867-1877 APR 15 2007
http://dx.doi.org/10.1016/j.ins.2006.07.023
Fullér and Majlender [A13] showed that the maximum entropy model could be converted into a
polynomial equation that can be solved analytically. (page 1867)
A13-c127 Wu J, Liang CY, Huang YQ, An argument-dependent approach to determining OWA operator weights
based on the rule of maximum entropy INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 22
(2): 209-221 FEB 2007
http://dx.doi.org/10.1002/int.20201
132
Fullér and Majlender [A13] transformed the maximum entropy model into a polynomial equation
that can be solved analytically. (page 209)
A13-c126 Xu ZS, Chen J, An interactive method for fuzzy multiple attribute group decision making INFORMATION SCIENCES, 177 (1): 248-263 JAN 1 2007
http://dx.doi.org/10.1016/j.ins.2006.03.001
Fullér and Majlender [A13] used the method of Lagrange multipliers to solve O’Hagan’s procedure analytically. (page 251)
A13-c125 Sadiq, R., Tesfamariam, S. Probability density functions based weights for ordered weighted averaging (OWA) operators: An example of water quality indices EUROPEAN JOURNAL OF OPERATIONAL
RESEARCH, 182 (3), pp. 1350-1368. 2007
http://dx.doi.org/10.1016/j.ejor.2006.09.041
Yager and Filev (1999) suggested an algorithm to obtain the OWA weights from a collection
of samples with the relevant aggregated data. Fullér and Majlender (2001) used the method of
Lagrange multipliers to solve O’Hagan’s procedure analytically. (page 1356)
A13-c124 Liu, X., The solution equivalence of minimax disparity and minimum variance problems for OWA
operators, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 45 (1), pp. 68-81. 2007
http://dx.doi.org/10.1016/j.ijar.2006.06.004
Recently, Fullér [A13] transformed the maximum entropy model into a polynomial equation,
which can be solved in an analytical way. (page 69)
A13-c123 Cheng CH, Chang JR, Ho TH Dynamic fuzzy OWA model for evaluating the risks of software
development CYBERNETICS AND SYSTEMS, 37 (8): 791-813 DEC 2006
http://dx.doi.org/10.1080/01969720600939797
A13-c122 Xu ZS, A note on linguistic hybrid arithmetic averaging operator in multiple attribute group decision
making with linguistic information GROUP DECISION AND NEGOTIATION, 15 (6): 593-604 NOV 2006
http://dx.doi.org/10.1007/s10726-005-9008-4
Fullér and Majlender (2001) used the method of Lagrange multipliers to solve O’Hagan’s procedure analytically. (page 595)
A13-c121 Liu XW, Lou HW Parameterized additive neat OWA operators with different orness levels INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 21(10): 1045-1072 OCT 2006
http://dx.doi.org/10.1002/int.20176
The maximum entropy OWA operator was first suggested by O’Hagan [40] and later was discussed
by Filev and Yager [21] and Fullér and Majlender [A13]. (page 1055)
A13-c120 Liu XW, On the properties of equidifferent OWA operator INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 43 (1): 90-107 SEP 2006
http://dx.doi.org/10.1016/j.ijar.2005.11.003
The consistent condition of geometric (maximum entropy) OWA operator was proved, some properties associated with the orness level are discussed, which extended the results of O’Hagan [14],
Filev and Yager [6,7], Fullér and Majlender [A13]. (page 91)
A13-c119 Cheng CH, Chang JR, MCDM aggregation model using situational ME-OWA and ME-OWGA operators, INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED
SYSTEMS, 14 (4): 421-443 AUG 2006
http://dx.doi.org/ 10.1142/S0218488506004102
In 2001, Fuller and Majlender [10] have used Lagrange multipliers to derive a polynomial equation
to solve constrained optimization problem and to determine the optimal weighting vector. Meanwhile, Smolikova and Wachowiak [24] have described and compared aggregation techniques for
expert multi-criteria decision-making method. Furthermore, Ribeiro and Pereira [21] have presented an aggregation schema based on generalized mixture operators using weighting functions,
and have compared it with these two standard aggregation method: weighting averaging and ordered weighted averaging in the context of multiple attribute decision making. (page 423)
133
A13-c118 Ahn BS, On the properties of OWA operator weights functions with constant level of orness, IEEE
TRANSACTIONS ON FUZZY SYSTEMS, 14(4): 511-515 AUG 2006
http://dx.doi.org/10.1109/TFUZZ.2006.876741
A13-c117 Xu ZH, Induced uncertain linguistic OWA operators applied to group decision making, INFORMATION FUSION, 7(2): 231-238 JUN 2006
http://dx.doi.org/10.1016/j.inffus.2004.06.005
A13-c116 Marchant T, Maximal orness weights with a fixed variability for owa operators, INTERNATIONAL
JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 14(3): 271-276
JUN 2006
http://dx.doi.org/10.1142/S021848850600400X
A13-c115 Wang JW, Chang JR, Cheng CH, Flexible fuzzy OWA querying method for hemodialysis database,
SOFT COMPUTING, 10 (11): 1031-1042 SEP 2006
http://dx.doi.org/10.1007/s00500-005-0030-x
Fullér and Majlender [A13] use the method of Lagrange multipliers to transfer Eq. (12) to a
polynomial equation, which can determine the optimal weighting vector. By their method, the
associated weighting vector is easily obtained by Eqs. (13)-(18). (page 1033)
A13-c114 Xinwang Liu, On the maximum entropy parameterized interval approximation of fuzzy numbers,
FUZZY SETS AND SYSTEMS, 157, pp. 869-878. 2006
http://dx.doi.org/10.1016/j.fss.2005.09.010
A13-c113 J.-R. Chang, T.-H. Ho, C.-H. Cheng, A.-P. Chen, Dynamic fuzzy OWA model for group multiple
criteria decision making, SOFT COMPUTING, 10 543-554. 2006
http://dx.doi.org/10.1007/s00500-005-0484-x
To resolve this problem, this study proposes a dynamic OWA aggregation model based on the
faster OWA operator, which has been introduced by Fullér and Majlender [A13] and can work like
a magnifying lens and adjust its focus based on the sparest information to change the dynamic
attribute weights to revise the weight of each attribute based on aggregation situation, and then to
provide suggestions to decision maker (DM). (page 544)
A13-c112 Liu XW, Some properties of the weighted OWA operator, IEEE TRANSACTIONS ON SYSTEMS
MAN AND CYBERNETICS PART B-CYBERNETICS, 36(1): 118-127 FEB 2006
http://dx.doi.org/10.1109/TSMCA.2005.854496
Comparing the researches on the weights obtaining methods in OWA operator, such as the quantifier guided aggregation [2], [37], exponential smoothing [14], learning [25], especially the maximum entropy method [16], [28], [38], [A13], the WOWA aggregation methods are relatively rare
[30], [40]. (pages 118-119)
2005
A13-c111 Nasibov, E.N., Aggregation of fuzzy information on the basis of decompositional representation,
CYBERNETICS AND SYSTEMS ANALYSIS, 41 (2), pp. 309-318. 2005
http://dx.doi.org/10.1007/s10559-005-0065-0
A13-c110 Xu ZS, An overview of methods for determining OWA weights, INTERNATIONAL JOURNAL OF
INTELLIGENT SYSTEMS, 20 (8): 843-865 AUG 2005
http://dx.doi.org/10.1002/int.20097
Fullér and Majlender [A13] used the method of Lagrange multipliers to solve problem 12 analytically and got the following:
1. If n = 2 then w1 = α and w2 = 1 − α.
2. If α = 0 or α = 1 then the associated weighting vectors are uniquely defined as w =
(0, 0, . . . , 1)T and w = (1, 0, . . . , 0)T respectively, with value of dispersion zero.
134
3. If n ≥ 3 and 0 < α < 1 then
q
wj = n−1 w1n−j wnj−1
(15)
((n − 1)α − n)w1 + 1
(n − 1)α + 1 − nw1
w1 [(n − 1)α + 1 − nw1 ]n = ((n − 1)α)n−1 [((n − 1)α − n)w1 + 1]
wn =
(16)
(17)
Solving Equations 15-17, the optimal OWA weights can be determined. (page 847)
A13-c109 Lan H, Ding Y, Hong J, Decision support system for rapid prototyping process selection through
integration of fuzzy synthetic evaluation and an expert system INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, 43 (1): 169-194 JAN 1 2005
http://dx.doi.org/10.1080/00207540410001733922
A13-c108 Arfi B, Fuzzy decision making in politics: A linguistic fuzzy-set approach (LFSA), POLITICAL
ANALYSIS, 13 (1): 23-56 WIN 2005
http://dx.doi.org/10.1093/pan/mpi002
A13-c107 Ying-Ming Wang, Celik Parkan, A minimax disparity approach for obtaining OWA operator weights,
INFORMATION SCIENCES, 175(2005) 20-29. 2005
http://dx.doi.org/10.1016/j.ins.2004.09.003
Fullér and Majlender [A13] showed that the maximum entropy model could be transformed into
a polynomial equation that can be solved analytically. (page 21)
2004
A13-c106 Liu Xinwang, Preference Representation with Geometric OWA Operator, SYSTEMS ENGINEERING, 22(2004), number 9, pp. 82-86 (in Chinese). 2004
http://d.wanfangdata.com.cn/Periodical_xtgc200409019.aspx
A13-c105 Liu Xinwang, Three methods for generating monotonic OWA operator weights with given orness
level, JOURNAL OF SOUTHEAST UNIVERSITY (ENGLISH EDITION), Vol. 20 No. 3, pp. 369-373.
2004
http://www.wanfangdata.com.cn/qikan/periodical.articles/dndxxb-e/dndx2004/0403/040321.htm
A13-c104 Liu XW, On the methods of decision making under uncertainty with probability information, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 19(12): 1217-1238 DEC 2004
http://dx.doi.org/10.1002/int.20045
The maximum entropy OWA operator was first suggested by O’Hagan [11] and later was discussed
by Filev and Yager [10] and Fullér and Majlender [A13]. (page 1225)
A13-c103 Xinwang Liu and Lianghua Chen, On the properties of parametric geometric OWA operator, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 35 pp. 163-178. 2004
http://dx.doi.org/10.1016/j.ijar.2003.09.001
Recently, Fullér and Majlender [A13] proposed another method to generate MEOWA weights, the
method get the weights by solving a polynomial equation. (page 164)
A13-c102 Chiclana F, Herrera-Viedma E, Herrera F, et al. Induced ordered weighted geometric operators and
their use in the aggregation of multiplicative preference relations INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 19(3): 233-255 MAR 2004
http://dx.doi.org/10.1002/int.10172
2003
A13-c101 Beliakov G., How to build aggregation operators from data INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 18(8): 903-923 AUG 2003
http://dx.doi.org/10.1002/int.10120
135
A13-c100 Xu, Z., Da, Q. Approaches to obtaining the weights of the ordered weighted aggregation operators
Dongnan Daxue Xuebao (Ziran Kexue Ban)/Journal of Southeast University (Natural Science Edition), 33
(1), pp. 94-96. 2003
in proceedings and edited volumes
2015
A13-c57 Mikael Collan, Mario Fedrizzi, Pasi Luukka, Multi-distance and Fuzzy Similarity Based Fuzzy TOPSIS, In: Kurosh Madani, Antnio Dourado, Agostinho Rosa, Joaquim Filip, Janusz Kacprzyk eds., Computational Intelligence, Studies in Computational Intelligence, vol. 613, Springer, 2016. (ISBN 978-3-31923391-8) pp. 227-244. 2015
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A13-c56 Mikael Collan, Pasi Luukka, Strategic R&D Project Analysis: Keeping It Simple and Smart, In:
Mikael Collan, Mario Fedrizzi, Janusz Kacprzyk eds., Fuzzy Technology: Present Applications and Future
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169-191. 2015
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A13-c55 Umut Asan, Ayberk Soyer, Failure Mode and Effects Analysis Under Uncertainty: A Literature Review and Tutorial, In: Intelligent Decision Making in Quality Management, ntelligent Systems Reference
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A13-c54 Wlodzimierz Ogryczak, Jaroslaw Hurkala, Determining OWA Operator Weights by Maximum Deviation Minimization, In: Pattern Recognition and Machine Intelligence, Lecture Notes in Computer Science,
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A13-c53 Song Wang, ME-OWA based DEMATEL-ISM Accident Causation Analysis of Complex System,
In: Proceedings of the 5th International Asia Conference on Industrial Engineering and Management Innovation, Proceedings of the International Asia Conference on Industrial Engineering and Management
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A13-c52 Ankit Gupta, Shruti Kohli, An Analytical Study of Ordered Weighted Geometric Averaging Operator
on Web Data Set as a MCDM Problem, Proceedings of Fourth International Conference on Soft Computing
for Problem Solving, Advances in Intelligent Systems and Computing, vol. 335/2015, Springer, [ISBN
978-81-322-2216-3], pp. 585-597. 2015
http://dx.doi.org/10.1007/978-81-322-2217-0_47
A13-c51 David Koloseni, Mario Fedrizzi, Pasi Luukka, Jouni Lampinen, Mikael Collan, Differential Evolution
Classifier with Optimized OWA-Based Multi-distance Measures for the Features in the Data Sets, Proceedings of the 7th International Conference Intelligent Systems IEEE IS’2014, September 24-26, 2014,
Warsaw, Poland, Volume 1: Mathematical Foundations, Theory, Analyses, Advances in Intelligent Systems
and Computing, vol. 322, (ISBN 978-3-319-11312-8) pp. 765-777. 2015
http://dx.doi.org/10.1007/978-3-319-11313-5 67
2014
A13-c50 Song Wang, ME-OWA based DEMATEL-ISM Accident Causation Analysis of Complex System, In:
Proceedings of the 5th International Asia Conference on Industrial Engineering and Management Innovation, Atlantis Press, [ISBN 978-94-62520-18-9], pp. 24-29. 2014
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maximal entropy. (page 25)
2013
A13-c49 M Moradi, M R Delavar, B Moshiri, SENSITIVITY ANALYSIS OF ORDERED WEIGHTED AVERAGING OPERATOR IN EARTHQUAKE VULNERABILITY ASSESSMENT, H Arefi, M A Sharifi,
P Reinartz, M R Delavar eds., Sensors and Models in Photogrammetry and Remote Sensing, October 5-8,
2013, Tehran, Iran, pp. 277-282. 2013
http://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/
XL-1-W3/277/2013/isprsarchives-XL-1-W3-277-2013.pdf
A13-c48 Pasi Luukka, Mikael Collan, Using a Linguistic Scorecard for Peer-Assessment Through an On-Line
System, in: Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology
(EUSFLAT 2013), September 11-13, 2013, Milan, Italy, Atlantis Press, [ISBN 978-90786-77-78-9], pp.
174-179. 2013
http://dx.doi.org/10.2991/eusflat.2013.31
2011
A13-c47 Jian Wu, Qing-Wei Cao, An OWA Operator Based Approach to Aggregate Group Opinion by Similarity Degree, 2011 Fourth International Conference on Business Intelligence and Financial Engineering,
Wuhan, China, [ISBN: 978-0-7695-4527-1], pp. 665-667. 2011
http://dx.doi.org/10.1109/BIFE.2011.13
A13-c46 Xinwang Liu, Analytical solution for symmetrical OWA operator determination with given medianness
level Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), July 26-28,
2011, Shanghai, China, [ISBN: 978-1-61284-180-9], pp. 77-81. 2011
http://dx.doi.org/10.1109/FSKD.2011.6019523
A13-c45 Jing-Rong Chang, Yu-Jie Huang, A weighted fuzzy time series model based on adoptive OWA operators, International Conference on Uncertainty Reasoning and Knowledge Engineering, August 4-7, 2011,
Bali, Indonesia, [ISBN: 978-1-4244-9985-4], pp. 94-97. 2011
http://dx.doi.org/10.1109/URKE.2011.6007849
A13-c44 Xinwang Liu, A Review of the OWA Determination Methods: Classification and Some Extensions,
in: Ronald R Yager, Janusz Kacprzyk, Gleb Beliakov eds., Recent Developments in the Ordered Weighted
Averaging Operators: Theory and Practice. Studies in Fuzziness and Soft Computing, vol. 265/2011,
Springer, [ISBN 978-3-642-17909-9], pp. 49-90. 2011
http://dx.doi.org/10.1007/978-3-642-17910-5_4
2010
A13-c43 P. Pong, M. Morelande, S. Challa, Heterogeneous fusion with a combined evidential, probability and
OWA methods for target classification, 13th Conference on Information Fusion, Fusion 2010, July 26-29,
2010, Edinburgh, England, [ISBN: 978-098244381-1]. Paper 5711975. 2010
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5711975
The heterogeneous fusion method in this paper adopted the analytical approach based on the maximal entropy OWA operator weight algorithm in [A13], where the weight vector can be obtained
by (page 4)
A13-c42 Gleb Beliakov, Optimization and Aggregation Functions, in: Weldon A Lodwick, Janusz Kacprzyk
eds., Fuzzy Optimization: Recent Advances and Applications, Studies in Fuzziness and Soft Computing
vol. 254/2010, Springer [ISBN 978-3-642-13934-5], pp. 77-108. 2010
137
http://dx.doi.org/10.1007/978-3-642-13935-2_4
A13-c41 Jia-Wen Wang and Jing-Wen Chang, A Fusion Approach for Multi-criteria Evaluation, in: Ngoc
Thanh Nguyen, Radosław Katarzyniak, and Shyi-Ming Chen eds., Advances in Intelligent Information and
Database Systems, Studies in Computational Intelligence, vol. 283/2010, Springer Berlin / Heidelberg,
[ISBN 978-3-642-12089-3], pp. 349-358. 2010
http://dx.doi.org/10.1007/978-3-642-12090-9_30
2009
A13-c40 J. W. Wang, J. W. Liu, Information Fusion Technique for Fuzzy Time Series Model, International
Conference on Machine Learning and Computing, July 10-12, 2009, Perth, Ausztralia, [ISBN: 978-184626-018-6], pp. 45-49. 2009
A13-c39 X. Liu, On the methods of OWA operator determination with different dimensional instantiations, 6th
International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2009, 14-16 August 2009,
Tianjin, China, Volume 7, [ISBN 978-076953735-1], Article number 5359982, pp. 200-204. 2009
http://dx.doi.org/10.1109/FSKD.2009.312
A13-c38 Mostafa Keikha and Fabio Crestani, Effectiveness of Aggregation Methods in Blog Distillation, in:
Troels Andreasen, Ronald R.Yager, Henrik Bulskov, Henning Christiansen, Henrik Legind Larsen eds.,
Flexible Query Answering Systems, Lecture Notes in Computer Science, vol. 5822/2009, Springer, [ISBN
978-3-642-04956-9], pp. 157-167. 2009
http://dx.doi.org/10.1007/978-3-642-04957-6_14
A13-c37 Matteo Brunelli, Michele Fedrizzi, A Fuzzy Approach to Social Network Analysis, Social Network
Analysis and Mining, International Conference on Advances in Social Network Analysis and Mining,
Athens, Greece, July 20-July 22, [ISBN 978-0-7695-3689-7] pp. 225-230. 2009
http://doi.ieeecomputersociety.org/10.1109/ASONAM.2009.72
A13-c36 B. Fonooni; S. Moghadam, Applying induced aggregation operator in designing intelligent monitoring
system for financial market, IEEE Symposium on Computational Intelligence for Financial Engineering,
March 30, 2009 - April 2, 2009, Nashville, TN, [ISBN 978-1-4244-2774-1], pp. 80-84. 2009
http://dx.doi.org/10.1109/CIFER.2009.4937506
A13-c35 Benjamin Fonooni, Seied Javad Mousavi Moghadam, Automated trading based on uncertain OWA
in financial markets, in: Proceedings of the 10th WSEAS international conference on Mathematics and
computers in business and economics, Prague, Czech Republic, pp. 21-25. 2009
A13-c28 Victor M. Vergara, Shan Xia, and Thomas P. Caudell, Information fusion across expert groups with
dependent and independent components, Multisensor, Multisource Information Fusion: Architectures, Algorithms, and Applications 2009, Proceedings of SPIE - The International Society for Optical Engineering,
7345, art. no. 73450C. 2009
http://dx.doi.org/10.1117/12.818669
2008
A13-c34 R. X. Zhou, J. R. Xu,s A method for obtaining the maximum entropy OWA operator weights with
uncertain orness measure, 20th Chinese Control and Decision Conference, July 2-4, 2008, Yantai, China,
[ISBN: 978-1-4244-1733-9], pp. 2325-2328. 2008
A13-c33 Ming Li, Yan-Tao Zheng, Shou-Xun Lin, Yong-Dong Zhang and Tat-Seng Chua, Multimedia evidence
fusion for video concept detection via OWA operator, Lecture Notes in Computer Science, vol. 5371/2008,
pp. 208-216. 2008
http://dx.doi.org/10.1007/978-3-540-92892-8_21
138
We therefore formulate the multi-modal fusion as an information aggregation task in the framework of group decision making (GMD) problem. Specifically, we employ the Ordered Weighted
Average (OWA) operator to aggregate the group of decisions by uni-modal detectors, as it has
been reported to be an effective solution for GMD problem [A13]. (page 209)
In Dispersion Maxspace represented by Eqn (8), the weights of different Orness are given with
maximal dispersion which means most individual criteria are being used in the aggregation that
gives more robustness [A13]. (page 212)
A13-c32 Yao-Hsien Chen, Jing-Wei Liu, Ching-Huse Cheng, Intelligent Preference Selection for Evaluating
Studentsapos; Learning Achievement Third International Conference on Convergence and Hybrid Information Technology, Volume 2, Article number 4682412, 11-13 November, 2008, pp. 1214 -1219. 2008
http://dx.doi.org/10.1109/ICCIT.2008.410
A13-c31 K.-M. Björk, Obtaining minimum variability OWA operators under a fuzzy level of orness, ICINCO
2008 - Proceedings of the 5th International Conference on Informatics in Control, Automation and Robotics
ICSO, Volume ICSO, pp. 114-119. 2008
A13-c30 Xinwang Liu; Xiaoguang Yang; Yong Fang, The relationships between two kinds of OWA operator
determination methods, IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2008), pp. 264270, 1-6 June 2008
http://dx.doi.org/10.1109/FUZZY.2008.4630375
A13-c29 B. Fonooni; S. J. Moghadam, Designing financial market intelligent monitoring system based on OWA,
in: Proceedings of the WSEAS international Conference on Applied Computing, (Istanbul, Turkey, May 27
- 30, 2008). M. Demiralp, W. B. Mikhael, A. A. Caballero, N. Abatzoglou, M. N. Tabrizi, R. Leandre, M.
I. Garcia-Planas, and R. S. Choras, Eds. Mathematics And Computers In Science And Engineering. World
Scientific and Engineering Academy and Society (WSEAS), Stevens Point, Wisconsin, pp. 35-39. 2008
A13-c28 Calvo, T., Beliakov, G., Identification of weights in aggregation operators, in: Bustince, Humberto;
Herrera, Francisco; Montero, Javier (Eds.) Fuzzy Sets and Their Extensions: Representation, Aggregation
and Models Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer
Vision Series: Studies in Fuzziness and Soft Computing , Vol. 220 Springer, [ISBN: 978-3-540-73722-3]
2008, pp. 145-162. 2008
http://dx.doi.org/10.1007/978-3-540-73723-0_8
A13-c27 B. Llamazares, J.L. Garcia-Lapresta, Extension of some voting systems to the field of gradual preferences, in: Bustince, Humberto; Herrera, Francisco; Montero, Javier (Eds.) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models Intelligent Systems from Decision Making to Data Mining,
Web Intelligence and Computer Vision Series: Studies in Fuzziness and Soft Computing , Vol. 220 Springer,
[ISBN: 978-3-540-73722-3] 2008, pp. 297-315. 2008
http://dx.doi.org/10.1007/978-3-540-73723-0_15
2007
A13-c26 GW Wei, Dependent OWGA operator, 6th Wuhan International Conference on E-Business, May 2627, 2007, Wuhan, China, [ ISBN: 978-0-9604962-9-7], pp. 1632-1637. 2007
A13-c25 Benjamin Fonooni, Rational-Emotional Agent Decision Making Algorithm Design with OWA, 19th
IEEE International Conference on Tools with Artificial Intelligence, October 29-31, 2007, Paris, France,
pp. 63-66. 2007
http://doi.ieeecomputersociety.org/10.1109/ICTAI.2007.123
A13-c24 Cheng, Ching-Huse; Liu, Jing-Wei; Wu, Ming-Chang, OWA Based Information Fusion Techniques
for Classification Problem, 2007 International Conference on Machine Learning and Cybernetics, 19-22
Aug. 2007, vol.3, [ISBN 978-1-4244-0973-0 ], pp.1383-1388. 2007
http://dx.doi.org/10.1109/ICMLC.2007.4370360
139
Fullér and Majlender [A13] transform Yager’s OWA equation to a polynomial equation by using Lagrange multipliers. According to their approach, the associated weighting vector can be
obtained by (2) - (4). (page 1384)
A13-c23 Wang, Jia-Wen; Cheng, Ching-Hsue, Information Fusion Technique for Weighted Time Series Model,
International Conference on Machine Learning and Cybernetics, 19-22 Aug. 2007, [ISBN 978-1-42440973-0 ], vol.4, pp.1860-1865. 2007
http://dx.doi.org/10.1109/ICMLC.2007.4370451
Fullér and Majlender use the method of Lagrange multipliers to transfer equation (7) to a polynomial equation, which can determine the optimal weighting vector. By their method, the associated
weighting vector is easily obtained by (8)-(9) [A13].
(page 1861)
A13-c22 Na Cai; Ming Li; Shouxun Lin; Yongdong Zhang; Sheng Tang; AP-Based Adaboost in High Level
Feature Extraction at TRECVID, in: Proceedings of the 2nd International Conference on Pervasive Computing and Applications, (ICPCA 2007), 26-27 July 2007, pp. 194-198. 2007
http://dx.doi.org/10.1109/ICPCA.2007.4365438
A13-c21 Chang, Jing-Rong; Liao, Shu-Ying; Cheng, Ching-Hsue, Situational ME-LOWA Aggregation Model
for Evaluating the Best Main Battle Tank, 2007 International Conference on Machine Learning and Cybernetics, 19-22 Aug. 2007, vol.4, pp.1866-1870. 2007
http://dx.doi.org/10.1109/ICMLC.2007.4370452
A13-c20 Ching-Huse Cheng, Jing-Wei Liu, OWA Rough Set to Forecast the Industrial Growth Rate, International Conference on Convergence Information Technology, 21-23 Nov. 2007, pp. 1862-1867. 2007
http://doi.ieeecomputersociety.org/10.1109/ICCIT.2007.233
A13-c19 Benjamin Fonooni, Behzad Moshiri and Caro Lucas, Applying Data Fusion in a Rational Decision
Making with Emotional Regulation, in: 50 Years of Artificial Intelligence, Essays Dedicated to the 50th
Anniversary of Artificial Intelligence, Lecture Notes in Computer Science, Volume 4850/2007, Springer,
2007, pp. 320-331. 2007
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2006
A13-c18 Eric Levrat, Jean Renaud, Christian Fonteix, Decision compromise modelling based on OWA operators, Ninth IFAC Symposium on Automated Systems Based on Human Skill and Knowledge, Automated
Systems Based on Human Skill and Knowledge, May 22-24, 2006, [ISBN 978-3-902661-05-0], volume 9,
part I. 2006
http://www.ifac-papersonline.net/Detailed/38831.html
A13-c17 Yeh, Duen-Yian Cheng, Ching-Hsue Yio, Hwei-Wun, OWA and PCA integrated assessment model in
software project, in: 2006 World Automation Congress, WAC’06, 24-26 July 2006, Budapest, Hungary, art.
no. 4259935, pp. 1-6. 2006
http://dx.doi.org/10.1109/WAC.2006.376019
A13-c16 Zadrozny S, Kacprzyk J, On tuning OWA operators in a flexible querying interface, in: Flexible Query
Answering Systems, 7th International Conference, FQAS 2006, LECTURE NOTES IN COMPUTER SCIENCE 4027: 97-108 2006
http://dx.doi.org/10.1007/11766254_9
Filev and Yager [11] simplified this optimization problem using the Lagrange multipliers method.
Then the problem boils down to finding the root of a polynomial of degree m − 1. Fullér and
Majlender [A13], assuming the same approach, proposed a simpler formulae for the weight vector
W . (page 101)
140
A13-c15 Xu ZS, Dependent OWA operators, in: Modeling Decisions for Artificial Intelligence, Third International Conference, MDAI 2006, LECTURE NOTES IN ARTIFICIAL INTELLIGENCE 3885: 172-178
2006
http://dx.doi.org/10.1007/11681960_18
A13-c14 Troiano L, Yager RR On the relationship between the quantifier threshold and OWA operators, LECTURE NOTES IN ARTIFICIAL INTELLIGENCE 3885: 215-226 2006
http://dx.doi.org/10.1007/11681960_22
2005
A13-c13 Ching-Hsue Cheng, Jing-Rong Chang, Tien-Hwa Ho, and An-Pin Chen, Evaluating the Airline Service Quality by Fuzzy OWA Operators in: Vincent Torra, Yasuo Narukawa, Sadaaki Miyamoto (Eds.):
Proceedings of the Modeling Decisions for Artificial Intelligence: Second International Conference, MDAI
2005, Tsukuba, Japan, July 25-27, 2005, LNAI 3558, Springer, pp. 77-88. 2005
http://dx.doi.org/10.1007/11526018_9
Fullér and Majlender [A13] used the method of Lagrange multipliers to transfer Yager’s OWA
equation to a polynomial equation, which can determine the optimal weighting vector. By their
method, the associated weighting vector is easily obtained by (5)-(7).
q
n−j
j−1
(5)
ln wn +
ln w1 ⇒ wj = n−1 w1n−j wnj−1
ln wj =
n−1
n−1
((n − 1)α − n)w1 + 1
and wn =
(6)
(n − 1)α + 1 − nw1
then w1 [(n − 1)α + 1 − nw1 ]n = ((n − 1)α)n−1 [((n − 1)α − n)w1 + 1] (7)
(pages 79-80)
A13-c12 L. Troiano and R.R. Yager, A meaure of dispersion for OWA operators, in: Y. Liu, G. Chen and
M. Ying eds., Proceedings of the Eleventh International Fuzzy systems Association World Congress, July
28-31, 2005, Beijing, China, 2005 Tsinghua University Press and Springer, [ISBN 7-302-11377-7] pp.
82-87. 2005
Entropy has been generally adopted as a measure of weight dispersion of the OWA operators.
O’Hagan [2], in his ground braking work, suggests to select the vector that maximizes the entropy
of OWA weights (ME-OWA). Analytical solutions to this problem have been proposed by Filev
and Yager [3], and Fullér and Majlender [A13]. (page 82)
2003
A13-11 Liu, X.-W., Chen, L.-H. The equivalence of maximum entropy OWA operator and geometric OWA
operator, International Conference on Machine Learning and Cybernetics, 5, pp. 2673-2676. 2003
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1259989
A13-c10 H.B. Mitchell, Data Mining Using a Probabilistic Weighted Ordered Weighted Average (PWOWA)
Operator, in: Vicenc Torra ed., Information Fusion in Data Mining Series: Studies in Fuzziness and Soft
Computing , Vol. 123, Springer, [ISBN: 978-3-540-00676-3] pp. 41-58. 2003
in books
A13-c4 Hu-Chen Liu, FMEA Using Intuitionistic Fuzzy Hybrid Weighted Euclidean Distance Operator, Springer,
ISBN: 978-981-10-1465-9 (Print) 978-981-10-1466-6 (Online). 2016
http://dx.doi.org/10.1007/978-981-10-1466-6
141
A13-c3 G Beliakov, H Bustince Sola, T Calvo Sánchez, A Practical Guide to Averaging Functions, Studies in
Fuzziness and Soft Computing, vol. 329, Springer, (ISBN 978-3-319-24751-9). 2016
http://dx.doi.org/10.1007/978-3-319-24753-3
A13-c2 Badredine Artfi, Linguistic Fuzzy Logic Methods in Social Sciences, Studies in Fuzziness and Soft
Computing Series, vol 253/2010, Springer [ISBN 978-3-642-13342-8]. 2010
http://dx.doi.org/10.1007/978-3-642-13343-5
A13-c1 Beliakov, G., Pradera, A., Calvo, T., Aggregation Functions: A Guide for Practitioners, Studies in
Fuzziness and Soft Computing, Vol. 221(2007), [ISBN 978-3-540-73720-9], Springer. 2007
http://dx.doi.org/10.1007/978-3-540-73721-6_7
The solution is provided in [A13] and is called Maximum Entropy OWA (MEOWA). Using the
method of Lagrange multipliers, the authors obtain the following expressions for wi : (page78)
in Ph.D. dissertations
• Matteo Brunelli, Some Advances in Mathematical Models for Preference Relations, Turku Centre for Computer
Science, number 136/2011, [ISBN 978-952-12-2595-6], Finland. 2011
• Olivier Thonnard, A multi-criteria clustering approach to support attack attribution in cyberspace, Télécommunications
et électronique de Paris, France. 2010
https://pastel.archives-ouvertes.fr/pastel-00006003
Fullér and Majlender proposed two methods for choosing OWA weights that are based on various
measures of weights dispersion (or entropy) [56]. (page 81)
[A14] Christer Carlsson and Robert Fullér, On possibilistic mean value and variance of fuzzy numbers, FUZZY
SETS AND SYSTEMS, 122(2001) 315-326. [MR: 2002i:03063]. doi 10.1016/S0165-0114(00)00043-9
in journals
2016
A14-c496 S Muzzioli, B De Baets, Fuzzy approaches to option price modelling, IEEE TRANSACTIONS ON
FUZZY SYSTEMS (to appear). 2016
http://dx.doi.org/10.1109/TFUZZ.2016.2574906
A14-c495 Fu Sha, A Multi-attribute Decision Making Method Based on Dynamic Triangle Fuzzy Numbers,
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND STATISTICS, 54: (3) pp. 59-69.
2016
WOS: 000374231600006
A14-c494 Sini Guo, Lean Yu, Xiang Li, Samarjit Kar, Fuzzy multi-period portfolio selection with different
investment horizons, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 254: (3) pp. 1026-1035.
2016
http://dx.doi.org/10.1016/j.ejor.2016.04.055
With the introduction of fuzzy set theory, more and more scholars are engaged in portfolio selection studies based on fuzzy set theory. For instance, Carlsson and Fullér (2001) introduced lower
and upper possibilistic mean for fuzzy numbers. Zhang and Nie (2003) defined the lower and
upper variance and covariance for fuzzy numbers and formulated a fuzzy mean-variance model.
A14-c493 Abel Rubio, Jose D Bermudez, Enriqueta Vercher, Forecasting portfolio returns using weighted fuzzy
time series, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING (to appear). 2016
http://dx.doi.org/10.1016/j.ijar.2016.03.007
142
Other possibility moments could be used if the expert decides to apply weights to the γ-level cuts
of the membership function of the fuzzy returns [A14, A9].
A14-c492 Indah Simamora, Rahayu Sashanti, Optimization of Fuzzy Portfolio Considering Stock Returns and
Downside Risk, INTERNATIONAL JOURNAL OF SCIENCE AND RESEARCH, 5: (4) pp. 141-145.
2016
A14-c491 Oshmita Dey, Bibhas C Giri, Debjani Chakraborty, A fuzzy random continuous review inventory
model with a mixture of backorders and lost sales under imprecise chance constraint, INTERNATIONAL
JOURNAL OF OPERATIONAL RESEARCH (to appear). 2016
http://dx.doi.org/10.1504/IJOR.2016.075648
A14-c490 P Joel Ravindranath, M Balasubrahmanyam, M Suresh Babu, A Fuzzy Mean-Variance-Skewness
Portfolioselection Problem, INTERNATIONAL JOURNAL OF MATHEMATICS AND STATISTICS INVENTION, 4: (3) pp. 41-52. 2016
Carlsson and Fuller [A14] introduced the notation of lower and upper possibilistic means for fuzzy
numbers. (page 42)
A14-c489 XU Lan, LI Jiaming, ZHAO Yamin, Optimization of Project Portfolio Selection Considering Interactions Among Multiple Projects, Management Science and Engineering, 10: (1) pp. 1-7. 2016
http://dx.doi.org/10.3968/8221
A14-c488 Oktay Tas, Cengiz Kahraman and Celal Barkan Güran, A Scenario Based Linear Fuzzy Approach
in Portfolio Selection Problem: Application in the ?stanbul Stock Exchange, JOURNAL OF MULTIPLEVALUED LOGIC AND SOFT COMPUTING, 26(2016), number 3-5, pp. 269-294. 2016
A14-c487 Kezhong Liu, Jinfen Zhang, Xinping Yan, Yiliu Liu, Di Zhang, Weidong Hu, Safety assessment for
inland waterway transportation with an extended fuzzy TOPSIS, PROCEEDINGS OF THE INSTITUTION
OF MECHANICAL ENGINEERS PART O: JOURNAL OF RISK AND RELIABILITY (to appear). 2016
http://dx.doi.org/10.1177/1748006X16631869
A14-c486 Sushil Kumar Bhuiya, Debjani Chakraborty, A fuzzy random EPQ model with fuzzy defective rates
and fuzzy inspection errors, JOURNAL OF INTELLIGENT & FUZZY SYSTEMS (to appear). 2016
http://dx.doi.org/10.3233/IFS-162098
A14-c485 Luca Anzilli, Gisella Facchinetti, A Fuzzy Quantity Mean-Variance View and Its Application to a
Client Financial Risk Tolerance Model, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
(to appear). 2016
http://dx.doi.org/10.1002/int.21812
A14-c484 Fokrul Alom Mazarbhuiya, Finding standard deviation of a fuzzy number, International Journal of
Research - GRANTHAALAYAH, 4(2016), number 1, pp. 63-69. 2016
http://granthaalayah.com/Articles/Vol4Iss1/08_IJRG16_A01_11.pdf
Zadeh [1] proposed the concept of fuzziness into the realm of Mathematics. Accordingly, various
authors have made study on the mathematics related to the fuzzy measure and the associated fuzzy
expected value of a possibility distribution [[2], [3], [4], [5], [6], [7]]. In [A14] author discussed
the possibilistic means and variance of a fuzzy number.
A14-c483 Mikael Collan, Mario Fedrizzi, Pasi Luukka, Possibilistic risk aversion in group decisions: theory
with application in the insurance of giga-investments valued through the fuzzy pay-off method, APPLIED
SOFT COMPUTING (to appear). 2016
http://dx.doi.org/10.1007/s00500-016-2069-2
To determine the possibilistic risk premiums we will use the notions of possibilistic expected value
and possibilistic variance, as introduced by Carlsson and Fullér (2001), Carlsson et al. (2002) and
Fullér and Majlender (2003).
A14-c482 Reza Babazadeh, Jafar Razmi, Mir Saman Pishvaee, Masoud Rabbani, A sustainable second-generation
biodiesel supply chain network design problem under risk, OMEGA-INTERNATIONAL JOURNAL OF
MANAGEMENT SCIENCE (to appear). 2016
http://dx.doi.org/10.1016/j.omega.2015.12.010
143
As mentioned in previous section, the main parameters of the proposed model have been tainted
with uncertainty. In our case, due to lack of enough historical data making probabilistic distribution for uncertain parameters is not possible, instead limited historical data and expert?s opinions
can be efficiently used to construct possibility distribution of uncertain parameters [57]. One of
the main disadvantage of different available possibilistic programming method either based on expected value [58] or mean value [A14] is that they only consider expected or mean values of OF in
developing possibilistic-based solution methods. However, risk control of OF has been neglected
in these models and all decisions are made under average condition of uncertain parameters realization.
A14-c481 Xiajie Yi, Yunwen Miao Jian Zhou, Yujie Wang, Some novel inequalities for fuzzy variables on
the variance and its rational upper bound, JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016:
Paper 41. 18 p. 2016
http://dx.doi.org/10.1186/s13660-016-0975-6
Apart from the concept and calculation of the expected value, Carlsson and Fullér [A14] brought
up the notions of crisp possibilistic expected value and crisp possibilistic variance for fuzzy variables with continuous possibility distributions. They also presented the process about the calculation of the variance on linear combination of fuzzy variables, which turned out to be figured
in an analogous way as in probability theory. Chen and Tan [9] further studied the definitions of
variance and covariance in multiplication of fuzzy variables, which were applied in portfolio to
build possibilistic models for better selection under an uncertain situation. (page 2)
A14-c480 Zhuo Dai, Hong-mei Dai, Bi-objective closed-loop supply chain network design with risks in a fuzzy
environment, JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING, 33: (3) pp. 169-180.
2016
http://dx.doi.org/10.1080/21681015.2015.1126655
A14-c479 Dong Jiu-Ying, Wan Shu-Ping, A new method for prioritized multi-criteria group decision making
with triangular intuitionistic fuzzy numbers, JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 30:
(3) pp. 1719-1733. 2016
http://dx.doi.org/10.3233/IFS-151882
A14-c478 Peng Zhang, An interval mean-average absolute deviation model for multiperiod portfolio selection
with risk control and cardinality constraints, SOFT COMPUTING, 20(2016), number 3, pp. 1203-1212.
2016
http://dx.doi.org/10.1007/s00500-014-1583-3
Though probability theory is a major tool used for analyzing uncertainty in finance, it cannot
describe the uncertainty completely since there are many other uncertain factors that differ from
the random ones found in financial markets. Some other techniques can be applied to handle
uncertainty of financial markets. Carlsson and Fullér (2001) introduced the notions of lower and
upper possibilistic mean values of a fuzzy number, viewing them as possibility distributions. (page
1203)
A14-c477 Jiuying Dong, Shuping Wan, A new method for multi-attribute group decision making with triangular
intuitionistic fuzzy numbers, KYBERNETES, 45: (1) pp. 158-180. 2016
http://dx.doi.org/10.1108/K-02-2015-0058
A9-c476 Franco Molinari, A new criterion of choice between generalized triangular fuzzy numbers, FUZZY
SETS AND SYSTEMS, 296(2016), pp. 51-69. 2016
http://dx.doi.org/10.1016/j.fss.2015.11.022
Their work generalizes the concepts introduced by Carlsson and Fullér [A14], where lower and
upper possibilistic mean value of A are defined as
A14-c475 Zhuo Dai, Multi-objective fuzzy design of closed-loop supply chain network considering risks and
environmental impact, HUMAN AND ECOLOGICAL RISK ASSESSMENT, 22: (4) pp. 845-873. 2016
http://dx.doi.org/10.1080/10807039.2015.1113852
144
A14-c474 Zahra Mashayekhi, Hashem Omrani, An integrated multi-objective Markowitz-DEA cross-efficiency
model with fuzzy returns for portfolio selection problem, APPLIED SOFT COMPUTING, 38(2016), pp.
1-9. 2016
http://dx.doi.org/10.1016/j.asoc.2015.09.018
A14-c473 Gong Yanbing, Hu Na, Liu Gaofeng, A New Magnitude Possibilistic Mean Value and Variance of
Fuzzy Numbers, International Journal of Fuzzy Systems, 18(2016), number 1, pp. 140-150. 2016
http://dx.doi.org/10.1007/s40815-015-0072-x
Carlsson and Fullér (Fuzzy Sets Syst 122: 315-326, 2001) introduced the notations of lower possibilistic and upper possibilistic mean values of a fuzzy number, and investigated its relationship to
the interval-valued possibilistic mean and variance. In this paper, we introduce the new notations
of lower magnitude and upper magnitude mean values of a fuzzy number. The new interval-valued
magnitude mean and variance are defined, which differs from the one given by Carlsson and Fullér.
The relationship between the interval-valued magnitude mean and the interval-valued possibilistic
mean is investigated. Furthermore, we shall also introduce the notations of crisp magnitude possibilistic mean value, variance, and covariance of fuzzy numbers, which are consistent with the
extension principle. Finally, some comparative examples are used to illustrate the advantage of
the proposed interval-valued magnitude possibilistic mean and variance method to ranking fuzzy
numbers. (page 140)
In this section, we extended the concept of Carlsson and Fullér [A14] about the interval-valued
possibilistic mean value of fuzzy numbers. We explain now the way of thinking that has led us to
the introduction of notations of lower and upper magnitude mean values. First, let A be LR- type
fuzzy number, we note that from the equality (page 142)
A14-c472 Jussi Vimpari, Seppo Junnila, Theory of valuing building life-cycle investments, BUILDING RESEARCH AND INFORMATION, 44(2016), number 4, pp. 345-357. 2016
http://dx.doi.org/10.1080/09613218.2016.1098055
Carlsson and Fullér (2001) originally derived the possibilistic mean of fuzzy numbers. The weighing of the possibilistic mean to the positive side of the distribution is shown as follows: (page 350)
A14-c471 I-Fei Chen, Ruey-Chyn Tsaur, Fuzzy Portfolio Selection Using a Weighted Function of Possibilistic
Mean and Variance in Business Cycles, INTERNATIONAL JOURNAL OF FUZZY SYSTEMS, 18(2016),
issue 2, pp. 151-159. 2016
http://dx.doi.org/10.1007/s40815-015-0073-9
2015
A14-c470 Jirakom Sirisrisakulchai, Kittawit Autchariyapanitkul, Napat Harnpornchai, Songsak Sriboonchitta,
Portfolio Optimization of Financial Returns Using Fuzzy Approach with NSGA-II Algorithm, Journal of
Advanced Computational Intelligence and Intelligent Informatics, 19(2015), number 5, pp. 619-623. 2015
https://www.fujipress.jp/jaciii/jc/jacii001900050619/
A14-c469 Md Husamuddin, Fokrul Alom Mazarbhuiya, Clustering of Locally Frequent Patterns over Fuzzy
Temporal Datasets, INTERNATIONAL JOURNAL OF COMPUTER TRENDS AND TECHNOLOGY,
28: (3) pp. 131-134. 2015
http://dx.doi.org/10.14445/22312803/IJCTT-V28P124
A14-c468 Gastón S Milanesi, Emilio El Alabi, Gabriela Pesce, Continuity or Liquidation in Situations of Ambiguity: Fuzzy Binomial Model to Valuate Leveraged Firms, Research in Applied Economics, 7: (1) pp.
26-47. 2015
Central value calculation related to the fuzzy number is altered by the right bias that has the
project’s possible outcome distribution (Carlsson & Fuller, 2001). (page 32)
A14-c467 Amir Mohajeri, Mohammad Fallah, A carbon footprint-based closed-loop supply chain model under
uncertainty with risk analysis: A case study, TRANSPORTATION RESEARCH PART D: TRANSPORT
AND ENVIRONMENT (to appear). 2015
http://dx.doi.org/10.1016/j.trd.2015.09.001
145
Because the mean of the occurrence is always an ideal index for the DMs to make a decision
in the uncertain environment, we consider this concept for the defuzzification process. When a
fuzzy number is defuzzified by its level set, the information is disaggregated into an interval set.
Integrating all levels is a way to collect all information (Carlsson and Fuller, 2001). With respect
to this reference, the possibilistic mean of a fuzzy number is shown below.
A14-c466 Pasi Luukka, Mikael Collan, New Fuzzy Insurance Pricing Method for Giga-Investment Project
Insurance, INSURANCE MATHEMATICS & ECONOMICS, 65(2015), pp. 22-29. 2015
http://dx.doi.org/10.1016/j.insmatheco.2015.08.002
A14-c465 Sha Fu, Method for Multi-attribute Decision Making with Triangular Fuzzy Number Based on Multiperiod State, MATHEMATICS AND STATISTICS, 3: (4) pp. 89-94. 2015
http://dx.doi.org/10.13189/ms.2015.030402
Research of problems with multi-attribute decision making with triangular fuzzy numbers as the
attribute value has been drawing attention of foreign and domestic scholars for a long time and
some achievements have been made. Christer Carlsson and Robert Fullér [4] introduced the notations of lower possibilistic and upper possibilistic mean values we define the interval-valued
possibilistic mean and investigate its relationship to the interval-valued probabilistic mean. Didier
Dubois et al. [5] provided a justification of symmetric triangular fuzzy numbers in the spirit of
such inequalities. (page 89)
A14-c464 J Dong, D Y Yang, S P Wan, Trapezoidal intuitionistic fuzzy prioritized aggregation operators and
application to multi-attribute decision making, IRANIAN JOURNAL OF FUZZY SYSTEMS, 12(2015),
number 4, pp. 1-32. 2015
http://ijfs.usb.ac.ir/pdf_2083_b0bfd4eb1264f73143bcf1b0715c6d2f.html
A14-c463 Vahid Mohagheghi S Meysam Mousavi, Behnam Vahdani, A New Optimization Model for Project
Portfolio Selection Under Interval-Valued Fuzzy Environment, ARABIAN JOURNAL FOR SCIENCE
AND ENGINEERING, Volume 40, Issue 11, 1 November 2015, Pages 3351-3361. 2015
http://dx.doi.org/10.1007/s13369-015-1779-6
A14-c462 Yanyan He, Mahsa Mirzargar, Robert M Kirby, Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 66(2015),
pp. 1-15. 2015
http://dx.doi.org/10.1016/j.ijar.2015.07.002
A14-c461 Yue W, Wang YP, Dai C, An Evolutionary Algorithm for Multiobjective Fuzzy Portfolio Selection
Models with Transaction Cost and Liquidity, MATHEMATICAL PROBLEMS IN ENGINEERING, Paper
569415. 15 p. 2015
http://dx.doi.org/10.1155/2015/569415
In this paper, we regard a new weighted possibilistic mean value, variance, and skewness [26]
of fuzzy return to characterize the return level, risk level, and the corresponding asymmetry as
alternative approach, respectively. It is just because the weighted possibilistic mean (WPM) and
variance (WPV) of fuzzy number have all the properties of the possibilistic mean value and variance stated in [24, A14], and the WPV has all necessities and important properties for defining of
the possibilistic variance of a fuzzy number. In addition, WPM is the nearest weighted point to
the fuzzy number via minimizing a new weighted distance quantity; moreover, WPV of a fuzzy
number is consistent with the physical interpretation of the variance and well-known de nition of
variance in probability theory so that it can simply introduce the possibilistic moments about the
mean of fuzzy numbers [26]. Furthermore, Pasha et al. [26] pointed out that this definition of
weighted possibilistic moments on fuzzy number is more suitable for all fuzzy numbers than the
definitions of possibilistic moments introduced in [24, A14]. is indicates that WPM and WPV
are suitable and applicable and play an important role in fuzzy data analysis. For this reason, we
quantify the return, risk, and skewness by using the WPMs. (page 3)
146
A14-c460 Daniela Ungureanu, Raluca Vernic, On a fuzzy cash flow model with insurance applications, Decisions in Economics and Finance, 38(2015), number 1, pp. 39-54. 2015
http://dx.doi.org/10.1007/s10203-014-0157-2
A14-c459 A Saeidifar, Possibilistic Chararteristic Functions, FUZZY INFORMATION AND ENGINEERING,
7(2015), number 1, pp. 61-72. 2015
http://dx.doi.org/10.1016/j.fiae.2015.03.005
A14-c458 Shang Rui, Research on Science Award Judgment, International Journal of u- and e- Service, Science
and Technology, 8(2015), number 3, pp. 99-106. 2015
http://dx.doi.org/10.14257/ijunesst.2015.8.3.09
A14-c457 Masoud Rabbani, Neda Manavizadeh, Mehran Samavati, Moeen Sammak Jalali, Proactive and reactive inventory policies in humanitarian operations, Uncertain Supply Chain Management, 3(2015), pp.
253-272. 2015
http://dx.doi.org/10.5267/j.uscm.2015.3.004
A14-c456 Guangxu Li, Gang Kou, Changsheng Lin, Liang Xu, Yi Liao, Multi-attribute decision making with
generalized fuzzy numbers, Journal of the Operational Research Society (to appear). 2015
http://dx.doi.org/10.1057/jors.2015.1
However, the possibility degree formula developed in Nakahara et al (1992) and Xu (2002) can
only be applied to interval fuzzy numbers or triangular fuzzy numbers. Carlsson and Fuller (2001)
proposed the possibilistic mean value and variance of fuzzy numbers. Based on the possibilistic
mean value of fuzzy numbers, this paper proposed a modified possibility degree formula, which
can not only be applied to interval fuzzy numbers or triangular fuzzy numbers, but also applied to
GFNs, and a ranking method based on the Hausdorff distance, GFNs and the modified possibility
degree. A numerical example is used to demonstrate the applicability of the proposed method.
A14-c455 Xiang Li, Sini Guo, Lean Yu, Skewness of fuzzy numbers and its applications in portfolio selection,
IEEE Transactions on Fuzzy Systems, 23: (6) pp. 2135-2143. 2015
http://dx.doi.org/10.1109/TFUZZ.2015.2404340
Based on the membership function, this paper redefines the possibilistic mean (Carlsson and Fuller
[A14]) and possibilistic variance (Zhang and Nie [23]) and gives a new definition on skewness for
fuzzy numbers.
A14-c454 Wei Chen, Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem, Physica A: Statistical Mechanics and its Applications, 429(2015), pp. 125-139. 2015
http://dx.doi.org/10.1016/j.physa.2015.02.060
Carlsson and Fullér [55] introduced the lower and upper possibilistic mean values of fuzzy number
A (page 128)
A14-c453 Ting Li, Weiguo Zhang, Weijun Xu, A fuzzy portfolio selection model with background risk, Applied
Mathematics and Computation, 256(2015), pp. 505-513. 2015
http://dx.doi.org/10.1016/j.amc.2015.01.007
Corresponding to the upper and lower possibilistic means, Carlsson and Fullr [28] and Zhang
[29] introduced the crisp possibilistic variance and covariance of fuzzy numbers. (page 507)
Possibility theory was proposed by Zadeh [7] and was advanced by Dubois and Prade [8]. In
Zadeh’s theory, fuzzy variables are associated with possibility distributions, which is in the similar
way that random variables are associated with probability distribution. Carlsson and Fullér [A12,
B6] introduced the notions of possibilistic mean, possibilistic variance and covariance of fuzzy
numbers. (page 506)
A14-c452 Guido Schryen, Diana Hristova, Duality in fuzzy linear programming: a survey, OR Spectrum,
37(2015), number 1, pp. 1-48. 2015
http://dx.doi.org/10.1007/s00291-013-0355-2
147
A second option is to draw on a (lexicographic) ranking function R0 : F(R) → R × R (Hashemi
et al. 2006) based on the concepts of possibilistic mean value and variance of a fuzzy number
(Carlsson and Fullér 2001). Third, ranking fuzzy numbers can also draw on indices based on
possibility theory (Dubois and Prade 1983). (page 10)
A14-c451 Shu-Ping Wan, Jiu-Ying Dong, Power geometric operators of trapezoidal intuitionistic fuzzy numbers
and application to multi-attribute group decision making, Applied Soft Computing, 29(2015), pp. 153-168.
2015
http://dx.doi.org/10.1016/j.asoc.2014.12.031
These results of a triangular fuzzy number are the same as those of a triangular fuzzy number in
Example 2.1 of [A14]. (page 157)
Yanbing Gong, Na Hu, Jiguo Zhang, Gaofeng Liu, Jiangao Deng, Multi-attribute group decision making
method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers, Computers & Industrial Engineering, 81(2015), pp. 167-176. 2015
http://dx.doi.org/10.1016/j.cie.2014.12.030
In this section, we extended the concept of Carlsson and Fullér (2001) about the possibilistic mean
value of type-1 fuzzy numbers. We first introduce the lower and upper possibility mean value of
IT2 FS. (page 169)
A14-c449 Juan Jose Palacios, Ines Gonzalez-Rodriguez, Camino R Vela, Jorge Puente, Coevolutionary makespan
optimisation through different ranking methods for the fuzzy flexible job shop FUZZY SETS AND SYSTEMS (to appear). 2015
http://dx.doi.org/10.1016/j.fss.2014.12.003
A14-c448 Ruey-Chyn Tsaur, Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions
International Journal of Systems Science, 46(2015), number 3, pp. 438-450. 2015
http://dx.doi.org/10.1080/00207721.2013.784820
A14-c447 Peng Zhang, Multi-period Possibilistic Mean Semivariance Portfolio Selection with Cardinality Constraints and its Algorithm, JOURNAL OF MATHEMATICAL MODELLING AND ALGORITHMS IN
OPERATIONS RESEARCH, 14: (2) pp. 239-253. 2015
http://dx.doi.org/10.1007/s10852-014-9268-6
Zhang et al. [20] discussed the admissible efficient portfolio selection under the assumption that
the expected return and risk of asset have admissible errors to reflect the uncertainty in real investment actions and gave an analytic derivation of admissible efficient frontier when short sales are
not allowed on all risky assets. Carlsson and Fullér [21] introduced the notions of lower and upper possibilistic mean values of a fuzzy number, viewing them as possibility distributions. Huang
[22] proposed mean risk curve portfolio selection models. Zhang et al. [23] proposed the portfolio
selec- tion models based on the lower and upper possibilistic means and possibilistic variances of
fuzzy numbers Li et al [24] applied a genetic procedure to solve mean variance skewness fuzzy
portfolio. Carlsson et al. [25] introduced a possibilistic approach to select portfolios with highest
utility score under the assumption that the returns of assets are trapezoidal fuzzy numbers. (page
240)
A14-c446 Yong-Jun Liu, Wei-Guo Zhang, A multi-period fuzzy portfolio optimization model with minimum
transaction lots, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 242(2015), issue 3, pp. 933941. 2015
http://dx.doi.org/10.1016/j.ejor.2014.10.061
Let A ∈ F be a fuzzy number with [A]γ = [a1 (γ), a2 (γ)], (γ ∈ [0, 1]). Carlsson and Fullér
(2001) defined the possibilistic mean value of fuzzy number A as follows
Z 1
E(A) =
γ(a1 (γ) + a2 (γ))dγ.
0
(page 934)
148
A14-c445 V M Cabral, L C Barros, Fuzzy differential equation with completely correlated parameters, FUZZY
SETS AND SYSTEMS, 265(2015), pp. 86-98. 2015
http://dx.doi.org/10.1016/j.fss.2014.08.007
A14-c444 Thanh T Nguyen, Lee Gordon-Brown, Abbas Khosravi, Douglas Creighton, Saeid Nahavandi, Fuzzy
Portfolio Allocation Models through a New Risk Measure and Fuzzy Sharpe Ratio, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 23: (3) pp. 656-676. 2015
http://dx.doi.org/10.1109/TFUZZ.2014.2321614
Contrasting with the simple expected values calculation, the covariance of fuzzy random variables
is, however, more complicated to be determined. Since initiated, there have been a variety of approaches studying covariance of fuzzy random variables. A recent literature review on covariance
of fuzzy random variables was presented in Couso and Dubois [31]. There are two major comprehensions of fuzzy covariance: treating it as either crisp numbers, or fuzzy numbers. The crisp
numbers approach includes studies of Körner [32], Chiang and Lin [33], Feng et al. [34], Carlsson
and Fullér [A14], Fullér and Majlender [A9], and recently Kamdem [37]. Alternatively, the fuzzy
covariance approach comprises Lee [38], Liu and Kao [39], Wu [40], Hong [41], etc. Tsao [42]
used requisite equality constraint introduced by Klir [43] and Klir and Pan [44] to mend the fuzzy
covariance calculation algorithms and applied to a portfolio selection application. (page 658)
2014
A14-c443 S Bag, D Chakraborty, Fuzzy EPQ model with dynamic demand under bi-level trade credit policy,
Annals of Fuzzy Mathematics and Informatics, 7(2014), number 6, pp. 959-989. 2014
http://www.afmi.or.kr/papers/2014/Vol-07_No-06/AFMI-7-6(859-1020)/AFMI-7-6(959-989
Here the carrying cost rate, ordering cost, unit purchasing price and unit selling price are assumed
as fuzzy number to fit the real world. Model is formulated as profit maximization principle. Here
the average profit is fuzzy in nature. The possibilistic mean value of a fuzzy number ([A14]) is
used to rank fuzzy numbers for the optimal decision.
A14-c442 Gaston S Milanesi, Diego Broz, Fernando Tohme, Daniel Rossit, Strategic Analysis Of Forest Investments Using Real Option: The Fuzzy Pay-Off Model (Fpom), Fuzzy Economic Review, XIX(2014), issue
1, pp. 33-44. 2014
A14-c441 Irina Georgescu, Risk aversion, prudence and mixed optimal saving models, Kybernetika 50:(2014),
number 5, pp. 706-724. 2014
http://dx.doi.org/10.14736/kyb-2014-5-0706
A14-c440 Shuping Wang, Jiuying Dong, Multi-Attribute Group Decision Making with Trapezoidal Intuitionistic Fuzzy Numbers and Application to Stock Selection, INFORMATICA 25: pp. 663-697. 2014
http://dx.doi.org/10.15388/Informatica.2014.34
In statistics, central tendency and distribution dispersion are considered to be the important measures. For fuzzy numbers, two of the most useful measures are the mean and variance of fuzzy
numbers. The possibility mean and variance are the important mathematical characteristics of
fuzzy numbers. The possibilistic mean, variance and covariance of fuzzy numbers, defined by
Carlsson and Fullér (2001) and Fullér and Majlender (2003) are usually used to the research of
fuzzy optimal portfolio selection (Zhang et al., 2009). (page 666)
A14-c439 Ana Maria Lucia Casademunt, Irina Georgescu, The Optimal Saving with Mixed Parameters, Procedia Economics and Finance, 15(2014), pp. 326-333. 2014
http://dx.doi.org/10.1016/S2212-5671(14)00517-6
A14-c438 C C Popescu, A Fuzzy Optimization Model, ECONOMIC COMPUTATION AND ECONOMIC
CYBERNETICS STUDIES AND RESEARCH, 48(2014), number 2, pp. 201-213. 2014
WOS: 000338090100012
149
A14-c437 S S Appadoo, A Thavaneswaran, Heather H Kim, Jagbir Singh, An Integrated Group Solution Strategy in Supply Chain Management, Journal of Business and Management, 3(2014), number 3, pp. 1-11.
2014
A14-c436 Peng Zhang, Wei-Guo Zhang, Multiperiod mean absolute deviation fuzzy portfolio selection model
with risk control and cardinality constraints, FUZZY SETS AND SYSTEMS, 255(2014), pp. 74-91. 2014
http://dx.doi.org/10.1016/j.fss.2014.07.018
Carlsson and Fullér [A14] introduced the notions of lower and upper possibilistic mean values of
a fuzzy number, viewing them as possibility distributions. (page 76)
A14-c435 S S Appadoo, Possibilistic Fuzzy Net Present Value Model and Application, Mathematical Problems
in Engineering 2014: Paper 865968. 11 p. 2014
http://dx.doi.org/10.1155/2014/865968
Possibility theory (Carlsson and Fullér [A14]) along with fuzzy set theory and fuzzy systems
(see (Zadeh [6]; Zimmermann [3]), Kaufmann and Gupta [2] provide a new avenue to deal with
impreciseness in decision making problems. (page 1)
A14-c434 Adel Azar, Hossein Sayyadi Tooranloo, Ali Rajabzadeh, Laya Olfat, A Model for Assessing Agility
Drivers with Possibility Theory, Applied mathematics in Engineering, Management and Technology, June
2014: (1119) p. 1134. 2014
http://amiemt.megig.ir/test/sp2/136.pdf
A14-c433 Zoran Gligoric, Lazar Kricak, Cedomir Beljic, Suzana Lutovac, Jelena Milojevic, Evaluation of
Underground Zinc Mine Investment Based on Fuzzy-Interval Grey System Theory and Geometric Brownian
Motion, Journal of Applied Mathematics, 2014(2014). Paper 914643. 2014
http://dx.doi.org/10.1155/2014/914643
Carlsson and Fuller [A14] introduced the interval-valued possibilistic mean of a fuzzy number Ã
as the interval (page 2)
A14-c432 J Vimpari, S Junnila, Valuing green building certificates as real options, Journal of European Real
Estate Research (to appear). 2014
http://www.emeraldinsight.com/journals.htm?articleid=17112415&show=abstract
A14-c431 K. Chrysafis,. and B. Papadopoulos, Possibilistic Moments for the Task Duration in Fuzzy PERT,
Journal of Management in Engineering (to appear). 2014
http://dx.doi.org/10.1061/(ASCE)ME.1943-5479.0000296
A14-c430 S Sefi, R Saneifard, Fuzzy Risk Analysis Based on Measure of Fuzzy Numbers and Its Application
in the Extended Air Fighter Selection Problem, Advances in Environmental Biology, 8(2014), number 10,
pp. 513-518. 2014
A14-c429 Rahim SANEIFARD, Mohammad FARROKHY, Comparison of Fuzzy Numbers by Using a Statistical Index, International Journal of Natural and Engineering Sciences, 8(2014), number 1, pp. 23-26.
2014
A14-c428 ZM Gligoric, CR Beljic, SM Jovanovic, CM Cvijovic Optimization of underground mine development system using fuzzy shortest path length algorithm Journal of the Chinese Institute of Engineers,
37(2014), number 8, pp. 965-982. 2014
http://dx.doi.org/10.1080/02533839.2014.912772
A14-c427 Kumar Ravi Shankar, Tiwari MK, Goswami A, Two-echelon fuzzy stochastic supply chain for the
manufacturer-buyer integrated production-inventory system, Journal of Intelligent Manufacturing (to appear). 2014
http://dx.doi.org/10.1007/s10845-014-0921-8
If λ = 1/2, then Eq. (3.3) becomes Carlsson and Fullér (2001) possibilistic mean value. We now
propose a proposition that stated as below.
150
A14-c426 Wei Chen, Hui Ma, Yiping Yang, Mengrong Sun, Application of artificial bee colony algorithm to
portfolio adjustment problem with transaction costs, Journal of Applied Mathematics. Paper 192868. 2014
http://dx.doi.org/10.1155/2014/192868
That is the f -weighted possibilistic mean value can be considered as a generalization of possibilistic mean value introduced by Carlsson and Fullr [A14]. (page 3)
A14-c425 Dabuxilatu Wang, Pinghui Li, Masami Yasuda, Construction of Fuzzy Control Charts Based on
Weighted Possibilistic Mean, Communications in Statistics - Theory and Methods, 43(2014), number 15,
pp. 3186-3207. 2014
http://dx.doi.org/10.1080/03610926.2012.695852
Recently, possibility theory has received much attention in the area of uncertainty modelling.
Carlsson and Fullér (2001) proposed the possibilistic mean and possibilistic variance for fuzzy
numbers, these concepts behave properly in measuring central tendency of fuzzy numbers based
on a ranking of fuzzy numbers by the desire to give less importance to the lower levels of fuzzy
numbers. Fullér and Majlender (2003) introduced the weighted possibilistic mean and variance
for fuzzy numbers, which are the possibilistic mean and variance with weighting functions that
give corresponding importance to different α-levels of fuzzy numbers.
In this paper, the weighted possibilistic mean (WPV) and weighted interval valued possibilistic
mean (WIVPM) of a fuzzy number (Carlsson and Fullér, 2001, Fullér and Majlender, 2003) are
introduced to be representative values of a fuzzy attribute data, and fuzzy c-charts are established
with WPV and WIVPM. The performance of the charts have been compared to existing fuzzy
charts with a newly defined ANIVCS.
A14-c424 Soumen Bag, Debjani Chakraborty, An inventory model for deteriorating items with fuzzy random
planning horizon, Advanced Modeling and Optimization, 16(2014), pp. 185-197. 2014
http://camo.ici.ro/journal/vol16/v16a14.pdf
A14-c422 Collan Mikael, Björk KajMikael, Kyläheiko Kalevi, Evaluation of an information systems investment
into reducing the bullwhip effect - a threéstep process, INTERNATIONAL JOURNAL OF LOGISTICS
SYSTEMS AND MANAGEMENT, 17: (3) pp. 340-356. 2014
http://dx.doi.org/10.1504/IJLSM.2014.059766
A14-c412 Dixit Vijaya, Srivastava K Rajiv, Chaudhuri Atanu, Procurement scheduling for complex projects
with fuzzy activity durations and lead times, Computers & Industrial Engineering, 76(2014), pp. 401-414.
2014
http://dx.doi.org/10.1016/j.cie.2013.12.009
A14-c420 Xue Deng, Rongjun Li, Gradually tolerant constraint method for fuzzy portfolio based on possibility
theory, INFORMATION SCIENCES, 259(2014), pp. 16-24. 2014
http://dx.doi.org/10.1016/j.ins.2013.10.016
In the past, a number of researchers investigated the fuzzy portfolio selection problem. Bellman
and Zadeh [7] proposed the basic fuzzy decision theory. Carlsson and Fullér [A14] discussed
some basic properties about possibilistic mean and possibilistic variance of fuzzy numbers when
the variable had some fuzzy uncertainties. Moreover, Amelia et al. [1] presented a model to select
portfolios when an ethical dimension on financial products is considered. (page 17)
A14-c419 T. Pedro, Law of large numbers for the possibilistic mean value, Fuzzy Sets and Systems, 245(2014),
pp. 116-124. 2014
http://dx.doi.org/10.1016/j.fss.2013.10.011
Our second ingredient is the notion of a possibilistic mean value introduced by Carlsson and Fullér
[A14] (who acknowledge the prior work of Goetschel and Voxman [7]), a ’fuzzy’ or ’possibilistic’
version of the expected value for fuzzy information. The possibilistic mean value of a fuzzy
number is very popular (Google Scholar finds over 450 citations to the Carlsson-Fullér paper) and
easy to adapt to variables instead of fuzzy numbers. (page 117)
151
A14-c418 Gong Yanbing, The new weighted magnitude mean value and variance of fuzzy numbers, Journal of
Intelligent and Fuzzy Systems, 26(2014), number 5, pp. 2303-2313. 2014
http://dx.doi.org/10.3233/IFS-130903
A14-c417 Mikael Collan, Pasi Luukka, Evaluating R&D Projects as Investments by Using an Overall Ranking
from Four New Fuzzy Similarity Measure Based TOPSIS Variants, IEEE TRANSACTIONS ON FUZZY
SYSTEMS, 22(2014), issue 3, pp. 505-515. 2014
http://dx.doi.org/10.1109/TFUZZ.2013.2260758
A14-c416 Shu-Ping Wan, Jiu-Ying Dong, Possibility Method for Triangular Intuitionistic Fuzzy Multi-attribute
Group Decision Making with Incomplete Weight Information, International Journal of Computational Intelligence Systems, 7: (1) pp. 65-79. 2014
http://dx.doi.org/10.1080/18756891.2013.857150
2013
A14-c415 Fei Ye, Qiang Lin, Partner selection in a virtual enterprise: a group multi-attribute decision model
with weighted possibilistic mean values, Mathematical Problems in Engineering, Paper 519629. 14 p. 2013
http://dx.doi.org/10.1155/2013/519629
A14-c414 LIU Yong-jun, ZHANG Wei-guo, XU Wei-jun, Fuzzy multiple criteria portfolio selection optimization model under real constrains, Systems Engineering - Theory & Practice, 33(2013), number 10, pp.
2462-2470. 2013
A14-c413 Ana Maria Lucia Casademunt, Irina Georgescu, Connecting possibilistic prudence and optimal saving, INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE AND INTERACTIVE MULTIMEDIA, 4(2013), number 2, pp. 38-45. 2013
http://dx.doi.org/10.9781/ijimai.2013.244
A14-c412 Liu Yong-Jun, Zhang Wei-Guo, Fuzzy portfolio optimization model under real constraints, Insurance:
Mathematics and Economics, 53(2013), number 3, pp. 704-711. 2013
http://dx.doi.org/10.1016/j.insmatheco.2013.09.005
Carlsson and Fullér (2001) reported that the possibilistic mean value and variance concepts of
fuzzy number which gain popularity among scholars. After that, many scholars used the possibility measure to investigate fuzzy portfolio selection problems such as Zhang (2007), Zhang et al.
(2009) and Carlsson et al. (2002). In addition, some researchers, such as Huang (2008), Qin et al.
(2009) and Zhang et al. (2009), Zhang et al. (2010), Zhang et al. (2011), Kamdem et al. (2012)
and Gupta et al. (2013) studied portfolio selection problems by using credibility measure. (page
705)
A14-c411 Zhang Wei-Guo, Liu Yong-Jun, Xu Wei-Jun, A new fuzzy programming approach for multi-period
portfolio optimization with return demand and risk control, Fuzzy Sets and Systems, 246(2014), number 1,
pp. 107-126. 2014
http://dx.doi.org/10.1016/j.fss.2013.09.002
For fuzzy portfolio selection problems, there are two popular definitions of risk measures. One
form of risk measure is variance which is widely accepted by many scholars, see for example
[6,26,42]. In particular, Carlsson and Fullér [A14] employed the variance of a portfolio return
based on the possibilistic theory as the risk measure. (page 111)
A14-c410 Soumen Bag, Debjani Chakraborty, Fuzzy EOQ model under bi-level trade credit policy, Annals of
Fuzzy Mathematics and Informatics (to appear). 2013
http://www.afmi.or.kr/
articles_in_%2520press/2013-08/AFMI-H-130201-1R1/Manuscript.pdf
A14-c409 R Saneifard, Nader Hassasi, Parametric correlation coefficient of fuzzy numbers African Journal of
Business Management 7: (35) 3410-3415 (2013)
http://dx.doi.org/10.5897/AJBM11.1588
152
A14-c408 Liu Wen-qiong, Li Sheng-hong, European option pricing model in a stochastic and fuzzy environment, Applied Mathematics - A Journal of Chinese Universities, 8(2013), number 3, pp. 321-334. 2013
http://dx.doi.org/10.1007/s11766-013-3030-0
In order to find a crisp number of a fuzzy number à that synthesizes the fuzzy number, Carlsson
and Fullér [A14] introduced the weighted possibilistic mean value of the fuzzy number à defined
by (page 324)
A14-c407 Favato Giampiero, Baio Gianluca, Capone Alessandro, Marcellusi Andrea, Saverio Mennini Francesco,
A Novel Method to Value Real Options in Health Care: The Case of a Multicohort Human Papillomavirus
Vaccination Strategy, Clinical Therapeutics, 35(2013), number 7, pp. 904-914. 2013
http://dx.doi.org/http://dx.doi.org/10.1016/j.clinthera.2013.05.003
A14-c406 Luca Anzilli, Gisella Facchinetti, The Total Variation of Bounded Variation Functions to Evaluate and
Rank Fuzzy Quantities, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 28(2013), issue
10, pp. 927-956. 2013
http://dx.doi.org/10.1002/int.21604
A14-c404 Yang Hui Mei Lulun, Fuzzy expected value of the securities portfolio model and empirical analysis,
Journal of Chongqing Technology and Business University (Natural Science Edition), 2013(2013), number
3, pp. 22-28 (in Chinese). 2013
A14-c403 Fu Yunpeng, Ma Shu-Cai, Song Qi, Mean-variance model is based on the possibility of a portfolio of
social security funds, Economy and Management Review, 2013(2013), number 3, pp. 111-114 (in Chinese).
2013
A14-c402 Li Rui, Yield with fuzzy portfolio selection model, Journal of Xinyang Normal University: Natural
Science, 2013(2013), number 2, pp. 169-172 (in Chinese). 2013
A14-c401 Irina Georgescu, Possibilistic risk aversion and coinsurance problem, FUZY INFORMATION AND
ENGINEERING, Volume 5, Issue 2, pp 221-233. 2013
http://dx.doi.org/10.1007/s12543-013-0136-2
A14-c400 Srimantoorao S Appadoo, Aerambamoorthy Thavaneswaran, Recent Developments in Fuzzy Sets
Approach in Option Pricing, JOURNAL OF MATHEMATICAL FINANCE, 3(2013), pp. 312-322. 2013
http://dx.doi.org/10.4236/jmf.2013.32031
In this section following Carlsson and Fuller [A14], we introduce the following moments. (page
315)
A14-c399 LI Ai-zhong, REN Ruo-en, DONG Ji-chang, Mean-variance-entropy fuzzy portfolio selection based
on integrated forecast, Systems Engineering - Theory & Practice, 33(2013), number 5, pp. 1116-1125.
2013
Scopus: 84879129110
A14-c398 Collan M, Fedrizzi M, Luukka P, A multi-expert system for ranking patents: An approach based on
fuzzy pay-off distributions and a TOPSIS-AHP framework, EXPERT SYSTEMS WITH APPLICATIONS,
40(2013), number 12, pp. 4749-4759. 2013
http://dx.doi.org/10.1016/j.eswa.2013.02.012
Here the notion of crisp possibilistic mean of N introduced in Carlsson and Fullér (2001) and
Fuller and Majlender (2003) is used and defined as the arithmetic mean of its lower and upper
possibilistic mean values L(N ) and U (N ) where (page 4573)
A14-c397 Manoj Kumar, S Srinivasan, Gundeep Tanwar, Tackling Rationing and Shortage Gaming Reason of
Bullwhip Effect With Fuzzy Logic Approach, RESEARCH INVENTORY: INTERNATIONAL JOURNAL
OF ENGINEERING AND SCIENCE, 2(2013), number 10, pp. 48-52. 2013
http://www.researchinventy.com/papers/v2i10/I0210048052.pdf
A14-c396 Wan S-P, Li D-F, Possibility mean and variance based method for multi-attribute decision making
with triangular intuitionistic fuzzy numbers, JOURNAL OF INTELLIGENT AND FUZZY SYSTEMS,
24(2013), number 4, pp. 743-754. 2013
http://dx.doi.org/10.3233/IFS-2012-0594
153
A14-c395 Shu-Ping Wan, MULTI-ATTRIBUTE DECISION MAKING METHOD BASED ON POSSIBILITY
VARIANCE COEFFICIENT OF TRIANGULAR INTUITIONISTIC FUZZY NUMBERS, International
Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21(2013), number 2, pp. 223-243. 2013
http://dx.doi.org/10.1142/S0218488513500128
For fuzzy numbers, two of the most useful measures are the mean and variance of fuzzy numbers.
The possibility mean and variance are the important mathematical characteristics of fuzzy numbers. The possibilistic mean, variance and covariance of fuzzy numbers, defined by Carlsson and
Fullér, [43] are usually used to the research of fuzzy optimal portfolio selection (Zhang [44]). They
are similar to the mean, variance and covariance of random variance, which may quantificationally
express the uncertain information implied in the fuzzy numbers. (pages 224-225)
A14-c394 Luca Anzilli, A POSSIBILISTIC APPROACH TO INVESTMENT DECISION MAKING, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21(2013), number 2, pp. 201-221.
2013
http://dx.doi.org/10.1142/S0218488513500116
Carlsson and Fuller [A14] defined the interval-valued possibilistic mean, the crisp possibilistic
mean value and the crisp possibilistic variance of a continuous fuzzy number which are consistent
with the extension principle. The concept of possibilistic mean value and variance is used in many
different areas (see Carlsson and Fuller [C10]). (page 201)
A14-c392 Takashi Hasuike, Hideki Katagiri, Robust-based interactive portfolio selection problems with an
uncertainty set of returns, FUZZY OPTIMIZATION AND DECISION MAKING, 12 (2013), number 3,
pp. 263-288. 2013
http://dx.doi.org/10.1007/s10700-013-9157-x
P4: Fuzzy mean-variance model with fuzzy possibilistic mean and variance based on Carlsson
and Fuller (2001) (page 277)
A14-c391 R Saneifard, S Salmanion, A new effect of approximation of trapezoidal fuzzy quantity with weighted
function, JOURNAL OF SOFT COMPUTING AND APPLICATIONS, 2013: Paper /jsca-00009.2013
http://dx.doi.org/10.5899/2013/jsca-00009
A14-c390 Mikael Collan, Fuzzy or linguistic input scorecard for IPR evaluation, JOURNAL OF APPLIED
OPERATIONAL RESEARCH, 5(2013), number 1, pp. 22-29. 2013
http://www.tadbir.ca/jaor/archive/v5/n1/jaorv5n1p22.pdf
Using fuzzy numbers can help; we can calculate a ”smart” mean value, a possibilistic mean value
(Carlsson and Fullér, 2001), for the asset score that takes into consideration the downside and the
asset potential, defined in Definition 1. (page 27)
A14-c389 Irina Georgescu, A new notion of possibilistic covariance, NEW MATHEMATICS AND NATURAL
COMPUTATION, 9(2013), number 1, pp. 1-11. 2013
http://dx.doi.org/10.1142/S1793005713500014
A14-c388 Tsaur R-C, Fuzzy portfolio model with different investor risk attitudes, European Journal of Operational Research, 227(2013), number 2, pp. 385-390. 2013
http://dx.doi.org/10.1016/j.ejor.2012.10.036
A14-c387 Matteo Brunelli, József Mezei, How different are ranking methods for fuzzy numbers? A numerical
study, INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 54(2013), number 5, pp. 627639. 2013
http://dx.doi.org/10.1016/j.ijar.2013.01.009
The possibilistic mean value [A14] of a fuzzy number A ∈ F is the weighted average of the
middle points of the α-cuts of a fuzzy number A:
A14-c386 Jun Li, Jiuping Xu, Multi-objective portfolio selection model with fuzzy, random returns and a compromise approach-based genetic algorithm, INFORMATION SCIENCES, 220(2013), pp. 507-521. 2013
http://dx.doi.org/10.1016/j.ins.2012.07.005
154
A14-c385 A. Thavaneswaran, S. S. Appadoo, J. Frank, Binary option pricing using fuzzy numbers, APPLIED
MATHEMATICS LETTERS, Volume 26, Issue 1, January 2013, Pages 65-72. 2013
http://dx.doi.org/10.1016/j.aml.2012.03.034
A14-c384 Ting Li, Weiguo Zhang, Weijun Xu, Fuzzy possibilistic portfolio selection model with VaR constraint
and risk-free investment ECONOMIC MODELLING, 31(2013), number 1, pp. 12-17. 2013
http://dx.doi.org/10.1016/j.econmod.2012.11.032
Carlsson and Fullér (2001) introduced the notations of lower and upper possibilistic mean values,
and introduced the notation of crisp possibilistic mean value and crisp possibilistic variance of
continuous possibility distributions. Zhang and Nie (2003) extended the concepts of possibilistic
mean and possibilistic variance proposed by Carlsson and Fullér, and presented the notions of
upper and lower possibilistic variances and covariances of fuzzy numbers. (page 13)
A14-c383 Shu-Ping Wan, Deng-Feng Li, Zhen-Feng Rui, Possibility mean, variance and covariance of triangular intuitionistic fuzzy numbers, JOURNAL OF INTELLIGENT AND FUZZY SYSTEMS, 24(2013),
number 4, pp. 847-858. 2013
http://dx.doi.org/10.3233/IFS-2012-0603
A14-c382 Wen-Yeh Hsieh, Ruey-Chyn Tsaur, Epidemic forecasting with a new fuzzy regression equation,
QUALITY & QUANTITY, 47(2013), issue 6, pp. 3411-3422. 2013
http://dx.doi.org/10.1007/s11135-012-9729-9
The traditional fuzzy regression model involves two solving processes. First, the extension principle is used to derive the membership function of extrapolated values, and then, attempts are made
to include every collected value with a membership degree of at least h in the fuzzy regression
interval. However, the membership function of extrapolated values is sometimes highly complex,
and it is difficult to determine the h value, i.e., the degree of fit between the input values and
the extrapolative fuzzy output values, when the information obtained from the collected data is
insufficient. To solve this problem, we proposed a simplified fuzzy regression equation based on
Carlsson and Fullér’s possibilistic mean and variance method and used it for modeling the constraints and objective function of a fuzzy regression model without determining the membership
function of extrapolative values and the value of h.
2012
A14-c381 Ying Xie, Li Zhou, Measuring Bullwhip Effect in a Single Echelon Supply Chain Using Fuzzy
Approach, International Journal of Innovation, Management and Technology, 3(2012), number 5, pp. 494498. 2012
http://dx.doi.org/10.7763/IJIMT.2012.V3.283
According to reference [A14], the possibilistic variance of a symmetric triangle fuzzy number is
defined as: (page 496)
A14-c380 Sari IU, Kuchta D, Fuzzy global sensitivity analysis of fuzzy net present value, CONTROL AND
CYBERNETICS, 41(2012), number 2, pp. 481-496.2 012
Scopus: 84868278448
A14-c379 Yong-Jun Liu, Wei-Guo Zhang, Wei-Jun Xu, Fuzzy multi-period portfolio selection optimization
models using multiple criteria, AUTOMATICA, 48(2012), number 12, pp. 3042-3053. 2012
http://dx.doi.org/10.1016/j.automatica.2012.08.036
In the following, we will introduce the notions of possibilistic mean value, variance and covariance
of fuzzy numbers introduced in Carlsson and Fullér (2001), and Saeidifar and Pasha (2009). (page
3043)
A14-c378 Jha GK, Thulasiram RK, Thavaneswaran A, APPLICATIONS OF POSSIBILITY THEORY IN FINANCE, INTERNATIONAL JOURNAL OF AGRICULTURAL AND STATISTICAL SCIENCES, 8(2012),
number 1, pp. 79-95. 2012
WOS: 000307372000010
155
A14-c377 I. Georgescu, Expected utility operators and possibilistic risk aversion, SOFT COMPUTING, Volume
16, Issue 10, September 2012, Pages 1671-1680. 2012
http://dx.doi.org/10.1007/s00500-012-0851-3
A14-c376 Hassanzadeh F, Collan M, Modarres M, A practical approach to R&D portfolio selection using the
fuzzy pay-off method, IEEE Transactions on Fuzzy Systems, 20(2012), number 4, pp. 615-622. Paper
6109284. 2012
http://dx.doi.org/10.1109/TFUZZ.2011.2180380
A14-c375 Rahim Saneifard, Rasoul Saneifard, Anteriority Indicator For Managing Fuzzy Dates Based on Maximizing And Minimizing Sets, INTERNATIONAL JOURNAL OF NATURAL AND ENGINEERING SCIENCES 6(2012), number 2, pp. 29-32. 2012
http://www.nobel.gen.tr/MakaleSayac.aspx?ID=2881
Recently many authors have studied different methods of maximizing set and minimizing set of
fuzzy numbers. Carlsson and Fullér [A14] suggested an index of difference based on α-level sets,
fuzzy subtraction operation and area measurement. (page 29)
A14-c374 Jules Sadefo Kamdem, Christian Deffo Tassak, Louis Aime Fono, Moments and semi-moments for
fuzzy portfolios selection, Insurance: Mathematics and Economics, 51(2012), number 3, pp. 517-530. 2012
http://dx.doi.org/10.1016/j.insmatheco.2012.07.003
A14-c373 S. S. Appadoo, C. R. Bector, Fuzzy EOQ model using possibilistic approach, JOURNAL OF ADVANCES IN MANAGEMENT RESEARCH, 9(2012), number 1, pp. 139-164. 2012
http://dx.doi.org/10.1108/09727981211225707
A14-c372 Zhang W -G, Liu Y -J, Xu W -J, A possibilistic mean-semivariance-entropy model for multi-period
portfolio selection with transaction costs, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH,
222(2012), number 2, pp. 341-349. 2012
http://dx.doi.org/10.1016/j.ejor.2012.04.023
A14-c371 Yuanji Xu, Jinsong Hu, Random Fuzzy Demand Newsboy Problem, PHYSICS PROCEDIA, 25(2012),
pp. 924-931. 2012
http://dx.doi.org/10.1016/j.phpro.2012.03.179
A14-c370 Hsiao-Fan Wang, Hsin-Wei Hsu, A possibilistic approach to the modeling and resolution of uncertain
closed-loop logistics, FUZZY OPTIMIZATION AND DECISION MAKING, 11(2012), number 2, pp.
177-208. 2012
http://dx.doi.org/10.1007/s10700-012-9120-2
One method for collecting the information is to integrate all levels, which can be attributed to
Carlsson and Fullér (2001) based on the concept of mean in the probability theory. The fuzzy
numbers can be ranked using the method of Goetschel and Voxman (1986), which compares the
possibilistic means of the fuzzy numbers, as defined by the arithmetic means of all γ-level sets, as
shown below. (page 182)
Carlsson and Fullér (2001) proposed a variance based on the end points of a fuzzy number in
relation to the possibilistic mean, and as previously explained, the information of end points are
insufficient for the determination of shortage and surplus. Therefore, the MSII of a fuzzy number
is given below using the arithmetic means of γ-level sets based on all continuous points: (page
187)
A14-c369 Dey O, Chakraborty D, A fuzzy random periodic review system: A technique for real-life application,
International Journal of Operational Research, 13(2012), number 4, pp. 395-405. 2012
http://dx.doi.org/10.1504/IJOR.2012.046224
A14-c368 Mazarbhuiya F A, Abulaish M, Clustering periodic frequent patterns using fuzzy statistical parameters, International Journal of Innovative Computing, Information and Control, 8(2012), number 3B, pp.
2113-2124. 2012
Scopus: 84857583039
156
A14-c367 Xiaoxia Huang, Mean-variance models for portfolio selection subject to experts’ estimations, EXPERT SYSTEMS WITH APPLICATIONS, 39(2012), issue 5, pp. 5887-5893. 2012
http://dx.doi.org/10.1016/j.eswa.2011.11.119
A14-c366 Konstantinos A Chrysafis, Corporate Investment Appraisal with Possibilistic CAPM, MATHEMATICAL AND COMPUTER MODELLING, 55(2012), issues 3-4, pp. 1041-1050. 2012
http://dx.doi.org/10.1016/j.mcm.2011.09.029
Abstract: The Capital Asset Pricing Model (CAPM) is a useful tool in the estimation of the equity
cost in the cost of capital computation. This work proposes a method to limit problems arising
from the CAPM assumptions. The main tools are the possibilistic mean and the possibilistic
variance/covariance of fuzzy numbers as they are introduced by Carlsson and Fullér (2001). The
results of this method are a possibilistic CAPM beta value and a possibilistic value for the market
premium. (page 1041)
A method that combines Fuzzy Sets Theory and Possibility Theory is the one developed by Carlsson and Fullér [A14]. This method has been extensively applied (e.g. the author refers to some
applications related to this work such as Chrysafis and Papadopoulos [4], Appadoo et. al [5], Appadoo et. al [6], Georgesku [7], Georgesku and Kinnunen [8],Paseka et. Al [9], Zimmerman [10],
Thiagarajah et al. [11], Xu et al. [12] and much more), a fact that asserts its efficiency and its
applicability in the modeling of uncertainty. (page 1041)
Carlsson and Fullér [A14] motivated by Dubois and Prade [21] and Goetschel and Voxman [22],
introduce the notations of lower possibilistic and upper possibilistic mean values and also define
the crisp possibilistic mean value and the crisp possibilistic variance of a continuous possibility
distribution. These values are consistent with the Zadeh’s Extension Principle [1] and the definitions of expectation and variance in probability theory. The data used for the derivation of these
values is fuzzy numbers. To derive the results in this section we implicitly use the following results
as in Carlsson and Fullér [A14], where Pos denotes possibility: (page 1043)
A14-c365 Lin Wang, Qing-Liang Fu, Yu-Rong Zeng, Continuous review inventory models with a mixture of
backorders and lost sales under fuzzy demand and different decision situations, EXPERT SYSTEMS WITH
APPLICATIONS 39(2012), number 4, pp. 4181-4189. 2012
http://dx.doi.org/10.1016/j.eswa.2011.09.116
A14-c364 J D Bermúdeza, J V Segurab, E Vercher, A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection, FUZZY SETS AND SYSTEMS, 188(2012), number 1, pp. 16-26. 2012
http://dx.doi.org/10.1016/j.fss.2011.05.013
A14-c363 Xue Deng, Rongjun Li, A portfolio selection model with borrowing constraint based on possibility
theory, APPLIED SOFT COMPUTING, 12(2012), number 2, pp. 754-758. 2012
http://dx.doi.org/10.1016/j.asoc.2011.10.017
There are many non-probabilistic factors that affect the financial market such that the return of
risky asset is fuzzy uncertainty. Recently, a number of researchers investigated fuzzy portfolio
selection problem. Bellman and Zadeh (1970) proposed the basic fuzzy decision theory. Carlsson
and Fullér (2001) discussed some basic knowledge about possibilistic mean and variance of fuzzy
numbers. (page 754)
A14-c362 Farhad Hassanzadeh, Mikael Collan, Mohammad Modarres, A practical R&D selection model using fuzzy pay-off method, INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 58(2011), numbers 1-4, pp. 227-236. 2012
http://dx.doi.org/10.1007/s00170-011-3364-9
A14-c361 Chung-Tsen Tsao, Fuzzy net present values for capital investments in an uncertain environment,
COMPUTERS & OPERATIONS RESEARCH, 39(2102), issue 8, pp. 1885-1892. 2012.
http://dx.doi.org/10.1016/j.cor.2011.07.015
A14-c360 Tohid Erfani, Sergei V Utyuzhnikov, Control of robust design in multiobjective optimization under
uncertainties, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, 45(2012), number 2, pp.
247-256. 2012
http://dx.doi.org/10.1007/s00158-011-0693-0
157
A14-c359 O Dey, D Chakraborty, A Fuzzy Random Periodic Review System with Variable Lead-time and
Negative Exponential Crashing Cost, APPLIED MATHEMATICAL MODELLING, 36(2012), number 12,
pp. 6312-6322. 2012
http://dx.doi.org/10.1016/j.apm.2011.09.047
2011
A14-c358 Collan M, Valuation of industrial giga-investments: Theory and practice, FUZZY ECONOMIC REVIEW, 16(2011), number 1, pp. 21-37. 2011
Scopus: 84858031424
A14-c357 Appadoo S S, Bector C R, Bhatt S K, Possibilistic characterization of (m,n)-Trapezoidal fuzzy numbers with applications, Journal of Interdisciplinary Mathematics, 14(2011), number 4, pp. 347-372. 2011
Scopus: 84856195004
A14-c356 ZHANG Weiguo, MEI Qin, CHEN Chiwen, Optimization Method on Multi-Project Portfolio with
Fuzzy Returns CHINESE JOURNAL OF MANAGEMENT, 8(2011), number 6, pp. 938-942 (in Chinese).
2011
www.glxb.ac.cn/CN/article/downloadArticleFile.do?attachType=PDF&id=9697
A14-c355 Jinquan Li, Xuehai Yuan, E S Lee, Dehua Xu, Setting due dates to minimize the total weighted
possibilistic mean value of the weighted earliness - tardiness costs on a single machine, COMPUTERS
AND MATHEMATICS WITH APPLICATIONS, 62(2011), number 11, pp. 4126-4139. 2011
http://dx.doi.org/10.1016/j.camwa.2011.09.063
A14-c354 Yihua Mao, Wenjing Wu, Fuzzy Real Option Evaluation of Real Estate Project Based on Risk Analysis, SYSTEMS ENGINEERING PROCEDIA, 1(2011), pp. 228-235. 2011
http://dx.doi.org/10.1016/j.sepro.2011.08.036
Where V is the value of the initial project estimated income and C is of the expected cost those
are all fuzzy sets; While V’ and C’ are represented for adjustment values; E(V) and E(C) are
the probability averages of the initial income and cost. To determine the average of fuzzy sets,
Carlsson C. and Fuller R. [A14] gave the computation formula as follows: (page 231)
A14-c353 Fei Ye, Yina Li, A Stackelberg single-period supply chain inventory model with weighted possibilistic
mean values under fuzzy environment, APPLIED SOFT COMPUTING, 11(2011), number 8. pp. 55195527. 2011
http://dx.doi.org/10.1016/j.asoc.2011.05.007
Different from the previous related literature, we further take the risk preferences of decision
makers into consideration, which making our model more consistent with real situation. We adopt
the weighted possibilistic mean value method proposed by Carlsson and Fullér [A14], Zhang et
al. [23] to solve the fuzzy optimization problem. (page 5520)
A14-c352 Rupak Bhattacharyya, Samarjit Kar, Possibilistic mean- variance- skewness portfolio selection models, INTERNATIONAL JOURNAL OF OPERATIONS RESEARCH, 8(2011), number 3, pp. 44-56. 2011
http://www.orstw.org.tw/IJOR/vol8no3/5-Vol_8,%20No.%203,%20pp.44-56.pdf
A14-c351 Chien-Chang Chou, Jeng-Ming Yih, Ji-Feng Ding, Tzeu-Chen Han, Jin-Long Lu, Li-Jen Liu, The
representation of square root of generalized trapezoidal fuzzy number and its application to solving statistical problems, ICIC EXPRESS LETTERS, 5(2011), number 9B, 3303-3307. 2011
Scopus: 80052510252
http://www.ijicic.org/el-5%289%29b.htm
A14-c350 Alessandro Buoni, Mario Fedrizzi, Jozsef Mezei, Combining attack trees and fuzzy numbers in a
multi-agent approach to fraud detection, INTERNATIONAL JOURNAL OF ELECTRONIC BUSINESS,
9(2011), number 3, pp. 186-202. 2011
http://dx.doi.org/10.1504/IJEB.2011.042541
158
A14-c349 Shiu-Hwei Ho, Shu-Hsien Liao, A fuzzy real option approach for investment project valuation, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), issue 12, pp. 15296-15302. 2011
http://dx.doi.org/10.1016/j.eswa.2011.06.010
A14-c348 S. A. Farzad, Technology portfolio modeling in hybrid environment, AFRICAN JOURNAL OF
BUSINESS MANAGEMENT, 5(2011), number 5, pp. 4051-4058. 2011
http://www.academicjournals.org/ajbm/PDF/pdf2011/4June/Farzad.pdf
Recognizing optimized point for a decision maker is difficult task and usually due to plurality of
choices, it is time consuming. Inasmuch as such a decision making has to do with selection or
non-selection, mostly is formulated as 0-1 function (Lin and Hsieh, 2004). Applying integer programming to risk priority reduction (Glickman, 2008) and using linear programming with infinite
dimensions (Carlsson and Fuller, 2001) have been undertaken in recent years, which each of them
has attempted to get the optimal answer, in a way. Therefore discussing these two states simultaneously that combine fuzzy random return and integer selection as a comprehensive model can
lead to better results especially in contrast with initial models. (page 4052)
A14-c347 Mikael Collan, Markku Heikkilä, Enhancing patent valuation with the pay-off method, JOURNAL
OF INTELLECTUAL PROPERTY RIGHTS, 16(2011), pp. 377-384. 2011
http://nopr.niscair.res.in/handle/123456789/12687
A14-c346 Qian Wang, D Marc Kilgour, Keith W Hipel, Fuzzy Real Options for Risky Project Evaluation Using
Least Squares Monte-Carlo Simulation, IEEE SYSTEMS JOURNAL, 5(2011), issue 3, pp. 385-395. 2011
http://dx.doi.org/10.1109/JSYST.2011.2158687
A14-c345 Rahim Saneifard, A new algorithm for selecting equip system based on fuzzy operations, INTERNATIONAL JOURNAL OF THE PHYSICAL SCIENCES, 6(2011), number 14, pp. 3279-3287. 2011
http://www.academicjournals.org/IJPS/PDF/pdf2011/18Jul/Saneifard.pdf
In statistics, measures of central tendency and measures dispersion of distribution are considered
important. For fuzzy numbers, one of the most common and useful measures of central tendency
is the mean of fuzzy numbers (Carlsson and Fuller, 2001; Fullér and Majlender, 2003), defined the
weighted lower possibilistic and upper possibilistic mean values, crisp possibilistic mean value,
the variance and covariance of fuzzy numbers. In this paper we introduce the parametric interval
approximation of fuzzy numbers and their applications, for example, the measure and ranking of
the fuzzy numbers. (page 3279)
A14-c344 Irina Georgescu; Jani Kinnunen, Credibility measures in portfolio analysis: From possibilistic to
probabilistic models, JOURNAL OF APPLIED OPERATIONAL RESEARCH, 3(2011), number 2, pp.
91-102.
http://www.tadbir.ca/jaor/archive/v3/n2/jaorv3n2p91.pdf
A14-c343 Wei Chen, Yiping Yang, Hui Ma, Fuzzy Portfolio Selection Problem with Different Borrowing and
Lending Rates, MATHEMATICAL PROBLEMS IN ENGINEERING, vol. 2011, pp. 1-15. Paper 263240.
2011
http://dx.doi.org/10.1155/2011/263240
Carlsson and Fullér [A14] introduced the lower and upper possibilistic mean values of fuzzy number (page 6)
A14-c342 Irina Georgescu, Jani Kinnunen, Possibilistic risk aversion with many parameters, PROCEDIA
COMPUTER SCIENCE 4(2011), pp. 1735-1744. 2011
http://dx.doi.org/10.1016/j.procs.2011.04.188
A14-c341 R. Saneifard; R. Saneifard, On the weighted intervals of fuzzy numbers, JOURNAL OF APPLIED
SCIENCES RESEARCH, Volume 7, Issue 3, March 2011, pp. 229-235. 2011
Scopus: 79959831165
A14-c340 Zoran Gligoric, Hybrid model of evaluation of underground lead-zinc mine capacity expansion
project using Monte Carlo simulation and fuzzy numbers, SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION, 87(2011), number 8, pp. 726-742. 2011
http://dx.doi.org/10.1177/0037549711410902
159
A14-c339 Wei Chen, Cui-you Yao, Yue Qiu, PSO-based Possibilistic Portfolio Model with Transaction Costs,
PROCEEDINGS OF THE WORLD ACADEMY OF SCIENCE, ENGINEERING AND TECHNOLOGY,
77(2011), pp. 264-269. 2011
http://www.waset.org/journals/waset/v77/v77-48.pdf
Carlsson and Fullér [A14] introduced the notions of lower and upper possibilistic mean values of
a fuzzy number, then proposed a possibilistic approach to selecting portfolios with highest utility
score in [A12]. Chen [10] discussed the portfolio selection problem for bounded assets based on
weighted possibilistic means and variances. Zhang et al. [11] discussed the portfolio selection
problem for bounded assets with the maximum possibilistic mean-variance utility. (page 264)
A14-c338 Irina Georgescu; Jani Kinnunen, Multidimensional possibilistic risk aversion, MATHEMATICAL
AND COMPUTER MODELLING, 54(2011), issues 1-2, pp. 689-696. 2011
http://dx.doi.org/10.1016/j.mcm.2011.03.011
A14-c337 Oshmita Dey, Debjani Chakraborty, A fuzzy random continuous review inventory system, INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS, 132(2011), issue 1, pp. 101-106. 2011
http://dx.doi.org/10.1016/j.ijpe.2011.03.015
A14-c336 Young-Chan Lee, Seung-Seok Lee, The valuation of RFID investment using fuzzy real option, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), issue 10, pp. 12195-12201. 2011
http://dx.doi.org/10.1016/j.eswa.2011.03.076
However, since real options predicts expected cash flow in various situations that may result from
investment and the current value of investment costs with a single value, it has a problem of not
being realistic, and this problem can be solved by utilizing fuzzy set theory (Appadoo, Bhatt, &
Bector, 2008; Carlsson & Fuller, 2001, 2003). Thus, this study examines the strategic characteristic of RFID investment in which enterprises have recently expressed much interest, and it tries to
propose a fuzzy real options technique that can consider various situations of expected cash flow
or investment costs as a plan to support investment decisions for this effectively. (page 12195)
A14-c335 Xing Yu, Hongguo Sun, Guohua Che, Pricing European Call Currency option based on Adaptive
Fuzzy Numbers with Possibilistic Mean, PROGRESS IN APPLIED MATHEMATICS, 1(2011), number 2,
pp. 77-82. 2011
http://www.cscanada.net/index.php/pam/article/view/1806
A14-c334 R Saneifard, R Saneifard, An approximation approach to fuzzy numbers by continuous parametric
interval AUSTRALIAN JOURNAL OF BASIC AND APPLIED SCIENCES, 5(2011), number 3, pp. 505515. 2011
Scopus: 79955119749
A14-c333 Li Duan, Peter Stahlecker, A portfolio selection model using fuzzy returns, FUZZY OPTIMIZATION
AND DECISION MAKING, 10(2011), number 2, pp. 167-191. 2011
http://dx.doi.org/10.1007/s10700-011-9101-x
A review of models using credibility measures as a closely related approach is given by Huang
(2009). Considering the rates of return as fuzzy numbers Carlsson and Fullér (2001) introduce
the possibilistic mean value and the variance of fuzzy numbers. A model which integrates both
probability and possibility theory is analyzed by Tanaka et al. (2000). Another approach using
interval numbers can be referred to Lai et al. (2002) and Li and Xu (2007). Finally Inuiguchi and
Ramik (2000) compare the fuzzy approach with the classical probabilistic models. (page 168)
A14-c332 Costin-Ciprian POPESCU, Cristinca FULGA, POSSIBILISTIC OPTIMIZATION WITH APPLICATION TO PORTFOLIO SELECTION, PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A,
12(2011), number 2, pp. 88-94. 2011
http://www.acad.ro/sectii2002/proceedings/doc2011-2/02-Popescu.pdf
A14-c331 T Allahviranloo, S Abbasbandy, R Saneifard, AN APPROXIMATION APPROACH FOR RANKING
FUZZY NUMBERS BASED ON WEIGHTED INTERVAL - VALUE, MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 16(2011), number 3, pp. 588-597. 2011
http://www.mcajournal.org/volume16/vol16no3/v16no3p588.pdf
160
A14-c330 Irina Georgescu, A possibilistic approach to risk aversion, SOFT COMPUTING, 15(2011), pp. 795801. 2011
http://dx.doi.org/10.1007/s00500-010-0634-7
Secondly, starting from these possibilistic mean values one obtained more notions of possibilistic
variances. In paper (Carlsson and Fullér 2001), two concepts of possibilistic variances were defined. These have been generalized in case of a weighting function (Fullér and Majlender 2003).
The lower and upper possibilistic variances of a fuzzy number were studied in Fullér and Majlender (2003). (page 795)
A14-c329 A. Paseka, S.S. Appadoo, A. Thavaneswaran, Possibilistic moment generating functions, APPLIED
MATHEMATICS LETTERS, 24(2011), pp. 630-635. 2011
http://dx.doi.org/10.1016/j.aml.2010.11.027
Following Carlsson and Fuller (2001) [A14], recently Thavaneswaran et al. (2009) [1] have introduced higher order weighted possibilistic moments of fuzzy numbers. In this paper, we define
the weighted possibilistic moment generating functions (MGF) of fuzzy numbers and obtain the
closed form expressions for triangular, trapezoidal and parabolic fuzzy numbers. Applications
involve derivation of higher order possibilistic moments of volatility models (see Thavaneswaran
et al. (2009) [1] for details). (page 630)
A14-c328 A. Ban, A. Brandas, L. Coroianu, C. Negrutiu, O. Nica, Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value, COMPUTERS AND MATHEMATICS WITH
APPLICATIONS Volume 61, Issue 5, March 2011, Pages 1379-1401. 2011
http://dx.doi.org/10.1016/j.camwa.2011.01.005
A14-c327 M. Collan, J. Kinnunen, A Procedure for the Rapid Pre-acquisition Screening of Target Companies
Using the Pay-off Method for Real Option Valuation, JOURNAL OF REAL OPTIONS AND STRATEGY,
4(2011), number 1, pp. 117-141. 2011
http://www.jstage.jst.go.jp/browse/realopn/_vols
A14-c326 Yuji Yoshida, Risk Analysis of Portfolios Under Uncertainty: Minimizing Average Rates of Falling,
JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS, 15(2011), issue 1, pp. 56-62. 2011
http://www.fujipress.jp/finder/xslt.php?
mode=present&inputfile=JACII001500010006.xml
A14-c325 Rupak Bhattacharyya, Samarjit Kar, Dwijesh Dutta Majumder, Fuzzy mean-variance-skewness portfolio selection models by interval analysis, COMPUTERS AND MATHEMATICS WITH APPLICATIONS,
61(2011) 126-137. 2011
http://dx.doi.org/10.1016/j.camwa.2010.10.039
Using the fuzzy extension principle, the crisp possibilistic mean value of the turn over rate of the
portfolio x = (x1 , x2 , . . . , xn ) is obtained by [A14] as, (page 131)
A14-c324 G C Mahata, A single period inventory model for incorporating two-ordering opportunities under imprecise demand information, INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING COMPUTATIONS, 2(2011) 385-394. 2011
http://dx.doi.org/10.5267/j.ijiec.2010.08.002
As the demands are linguistic in nature and the optimal order quantity in the second slot depends
on the demand that arises in the first slot, so the profit function as well as the decision variable
during the second slot are also fuzzy quantity. Solution procedure is presented using ordering
of fuzzy numbers with respect to their possibilistic mean values (Carlsson & Fullér, 2001). The
objective is to determine a personal policy that will maximize the total resultant profit under the
above state of affairs. (page 386)
161
A14-c323 Wei-Guo Zhang, Qing-Sheng Shi, Wei-Lin Xiao, Fuzzy Pricing of American Options on Stocks
with Known Dividends and Its Algorithm, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS,
26(2011), issue 2, pp. 169-185. 2011
http://dx.doi.org/10.1002/int.20460
Carlsson and Fuller [A14] introduced the notions of crisp possibilistic mean and crisp possibilistic
variances of fuzzy numbers. The possibilistic mean value and possibilistic variance of A defined
by Refs. 19 as follows: (page 173)
A14-c322 Dug Hun Hong; Eunho L. Moon; Jae Duck Kim, Remarks on possibilistic variances of fuzzy numbers, JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 36(2011), number 3, pp. 163-171.
2011
http://dx.doi.org/10.1007/s12190-010-0394-7
Abstract: Carlsson and Fullér (Fuzzy Sets Syst. 122:315-326, 2001) introduced the definitions of
two crisp possibilistic variances of a fuzzy number A, Var(A) and Var’(A). They showed that the
subsethood does entail smaller variance in the sense of Var(·). Thus it is natural to ask whether
it holds in the sense of Var’(·). Yet we are able to prove that it actually does not hold. Zhang
and Wang (Appl. Math. Lett. 20:1167-1173, 2007) had introduced some conditions for which
the subsethood does entail smaller variance in the sense of Var’(·). In this paper we give more
generalized conditions for which it holds. (page 163)
Carlsson and Fullér [A14] introduced the notion of interval-valued possibilistic mean of fuzzy
numbers and investigated its relationship to interval-valued probabilistic mean. They also proved
that the proposed concepts behave properly in a similar way as their probabilistic counterparts. The
concepts of two crisp possibilistic variances of a fuzzy number A, Var(A) and Var’(A), were also
defined by Carlsson and Fullér [A14]. In [4-6] Zhang and Wang showed that many properties of
variance in probability theory are preserved by Var’(A), and investigated the important relationship
between Var(A) and Var’(A) such that Var(A) ≤ Var0 (A) for any fuzzy number A. Furthermore
they showed that the subsethood does entail smaller variance when they have the same shape
functions and the same lower and upper modal values like LR-type fuzzy numbers. However we
can see that this subsethood does not entail for some types of fuzzy number (see Example 1). Thus
the purpose of this paper is to find sufficient conditions that the subsethood does entail smaller
variance for any fuzzy numbers. We also show that for any fuzzy number A, Var(A) = Var0 (A)
if and only if A is symmetric. (pages 163-164)
2010
A14-c321 Jin Won Park, Yong Sik Yun, Kyoung Hun Kang, The mean value and variance of one-sided fuzzy
sets, JOURNAL OF THE CHUNGCHEONG MATHEMATICAL SOCIETY, 23(2010), number 3, pp. 511520. 2010
http://www.ccms.or.kr/data/pdfpaper/jcms23_3/23_3_511.pdf
In 2001, C. Carlsson and R Fullér [A14] introduced the concepts of possibilistic mean value and
variance of fuzzy numbers. And using these concepts, they defined the interval-valued possibilistic
mean, crisp possibilistic mean value and crisp (possibilistic) variance of a continuous possibilistic
distribution and they proved some properties of these concepts. In this paper, we define the onesided fuzzy set and calculate the mean value and variance of various type of on-sided fuzzy sets.
And we obtain a result that, in some special case, the mean of the product of two fuzzy sets is the
product of means of each fuzzy sets. This result can be considered as the similar result which is
well-known in the independence of events in probability theory. (page 511)
In this section, we introduce the notion of possibilistic mean value and variance of fuzzy sets
defined by C. Carlsson and R. Fullér. And, we calculate the possibilistic mean value and variance
of one-sided fuzzy sets. (page 514)
A14-c320 Jian Ming Xiao, Fuzzy environment with transaction costs of options pricing model - Memorial
Fellow Professor Wu Xinmou Guoping 100th anniversary, ACTA MATHEMATICA SCIENTIA - SERIES
A, 30(2010), number 5, pp. 1254-1262 (in Chinese). 2010
162
http://www.cqvip.com/qk/93833x/201005/35639142.html
A14-c319 YU Shao-wei, LI Xiu-hai, LIU Qing-ling, On real option pricing based on interval analysis and the
cloud model, JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 45(2010), number 5,
pp. 64-68 (in Chinese). 2010
http://d.wanfangdata.com.cn/periodical_sddxxb201005012.aspx
A14-c318 Xue Deng, Junfeng Zhao, Lihong Yang, Rongjun Li, Possibilistic mean-variance utility to portfolio
selection for bounded assets, INTERNATIONAL JOURNAL OF DIGITAL CONTENT TECHNOLOGY
AND ITS APPLICATIONS, 4(2010) number 6, pp. 150-160. 2010
http://www.aicit.org/jdcta/ppl/18%20-%20JDCTA4-460058.pdf
Fuzzy number is a powerful tool used to describe an uncertain environment with vagueness and
ambiguity to compare with the conventional probabilistic mean-variance methodology. In this
paper, we have considered the portfolio selection problem for bounded assets under assumption
each investor’s utility is the mean-variance type function, which can be regarded as a natural
extension of Carlsson et al. [A14]. Moreover, we propose three kinds of optimization portfolio
selection models: (page 58)
A14-c317 Weijun Xu, Weidong Xu, Hongyi Li, Weiguo Zhang, Uncertainty portfolio model in cross currency markets, INTERNATIONAL JOURNAL OF UNCERTAINTY, FUZZINESS AND KNOWLEDGEBASED SYSTEMS, 18(2010), Issue 6, pp. 759-777. 2010
http://dx.doi.org/10.1142/S0218488510006787
Possibility theory was proposed by Zadeh [18] and advanced by Dubois and Prade [19]. Since
the random variables are associated with probability distributions in the probability theory, the
possibility distribution function of a fuzzy variable is usually defined by the membership function
of the corresponding fuzzy set. Following Markowitz’s mean-variance methodology, Inuiguchi
and Tanino [20], Carlsson et al. [A14, A12], Tanaka and Guo [10,11] formulated the portfolio
selection model based on the possibilistic programming. (page 761)
A14-c316 Xue Deng, Junfeng Zhao, Lihong Yang, Rongjun Li, Constraint Method for Possibilistic Meanvariance Portfolio with Transaction Costs and Lending, JOURNAL OF CONVERGENCE INFORMATION
TECHNOLOGY, 5(2010), number 9, pp. 73-84. 2010
http://www.aicit.org/jcit/ppl/JCIT0509_07.pdf
Recently, a number of researchers investigated fuzzy portfolio selection problem. Bellman and
Zadeh (1970) proposed the basic fuzzy decision theory. Carlsson and Fullér (2001) discussed
some basic knowledge about possibilistic mean and variance of fuzzy numbers. (page 73)
A14-c315 E. Almaraz Luengo, Fuzzy mean-variance portfolio selection problems, ADVANCED MODELING
AND OPTIMIZATION, 12(2010), number 3, pp. 399-410. 2010
http://camo.ici.ro/journal/vol12/v12c9.pdf
There are different ways to define the expected value and variance of a fuzzy number, for example,
using the concepts of possibility, necessity and credibility (see Liu, 2004) or using the concept of
α-level set (see Carlsson and Fullér, 2001). We will use this second way in our development.
(page 400)
A14-c314 Xue Deng, Rongjun Li, A portfolio selection model based on possibility theory using fuzzy twostage algorithm, JOURNAL OF CONVERGENCE INFORMATION TECHNOLOGY 5(2010), number 6,
pp. 138-145. 2010
http://www.aicit.org/jcit/ppl/14.%20JCIT_vol5num6.pdf
There are many non-probabilistic factors that affect the financial market such that the return of
risky asset is fuzzy uncertainty. And a number of empirical studies showed the limitations of using probabilistic approaches in characterizing the uncertainty of the financial market. Recently,
a number of researchers investigated fuzzy portfolio selection problem. Bellman and Zadeh [12]
proposed the basic fuzzy decision theory. Carlsson and Fullér [A14] discussed some basic knowledge about possibilistic mean and variance of fuzzy numbers. (page 138)
163
A14-c313 Y -B Gong, D -W Fang, Two optimal aggregation approaches of fuzzy opinions in group decision
analysis, Journal of Donghua University (English Edition), 27(2010), number 2, pp. 139-142. 2010
A14-c312 Ehsanollah Mansourirad, Mohd Rizam Abu Bakar, Azmi Jafar and Lai Soon Lee, INTERVAL EFFICIENCY SCORES USING A NEW METHOD IN FUZZY DATA ENVELOPMENT ANALYSIS, ADVANCES IN FUZZY MATHEMATICS, 6(2010), Issue 1, pp. 1-12. 2010
http://pphmj.com/references/5181.htm
A14-c311 S. S. Appadoo and A. Thavaneswaran, Possibilistic moment generating functions of fuzzy numbers
with GARCH applications, ADVANCES IN FUZZY MATHEMATICS, 6(2010), Issue 1, pp. 33-62. 2010
http://pphmj.com/references/5183.htm
A14-c310 Guohua Chen, Fuzzy Data Decision Support in Portfolio Selection: a Possibilistic Safety-first Model,
COMPUTER AND INFORMATION SCIENCE 3(2010), number 4, pp. 116-124. 2010
http://www.ccsenet.org/journal/index.php/cis/article/view/8102/6121
Carlsson et al (2001) introduced the notation of crisp possibilitic mean value of continuous possibility distributions, which are consistent with the extension principle. (page 119)
A14-c309 Zhang Qian-Sheng; Jiang Sheng-Yi, On Weighted Possibilistic Mean, Variance and Correlation of
Interval-valued Fuzzy Numbers, COMMUNICATIONS IN MATHEMATICAL RESEARCH, 26(2010),
number 2, pp. 105-118. 2010
http://www.cqvip.com/qk/96600A/201002/34084956.html
A14-c308 Zhou Chun; Huang Jian Yuan; Semi-absolute deviation portfolio model and its application, MATHEMATICS IN ECONOMICS, 27(2010), number 2, pp. 57-61 (in Chinese). 2010
http://www.cqvip.com/qk/91594x/2010002/34366183.html
A14-c307 Seung Hoe Choi; Jin Hee Yoon, General fuzzy regression using least squares method, INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 41(2010), issue 5, pp. 477-485. 2010
http://dx.doi.org/10.1080/00207720902774813
A14-c306 Mikael Collan, Valuation of area development project investments as compound real option problems,
JOURNAL OF APPLIED OPERATIONAL RESEARCH, 2(2010), number 2, pp. 71-78. 2010
http://www.tadbir.ca/jaor/archive/v2/n1/jaorv2n1p71.pdf
A14-c305 Hsiao-Fan Wang, Hsin-Wei Hsu, Resolution of an uncertain closed-loop logistics model: An application to fuzzy linear programs with risk analysis, JOURNAL OF ENVIRONMENTAL MANAGEMENT,
91(2010), number 11, pp. 2148-2162. 2010
http://dx.doi.org/10.1016/j.jenvman.2010.05.009
Due to the uncertainty of information, using the mean of a data set to represent the data is an effective and common index. While our data are fuzzy numbers, based on Decomposition Theory [see
Zimmermann, 2001], each datum is an aggregation of level set defined by intervals. Therefore, the
mean value of a fuzzy interval is also an interval but without degree. That is, when defuzzifying a
fuzzy number by its level set, the information is disaggregated into an interval set; and one way to
collect the whole information is to integrate all levels. This can be referred to Carlsson and Fuller
(2001) as a possibilistic mean derived from the concept of mean in the Probability Theory and
used Goetschel and Voxman’s (1986) method for ranking fuzzy numbers.
A14-c304 Wei-Guo Zhang, Xi-Li Zhang, Wei-Jun Xu, A risk tolerance model for portfolio adjusting problem with transaction costs based on possibilistic moments, INSURANCE: MATHEMATICS AND ECONOMICS, 46(2010), issue 3, pp. 493-499. 2010
http://dx.doi.org/10.1016/j.insmatheco.2010.01.007
The variance of fuzzy number is defined as the possibility-weighted average of the squared distance between the mean value and the left-hand and right-hand endpoints of its level sets. The
variance is always positive and a measure of dispersion or spread of the fuzzy number. In the
physical interpretation of the variance, it gives the moment of inertia of the mass distributed about
the center of mass, also the variance gives information about the spread of variables around the
mean value and it is a very important factor to find out the fluctuation in the observed values (more
see [Carlsson and Fullér, 2001] and [Saeidifar and Pasha, 2009]). (page 494)
164
A14-c302 Shu-Hsien Liao, Shiu-Hwei Ho, Investment project valuation based on a fuzzy binomial approach,
INFORMATION SCIENCES, 180(2010), issue 11, pp. 2124-2133. 2010
http://dx.doi.org/10.1016/j.ins.2010.02.012
In essence, identical results are obtained in the case of possibilistic distribution which is adopted
by this study to characterize the NPV of an investment project. In other words, the characteristic of
right-skewed distribution also appears in the FENPV of an investment project when the parameters
(such as cash flows) are characterized with fuzzy numbers. Although many studies have proposed
a variety of methods to compute the mean value [A14,12] and median value [2] of fuzzy numbers,
these works did not consider the right-skewed characteristic present in the FENPV. Therefore, this
study proposes a new method to compute the mean value of the FENPV based on its right-skewed
characteristic. This mean value can be used to represent the FENPV with a crisp value. (page
2129)
A14-c301 Francisco Campuzano, Josefa Mula, David Peidro, Fuzzy estimations and system dynamics for improving supply chains, FUZZY SETS AND SYSTEMS, 161(2010), issue 11, pp. 1530-1542. 2010
http://dx.doi.org/10.1016/j.fss.2009.12.002
Carlsson and Fullér [A14] define the mean square imprecision index of Ã, E 2 (Ã) , as the expected
value of the square deviations between the arithmetic mean and the endpoints of their level sets, i.e.
the lower possibility – weighted average of the squared distance between the left-hand endpoint
and the arithmetic mean of the endpoints of their level sets plus the upper possibility – weighted
average of the squared distance between the right-hand endpoint and the arithmetic mean of the
endpoints of their level sets. (page 1534)
A14-c300 Jinquan Li, Kaibiao Sun, Dehua Xu, Hongxing Li, Single machine due date assignment scheduling
problem with customer service level in fuzzy environment, APPLIED SOFT COMPUTING, 10(2010),
issue 3, pp. 849-858. 2010
http://dx.doi.org/10.1016/j.asoc.2009.10.002
A14-c299 Weijun Xu, Weidong Xu, Hongyi Li, Weiguo Zhang, A study of Greek letters of currency option
under uncertainty environments, MATHEMATICAL AND COMPUTER MODELLING, 51(2010), issues
5-6, March 2010, pp. 670-681. 2010
http://dx.doi.org/10.1016/j.mcm.2009.10.041
At the same time, based on the possibilistic and weighted possibilistic mean values of a fuzzy
number introduced by Carlsson and Fullér [A14] and Fullér and Majlender [A9], respectively,
we propose in this paper the weighted possibilistic mean version of the G-K model and the crisp
weighted possibilistic mean version of the G-K model by assuming the input variables as weighted
possibilistic mean values of the fuzzy interest rates, fuzzy volatility, and fuzzy exchange rate.
(page 671)
A14-c298 W.-G. Zhang, W.-L. Xiao, W.-J. Xu, A possibilistic portfolio adjusting model with new added assets,
ECONOMIC MODELLING, 27(2010), Number 1, pp. 208-213. 2010
http://dx.doi.org/10.1016/j.econmod.2009.08.008
A14-c297 Chung-Tsen Tsao, The revised algorithms of fuzzy variance and an application to portfolio selection,
SOFT COMPUTING, 14(2010), pp. 329-337. 2010
http://dx.doi.org/10.1007/s00500-009-0407-3
The discussion of fuzzy statistical measures and fuzzy statistical inference have been found in
many previous studies (Carlsson and Fuller 2001; Chiang and Lin 1999; Dubois and Prade 1986;
Feng et al. 2001; Fruhwirth-Schnatter 1992; Fuller and Majlender 2003; Hong 2006; Hryniewicz
2006; Kwakernaak 1978, 1979; Lee 2001; Liu and Kao 2002; Puri and Ralescu 1986; Wu 2003).
A14-c296 Barbara Gladys, Adam Kasperski, Computing mean absolute deviation under uncertainty, APPLIED
SOFT COMPUTING, 10(2010), Issue 2, pp. 361-366. 2010
http://dx.doi.org/10.1016/j.asoc.2009.08.012
165
A14-c295 JIN Jian-hua; LI Yong-ming; LI Chun-quan, Securities investment portfolio optimization model
based on fuzzy coefficients, JOURNAL OF CHONGQING TECHNOLOGY AND BUSINESS: NATURAL SCIENCES EDITION, 27(2010), number 1, pp. 5-10 (in Chinese). 2010
http://www.cqvip.com/qk/95975b/2010001/33017166.html
A14-c294 WANG Zai-qi; XING Xiang-qin; WANG Bo-xuan, Research into Application of Fuzzy Real Option
Theory to China’s Mining Rights Assessment, SCIENCE TECHNOLOGY AND INDUSTRY, 10(2010),
number 2, pp. 78-81 (in Chinese). 2010.
http://www.cqvip.com/qk/98093a/2010002/33036496.html
2009
A14-c293 E. Pasha, A. Saiedifar, B. Asady, The percentiles of fuzzy numbers and their applications, IRANIAN
JOURNAL OF FUZZY SYSTEMS, 6(2009), Issue 1, 2009, pp. 27-44. 2009
A14-c292 G. Facchinetti and N. Pacchiarotti, A general defuzzification method for a fuzzy system output depending on different t-norms, ADVANCES IN FUZZY SETS AND SYSTEMS, Volume 4, Issue 2, Pages
167-187. 2009
http://pphmj.com/references/4120.htm
A14-c291 Guohua Chen, Xiaolian Liao, Shouyang Wang, A cutting plane algorithm for MV portfolio selection
model APPLIED MATHEMATICS AND COMPUTATION, Volume 215, Issue 4, 15 October 2009, pp.
1456-1462. 2009
http://dx.doi.org/10.1016/j.amc.2009.06.040
Carlsson and Fullér [A14] introduced the notation of crisp possibilitic mean value of continuous
possibility distributions, which are consistent with the extension principle. (page 1458)
A14-c290 Liping Hui; Su Yongying, Possibilities based on the weighted average of the fuzzy control chart,
COASTAL ENTERPRISES AND SCIENCE & TECHNOLOGY, 10(2009), pp. 24-25. 2009
http://d.wanfangdata.com.cn/Periodical_yhqyykj200910009.aspx
A14-c289 Guangyu Zheng, Changhua Hu, Wei Zhang, Yun Li, An approach for analyzing accelerated life test
with random stresses based on possibility theory, ELECTRONICS, OPTICS & CONTROL, Vol. 16, no. 7,
pp. 80-83 (in Chinese). 2009
http://www.cqvip.com/qk/91481X/200907/30870700.ht
A14-c288 Wei Chen, Shaohua Tan, On the possibilistic mean value and variance of multiplication of fuzzy
numbers, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 232(2009), pp. 327334. 2009
http://dx.doi.org/10.1016/j.cam.2009.06.016
Many practical problems are usually made in uncertain (random, fuzzy, etc.) environments. Exact
information can often not be provided. To solve this limitation, the applications of statistical
theory and fuzzy set theory prove to be practical approaches. In statistics, measures of central
tendency and measures dispersion of distribution are considered important. For fuzzy numbers,
two of the most useful measures are the mean and variance of fuzzy numbers. Carlsson and
Fullér [A14] defined the possibilistic mean values, variance and covariance of fuzzy numbers.
They have been used to solve many real world problems. For example, Carlsson et al. [A12]
and Zhang et al. [3,4] applied possibilistic mean value and variance to solve Markowitz meanvariance portfolio selection model [5] under the assumption that the returns of assets were fuzzy
numbers. In portfolio selection problem, most researchers focus so much attention on finance
theory that they ignore a very important practical problem: most investors would acknowledge
that, on entering the market, they do not know with certainty the time of exiting the market. (page
327)
In this paper, we introduce new definitions of possibilistic mean value, variance and covariance of
multiplication of fuzzy numbers based on the multiplication operation defined in [12]. Then, we
generalize the Markowitz’s model under fuzzy numbers in the elements of time horizon and asset
returns by using these definitions. (page 328)
166
A14-c287 Takashi Hasuike, Hideki Katagiri, Hiroaki Ishii, Portfolio selection problems with random fuzzy
variable returns, FUZZY SETS AND SYSTEMS, 160(2009), Issue 18, pp. 2579-2596. 2009
http://dx.doi.org/10.1016/j.fss.2008.11.010
A14-c286 Irina Georgescu, Possibilistic risk aversion, FUZZY SETS AND SYSTEMS, 160(2009), pp. 26082619. 2009
http://dx.doi.org/10.1016/j.fss.2008.12.007
Among the possibilistic indicators, the mean value and the variance play a central role. The
elaboration of the expected utility theory (= EU theory), in particular the probabilistic risk theory
[24] is based on them. The definition and the study of the notions of mean value and variance in
a possibilistic context have been tackled by several authors. One of the first contributions in this
direction was the introduction by Dubois and Prade [12] of the interval-valued expectation of a
fuzzy number. In [A14] Carlsson and Fullér have defined the mean value E(A) of a fuzzy number
A and in [A9] Fullér and Majlender have defined the weighted possibilistic mean Ef (A) of A.
At the same time with the mean value, in these papers, the corresponding notion of possibilistic
variance has been introduced: Var(A) in [A14] and V arf (A) in [A9]. These indicators of fuzzy
numbers have a good mathematical theory, which led to their application in multicriterial decision
making problems, finance theory, strategic investment planning, etc. (see [4,21]). (page 2609)
A14-c285 Wei Chen, Weighted portfolio selection models based on possibility theory, FUZZY INFORMATION
AND ENGINEERING, 1(2009), pp. 115-127. 2009
http://dx.doi.org/10.1007/s12543-009-0010-4
Tanaka and Guo [13,14] proposed two kinds of portfolio selection models based on fuzzy probabilities and exponential possibility distributions, respectively. Carlsson and Fullér [A14] introduced the notions of lower and upper possibilistic mean values of a fuzzy number, then proposed
a possibilistic approach to selecting portfolios with highest utility score in [16].
..
.
In this paper, we will discuss a portfolio selection problem with bounded constraint based on the
possibilistic theory. The rest of the paper is organized as follows. Some properties as in probability
theory based on the Fullér’s and Zhang’s notations are discussed in Section 2. In Section 3,
two weighted possibilistic portfolio models with bounded constraint are presented based on the
weighted lower and upper possibilistic means and variances. (page 116)
A14-c284 Emmanuel Valvis, A new linear ordering of fuzzy numbers on subsets of F(R), FUZZY OPTIMIZATION AND DECISION MAKING, 8(2009), pp. 141-163. 2009
http://dx.doi.org/10.1007/s10700-009-9057-2
Thus the points of supp(A) and supp(B) which fulfill the requirements of XFO definition, carry
the higher possibility values and so are the most important of these sets. These elements belong
to the upper α-cuts. The concept of giving less importance to the lower α-cuts of fuzzy numbers
motivates not only this study, but has driven the fuzzy order introduced by Goetschel and Voxman
(1986). In addition Carlsson and Fullér (2001) in their paper were fully inspired by this concept.
In any case, these studies support the basis of XFO method. (page 152)
A14-c283 Weidong Xu, Chongfeng Wu, Weijun Xu, Hongyi Li, A jump-diffusion model for option pricing
under fuzzy environments, INSURANCE: MATHEMATICS AND ECONOMICS, 44(2009), pp. 337-344.
2009
http://dx.doi.org/10.1016/j.insmatheco.2008.09.003
The development of fuzzy random variables enables the joint effort of randomness and fuzzy set
theory to better model imprecision. Dubois and Prade (1987, 1988) introduced the mean value of a
fuzzy number as a closed interval, bounded by the expectations calculated from its upper and lower
distribution functions. Carlsson and Fullér (2001) and Fullér and Majlender (2003) introduced the
possibilistic and weighted possibilistic mean values of a fuzzy number, respectively. (page 338)
A14-c182 Qian Wang, Keith Hipel, and Marc Kilgour, Fuzzy Real Options in Brownfield Redevelopment Evaluation, JOURNAL OF APPLIED MATHEMATICS AND DECISION SCIENCES, Volume 2009(2009),
Article ID 817137, 19 pages. 2009
167
http://dx.doi.org/10.1155/2009/817137
A14-c281 S. Saati; M.Memariani, SBM Model with Fuzzy Input-output Levels in DEA, AUSTRALIAN JOURNAL OF BASIC AND APPLIED SCIENCES, 3(2009), pp. 352-357. 2009
http://www.insinet.net/ajbas/2009/352-357.pdf
A14-c280 T. Chen, J.-L. Zhang, S. Liu, Assessment of information technology investment risk and value based
on real options, Xitong Gongcheng Lilun yu Shijian/System Engineering Theory and Practice, Volume 29,
Issue 2, 2009, pp. 30-37. 2009
A14-c279 Y. Yoshida, An estimation model of value-at-risk portfolio under uncertainty, FUZZY SETS AND
SYSTEMS, 160(2009), Issue 22, pp. 3250-3262. 2009
http://dx.doi.org/10.1016/j.fss.2009.02.007
We can find other approaches in Carlsson and Fullér [A14], Feng et al. [11], Dubois et al. [8] and
Couso et al. [5] in which they discuss the variance of fuzzy numbers by possibility theory, and we
may refer to Dubois and Prade [9], Campos and Munoz [3], Gonzlez [15], Campos and Gonzalez
[2] and Delgado et al. [6,7] for the pessimistic degree in decision making.
A14-c278 Wei-Guo Zhang and Wei-Lin Xiao, On weighted lower and upper possibilistic means and variances of fuzzy numbers and its application in decision, KNOWLEDGE AND INFORMATION SYSTEMS,
18(2009), pp. 311-330. 2009
http://dx.doi.org/10.1007/s10115-008-0133-7
Carlsson and Fullér [A14] introduced the notions of lower and upper possibilistic mean values of
a fuzzy number. On the basis of this, Zhang and Nie [33] presented the notions of lower and upper
possibilistic variances and covariances of fuzzy numbers. As a natural extension of [3], Fullér and
Majlender [A9] proposed a weighted function measuring the importance of γ-level sets of fuzzy
numbers and defined the weighted lower and upper possibilistic mean values of fuzzy numbers.
Liu [15] further extended the interval-valued weighted possibilistic mean of a fuzzy number to a
general weighted function without the monotonic increasing assumption. (page 312)
A14-c277 A. Saeidifar, E. Pasha, The possibilistic moments of fuzzy numbers and their applications, JOURNAL
OF COMPUTATIONAL AND APPLIED MATHEMATICS, 223(2009), pp. 1028-1042. 2009
http://dx.doi.org/10.1016/j.cam.2008.03.045
In this paper, we have used a defuzzification method to find the possibilistic moments and partial
possibilistic moments of a fuzzy number, and this method is not mentioned in the previous literature. In other words, alternative variance that has been introduced by Carlsson and Fullér [A14]
is extended to the weighted possibilistic moments of fuzzy numbers, and this definition of moments is consist with the extension principle of Zadeh and the well-know definition of moments
in probability theory. (page 1036)
A14-c276 Konstantinos A. Chrysas, Basil K. Papadopoulos, On theoretical pricing of options with fuzzy estimators, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 223 (2009), pp. 552-566.
2009
http://dx.doi.org/10.1016/j.cam.2007.12.006
In this paper we use the fuzzy estimators based on confidence intervals introduced by Papadopoulos and Sfiris in [12] in order to estimate the volatility of stock returns having sample data (historical volatility) and also a symmetric triangular fuzzy number in order to model the uncertainty of
the stock price in this model. Furthermore we apply a method proposed by Thiagarajah, Appadoo,
Thavaneswaran [15], which models the uncertainty of the characteristics such as stock price and
volatility using adaptive fuzzy numbers and replaces the fuzzy stock price and the fuzzy volatility
by the possibilistic mean value (see Carlsson, Fullér [A14]) in the fuzzy Black-Scholes formula.
(page 553)
A14-c275 A. Thavaneswaran, S.S. Appadoo, A. Paseka, Weighted possibilistic moments of fuzzy numbers
with applications to GARCH modeling and option pricing, MATHEMATICAL AND COMPUTER MODELLING, 9(2009) 352-368. 2009
http://dx.doi.org/10.1016/j.mcm.2008.07.035
168
Carlsson and Fullér [C. Carlsson, R. Fullér, On possibilistic mean value and variance of fuzzy
numbers, Fuzzy Sets and Systems 122 (2001) 315-326] have introduced possibilistic mean, variance and covariance of fuzzy numbers and Fullér and Majlender [R. Fullér, P. Majlender, On
weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003)
363-374] have introduced the notion of crisp weighted possibilistic moments of fuzzy numbers.
Recently, Thavaneswaran et al. [A. Thavaneswaran, K. Thiagarajah, S.S. Appadoo, Fuzzy coefficient volatility (FCV) models with applications, Mathematical and Computer Modelling 45 (2007)
777-786] have defined non-centered n-th order possibilistic moments of fuzzy numbers. In this
paper, we extend these results to centered moments and find the kurtosis for a class of FCA (Fuzzy
Coefficient Autoregressive) and FCV (Fuzzy Coefficient Volatility) models. We also demonstrate
the superiority of the fuzzy forecasts over the minimum square error forecast through a numerical
example. Finally, we provide a description of option price specification errors using the fuzzy
weighted possibilistic option valuation model. (page 352)
A14-c274 Wei-Guo Zhang, Wei-Lin Xiao, Ying-Luo Wang, A fuzzy portfolio selection method based on possibilistic mean and variance, SOFT COMPUTING, 13(2009), pp. 627-633. 2009
http://dx.doi.org/10.1007/s00500-008-0335-7
Zhang and Wang (2005), Zhang (2007) and Zhang et al. (2007) discussed the portfolio selection
problem based on the lower, upper and crisp possibilistic means and possibilistic variances introduced by Carlsson and Fullér (2001), Zhang and Nie (2003). In this paper, we obtain a new
possibilistic means-variance model for portfolio selection to replace Markowitz’s mean-variance
model when the returns of assets are LR-type fuzzy numbers. In particular, it can be transformed
to a linear programming problem when the returns of assets are symmetric LR-type fuzzy numbers
with center.
..
.
The following theorem was showed by Carlsson and Fullér (2001).
Theorem 1 Let λ, µ ∈ R and let A and B be fuzzy numbers. Then
Var(λA + µB) = λ2 Var(A) + µ2 Var(B) + 2|λµ|Cov(A, B)
where the addition and multiplication by a scalar of fuzzy numbers is defined by the sup-min
extension principle (Zadeh 1965). (page 628)
A14-c273 Wei-Guo Zhang, Xi-Li Zhang, Wei-Lin Xiao, Portfolio selection under possibilistic mean-variance
utility and a SMO algorithm, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 197(2009), pp.
693-700. 2009
http://dx.doi.org/10.1016/j.ejor.2008.07.011
A14-c277 Oshmita Dey, Debjani Chakraborty, Fuzzy periodic review system with fuzzy random variable demand, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 198(2009), pp. 113-120. 2009
http://dx.doi.org/10.1016/j.ejor.2008.07.043
2008
A14-c274 Efendi N Nasibov, Sinem Peker, On the nearest parametric approximation of a fuzzy number, FUZZY
SETS AND SYSTEMS 159(2008), issue 11, pp. 1365-1375. 2008
http://dx.doi.org/10.1016/j.fss.2007.08.005
Considering this problem, some researchers have proposed methods dealing with several kinds of
the nearest fuzzy approximations. For instance, Carlsson and Fuller introduced interval-valued
possibilistic mean [A124], and Chanas gave an interval approximation of a fuzzy number [4], and
Abbasbandy and Asady presented an approach of the nearest trapezoidal fuzzy number to general
fuzzy number [2]. (page 1365)
A14-c273 Y. Yoshida, Perception-Based Estimations of Fuzzy Random Variables: Linearity and Convexity,
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE BASED SYSTEMS, 16(2008), SUPP/1, pp. 71-87. 2008
http://dx.doi.org/10.1142/S021848850800525X
169
Finally we have proposed an approach to analyze convex/concave functions by a decomposition
with monotone functions, and we have obtained some results. We can also find different approaches for the variance in Carlsson and Fullér, [1] Feng et al., [3] Körner [4] and Yoshida [15].
(page 86)
A14-c272 Y.-B. Gong, Method for fuzzy multi-attribute decision making with preference on alternatives and
partial weights information, Kongzhi yu Juece/Control and Decision, 23 (2008), pp. 507-510. 2008
A14-c271 Malcolm J. Beynon, Max Munday, Considering the effects of imprecision and uncertainty in ecological footprint estimation: An approach in a fuzzy environment, ECOLOGICAL ECONOMICS, 67(2008),
pp. 373-383. 2008
http://dx.doi.org/10.1016/j.ecolecon.2008.07.005
Associated with the presented fuzzy sector Ecological Footprint MFs are their respective moments.
The notion of moments, such as mean and variance, is regularly considered in the more well
known stochastic input-output models (see West, 1986; Kop Jansen, 1994). Here, in the fuzzy
environment, these moments are viewed through the use of possibility theory (see Dubois, 2006),
and are subsequently termed possibilistic mean and variance (see Carlsson and Fullér (2001) and
Appendix A), see Fig. 3. (page 379)
A14-c270 Honghai Liu, David J Brown, George M Coghill, Fuzzy Qualitative Robot Kinematics, IEEE TRANSACTIONS ON FUZZY SYSTEMS 16(2008) pp. 808-822. 2008
http://dx.doi.org/10.1109/TFUZZ.2007.905922
A14-c269 Xiaoxia Huang, Mean-semivariance models for fuzzy portfolio selection, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol. 217, pp. 1-8. 2008
http://dx.doi.org/10.1016/j.cam.2007.06.009
A14-c268 S. S. Appadoo, S. K. Bhatt, C. R. Bector, Application of possibility theory to investment decisions,
FUZZY OPTIMIZATION AND DECISION MAKING, vol. 7, pp. 35-57. 2008
http://dx.doi.org/10.1007/s10700-007-9023-9
Carlsson and Fullér (2001, Fuzzy Sets and Systems, 122, 315-326) introduced the concept of
possibilistic mean, variance and covariance of fuzzy numbers. In this paper, we extend some of
these results to a nonlinear type of fuzzy numbers called adaptive fuzzy numbers (see Bodjanova
(2005, Information Science, 172, 73-89) for detail). (page 35)
In the next section we discuss, on the line of Carlsson and Fullér (2001) possibilistic mean, possibilistic variance and possibilistic covariance of the fuzzy numbers considered in this paper. We
also discuss some theorems along with their proofs. (page 38)
As in Carlsson and Fullér (2001), crisp possibilistic mean E(A) and possibilistic variance Var(A)
of a fuzzy number A, defined by their γ -level sets
Z
E(A) =
1
(a1 (γ) + a2 (γ))γ dγ
0
Carlsson and Fullér (2001) also define the crisp lower possibilistic mean value of a fuzzy number
EL (A) and crisp upper possibilistic mean value ER (A) of a fuzzy number as follows.
1
Z
EL (A) = 2
a1 (γ)γ dγ
0
Z
ER (A) = 2
1
a2 (γ)γ dγ
0
(page 39)
Carlsson and Fullér (2001) defined the variance of a fuzzy number A as the expected value of the
squared deviations between the arithmetic mean and the endpoints of its level sets. (page 40)
170
A14-c267 Michele Lalla; Gisella Facchinetti; Giovanni Mastroleo, Vagueness evaluation of the crisp output in
a fuzzy inference system, FUZZY SETS AND SYSTEMS, 159(2008) 3297-3312. 2008
http://dx.doi.org/10.1016/j.fss.2008.03.002
In many applications, the fuzzy set theory operates through a fuzzy inference system (FIS), which
is the key model enabling the description and functioning of a structure, a process or a real world
phenomenon. Its output is a fuzzy number. Measures summarizing the vagueness of a fuzzy
number, such as mean and variance, have been developed in the paradigm of the fuzzy set theory,
although déned consistently with the dénition of the corresponding concepts in probability theory
[A14,6,10,14]. (page 3297)
A14-c266 Cong GD, Zhang JL, Chen T, Lai KK, A variable precision fuzzy rough group decision-making model
for IT offshore outsourcing risk evaluation, JOURNAL OF GLOBAL INFORMATION MANAGEMENT,
16: (2), pp. 18-34. 2008
A14-c265 T. Allahviranloo; F. Hosseinzadeh Lotfi; M. Kh. Kiasary; N. A. Kiani; L. Alizadeh, Solving Fully
Fuzzy Linear Programming Problem by the Ranking Function, APPLIED MATHEMATICAL SCIENCES,
Vol. 2, no. 1, pp. 19-32. 2008
http://www.m-hikari.com/ams/ams-password-2008/ams-password1-4-2008/lotfiAMS1-4-2008-2.pdf
A14-c264 Xiaoxia Huang , Risk curve and fuzzy portfolio selection, COMPUTERS AND MATHEMATICS
WITH APPLICATIONS, 55(2008) 1102-1112. 2008
http://dx.doi.org/10.1016/j.camwa.2007.06.019
A14-c263 M. Soleimani-damaneh, Fuzzy upper bounds and their applications, CHAOS, SOLITONS AND
FRACTALS, 36 (2), pp. 217-225. 2008
http://dx.doi.org/10.1016/j.chaos.2006.06.042
Now, we extend the mean value concept, introduced by Carlsson and Fullér [A14], to a weighted
crisp possibilistic mean value, using the reducing function, as follows: (page 218)
A14-c262 M.H.F. Zarandi, M. Pourakbar, I.B. Turksen, A Fuzzy agent-based model for reduction of bullwhip
effect in supply chain systems, EXPERT SYSTEMS WITH APPLICATIONS, 34 (3), pp. 1680-1691. 2008
http://dx.doi.org/10.1016/j.eswa.2007.01.031
A14-c261 HOU Shi-wang; TONG Shu-rong, The Study of Control Chart for Fuzzy Process Quality Control
Based on Fuzzy Number, JOURNAL OF ZHENGZHOU UNIVERSITY: ENGINEERING SCIENCES,
29(2008), number 1, pp. 39-43 (in Chinese). 2008
http://www.cqvip.com/qk/95571b/2008001/26834315.html
A14-c260 Chen Jie, Liu Qiu-hua, Research into Application of Fuzzy Real Option Theory to Power Project
Evaluation, JOURNAL OF NANJING INSTITUTE OF TECHNOLOGY: NATURAL SCIENCE EDITION, 6(2008), number 3, pp. 50-53 (in Chinese). 2008
http://www.cqvip.com/qk/87122X/200803/28854092.html
A14-c259 Kongxiang Li, Fuzzy Real Option Valuation Equity, STATISTICS AND DECISION, 22(2008), pp.
134-136 (in Chinese). 2008
http://www.cqvip.com/qk/95927x/2008022/28806177.html
A14-c258 GONG Yan-bing, CHEN Sen-fa, On Priority Method of L-L Type Fuzzy Number Complementary
Judgment Matrix, FUZZY SYSTEMS AND MATHEMATICS, 22(2008), number 2, pp. 136-141. 2008
http://en.cnki.com.cn/Article_en/CJFDTotal-MUTE200802025.htm
A14-c257 DING Si-bo; HUANG Wei-lai; ZHANG Zi-gang, Real Option Pricing Method Based on Cloud,
SYSTEMS ENGINEERING, 26(2008), number 10, pp. 73-76 (in Chinese). 2008
http://www.cqvip.com/qk/93285x/2008010/29012808.html
A14-c256 LIU Ya-zheng; HUANG Zhu-lin, The synthesis theory of the Geske theory and the fuzzy number used
in the venture investment project, TECHNOECONOMICS & MANAGEMENT RESEARCH, 2(2008), pp.
3-5 (in Chinese). 2008
http://www.cqvip.com/qk/95695X/200802/26843905.html
171
A14-c255 Shao-wide, Group Selection Model of a Kind of Portfolio, JOURNAL OF SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY: NATURAL SCIENCE, 27(2008), number 6, pp. 102-105 (in
Chinese). 2008
http://www.cqvip.com/qk/96385a/2008006/29185479.html
A14-c254 FANG Yong; SUN Shao-rong, Behavioral Portfolio Optimization Model Based on Multiple Attribute
Fuzzy Decision-making, COMMERCIAL RESEARCH, 5(2008), number 5, pp. 11-15 (in Chinese). 2008
http://www.cqvip.com/qk/96318X/200805/27128414.html
A14-c253 Wang Jin; Zhang Ting, Evaluation of Power Supply Utility Service Process Based on Fuzzy Entropy,
MODERN ELECTRIC POWER, 25(2008), number 3, pp. (in Chinese). 2008
http://d.wanfangdata.com.cn/Periodical_xddl200803020.aspx
2007
A14-c250 Juan G Lazo Lazo, Marley Maria, B R Vellasco, Marco Aurelio, C Pacheco, Marco Antonio G Dias,
Real Options Value by Monte Carlo Simulation and Fuzzy Numbers, INTERNATIONAL JOURNAL OF
BUSINESS, 12(2007), number 2, pp. 181-189. 2007
http://law-journals-books.vlex.com/vid/monte-carlo-simulation-fuzzy-numbers-63870619
To determine the bound of optimal exercise (or threshold curve), the algorithm of Grant, Vora and
Weeks (1997) was adapted to work with fuzzy numbers (Lazo et al. 2004). After the construction
of the threshold curve, the proposed methodology to makes simulations for the oil price from the
initial price, the option value, will be the mean fuzzy (Gao 1999; Carlsson and Fullér 2001) of all
the values that reach or surpass the threshold curve in the simulation, brought to the present value.
(page 184)
A14-c249 Jiao Hong; Jin Feng, International Contract Project Fuzzy Real Option Evaluation, TECHNOECONOMICS & MANAGEMENT RESEARCH, 3(2007), pp. 38-39 (in Chinese). 2007
http://d.wanfangdata.com.cn/Periodical_jsjjyglyj200703014.aspx
A14-c248 Zhang Wanjun; Zhang Zi-jian, Fuzzy environment R&D Projects Real Option Valuation Method,
SCIENCE AND TECHNOLOGY MANAGEMENT RESEARCH, 27(2007), number 12, pp. 116-118 (in
Chinese). 2007
http://www.cqvip.com/qk/96013x/2007012/26363143.html
A14-c247 XUE Li-min; YUE Wei, The optional model of portfolio investment with fuzzy-coefficient, BASIC
SCIENCES JOURNAL OF TEXTILE UNIVERSITIES, 20(2007), number 2, pp. 133-136 (in Chinese).
2007
http://www.cqvip.com/qk/98150a/200702/24929584.html
A14-c246 Fang Yong, Optimization Model of Behavioral Portfolio Based on Fuzzy Probability, JOURNAL OF
SHANGHAI FINANCE UNIVERSITY, 4(2007), pp. 39-44 (in Chinese). 2007
http://d.wanfangdata.com.cn/Periodical_shjrxyxb200704006.aspx
A14-c245 José D Bermúdez, José Vicente Segura, Enriqueta Vercher González, Modelos borrosos de optimización para la selección de carteras basados en intervalos de medias, Cuadernos del CIMBAGE, vol. 9,
pp. 27-36. 2007
A14-c244 Pankaj Dutta, Debjani Chakraborty, A.R. Roy, An inventory model for single-period products with reordering opportunities under fuzzy demand, COMPUTERS & MATHEMATICS WITH APPLICATIONS,
Volume 53, Issue 10, May 2007, pp. 1502-1517. 2007
http://dx.doi.org/0.1016/j.camwa.2006.04.029
As the demand is linguistic in nature and the optimal order quantity in the second slot depends
upon the leftover items from slot 1, the decision variable during the second slot is clearly a fuzzy
quantity. To determine the optimal order quantity that maximizes the profit function we use the
possibilistic mean value of a fuzzy number to rank fuzzy numbers [A14]. (page 1503)
172
A14-c243 Jin-Hsien Wang; Jongyun Hao, Fuzzy Linguistic PERT, IEEE TRANSACTIONS ON FUZZY SYSTEMS, Volume 15, Issue 2, April 2007 , pp. 133-144. 2007
http://dx.doi.org/10.1109/TFUZZ.2006.879975
A14-c242 E. N. Nasibov and A. Mert, On Methods of Defuzzification of Parametrically Represented Fuzzy
Numbers, AUTOMATIC CONTROL AND COMPUTER SCIENCES, 2007, Vol. 41, No. 5, pp. 265-273.
2007
http://dx.doi.org/10.3103/S0146411607050057
A14-c241 Malcolm James Beynon; Max Munday, An Aggregated Regional Economic Input-Output Analysis
within a Fuzzy Environment, SPATIAL ECONOMIC ANALYSIS, 2(3) pp. 281-296, NOVEMBER 2007
http://dx.doi.org/10.1080/17421770701549787
A14-c240 D. Wu, J.M. Mendel, Uncertainty measures for interval type-2 fuzzy sets, INFORMATION SCIENCES, 177 (23), pp. 5378-5393. 2007
http://dx.doi.org/10.1016/j.ins.2007.07.012
A14-c239 Zhang, W.-G., Wang, Y.-L., Notes on possibilistic variances of fuzzy numbers, APPLIED MATHEMATICS LETTERS, 20 (11), pp. 1167-1173. 2007
http://dx.doi.org/10.1016/j.aml.2007.03.002
The definitions of two crisp possibilistic variances of a fuzzy number A, Var(A) and Var’(A),
were introduced by Carlsson and Fullér. In this work, we show that many properties of variance
in probability theory are preserved by Var’(A). We also get the important relationships between
Var(A) and Var’(A).
..
.
Dubois and Prade [2] defined an interval-valued expectation of fuzzy numbers, viewing them as
consonant random sets. They showed that this expectation remains additive in the sense of addition of fuzzy numbers. Carlsson and Fullér [A14] introduced the notions of lower and upper
possibilistic means, the interval-valued possibilistic mean, crisp possibilistic mean and crisp possibilistic variances of fuzzy numbers, viewing them as possibility distributions. (page 1167)
Furthermore, the following conclusions were shown in [A14].
Theorem 2.1 Let λ, µ ∈ R and let A and B be fuzzy numbers. Then
Var(λA + µB) = λ2 Var(A) + µ2 Var(B) + 2|λµ|Cov(A, B)
where the addition and multiplication by a scalar of fuzzy numbers is defined by the sup-min
extension principle [4].
In the next section, we show some properties of Var’(A) that are different from those of [A12].
We also investigate the relationship between Var’(A) and Var(A). (page 1169)
A14-c238 Zhang, W.-G., Wang, Y.-L. A comparative analysis of possibilistic variances and covariances of fuzzy
numbers, FUNDAMENTA INFORMATICAE, 79 (1-2), pp. 257-263. 2007
A14-c237 Supian Sudradjat, The Weighted Possibilistic Mean Variance and Covariance of Fuzzy Numbers,
JOURNAL OF APPLIED QUANTITATIVE METHODS, Volume 2, Issue 3, pp. 349-356, September 30,
2007
A14-c236 CHEN Wei; ZHANG Run-tong; YANG Ling, A Fuzzy Portfolio Selection Decision Methodology
under Borrowing Constraint, JOURNAL OF BEIJING JIAOTONG UNIVERSITY SOCIAL SCIENCES
EDITION, 6(2007), number 1, pp. 67-70 (in Chinese). 2007
http://www.cqvip.com/qk/87426a/2007001/24080096.html
A14-c235 Zhang, W.-G., Wang, Y.-L., Chen, Z.-P., Nie, Z.-K., Possibilistic mean-variance models and efficient
frontiers for portfolio selection problem, INFORMATION SCIENCES, 177 (13), pp. 2787-2801 2007
http://dx.doi.org/10.1016/j.ins.2007.01.030
Dubois and Prade [6] déned an interval-valued expectation of fuzzy numbers, Carlsson and Fullér
[A14] defined the lower and upper possibilistic means of a fuzzy number A (page 2788)
173
A14-c234 Xue, L.-M., Yue, W., The optional model of portfolio investment with fuzzy-coefficient, BASIC
SCIENCES JOURNAL OF TEXTILE UNIVERSITIES, 20 (2), pp. 133-136. 2007
A14-c233 Yuan-Horng Lin, The Methodology Fuzzy Theory in Social Science Research, JOURNAL OF QUANTITATIVE RESEARCH, vol 2007, pp. 53-84 (in Chinese). 2007
A14-c232 Dutta, P., Chakraborty, D., Roy, A.R., Continuous review inventory model in mixed fuzzy and
stochastic environment, APPLIED MATHEMATICS AND COMPUTATION, 188 (1), pp. 970-980. 2007
http://dx.doi.org/10.1016/j.amc.2006.10.052
The aim is to find the optimal order quantity along with the reorder point so that the associated
total cost is minimum. Using possibilistic mean value of a fuzzy number [A14] the fuzzy expected
cost has been minimized here. (page 971)
Definition 2. For a given fuzzy number Ã, the interval valued possibilistic mean is defined as
M (Ã) = [M∗ (Ã), M ∗ (Ã)], where M∗ (Ã) and M ∗ (Ã) are the lower and upper possibilistic mean
values of à [A14] and are respectively defined by
R1
M∗ (Ã) =
0
αA−
α dα
R1
0
α dα
R1
,
∗
M (Ã) =
αA+
α dα
R1
α dα
0
0
(page 971)
A14-c231 Thavaneswaran A, Thiagarajah K, Appadoo SS, Fuzzy coefficient volatility (FCV) models with applications, MATHEMATICAL AND COMPUTER MODELLING, 45 (7-8): 777-786 APR 2007
http://dx.doi.org/10.1016/j.mcm.2006.07.019
Recently, Carlsson and Fullér [C. Carlsson, R. Fullér, On possibilistic mean value and variance of
fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315-326] have introduced possibilistic mean,
variance and covariance of fuzzy numbers and Fullér and Majlender [R. Fullér, P. Majlender, On
weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003)
363-374] have introduced the notion of crisp weighted possibilistic moments of fuzzy numbers.
In this paper, we propose a class of FCV (Fuzzy Coefficient Volatility) models and study the
moment properties. The method used here is very similar to the method used in Appadoo et
al. [S.S. Appadoo, M. Ghahramani, A. Thavaneswaran, Moment properties of some time series
models, Math. Sci. 30 (1) (2005) 50-63]. The proposed models incorporate fuzziness, subjectivity,
arbitrariness and uncertainty observed in most financial time series. The usual forecasting method
does not incorporate parameter variability. Fuzzy numbers are used to model the parameters to
incorporate parameter variability. (page 777)
Recent studies has shown that a fuzzy random variable can be considered as a measurable mapping
from a probability space to a set of fuzzy variables. Fuzzy time series models provide a new avenue
to deal subjectivity observed in most financial time series models. We summarize the preliminaries
in Section 1. In Section 2, RCA and GARCH models are given and the corresponding FCV models
are introduced. Following Carlsson and Fuller [B1, A8], higher order moments of fuzzy numbers
are defined. We also derive the moments and possibilistic kurtosis of the proposed FCV models.
Section 3 concludes with an illustrative numerical example. (page 778)
Following Carlsson and Fullér [A14], crisp possibilistic mean and possibilistic variance of continuous possibility distributions are given below.
Z
M̄ (A) =
1
(a1 (γ) + a2 (γ))γ dγ
0
174
whereM̄ (A) is the level-weighted average of the arithmetic means of all -level sets.
2 !
Z 1
a1 (γ) + a2 (γ)
Var(A) =
Pos[A ≤ a1 (γ)]
− a1 (γ)
dγ
2
0
2 !
Z 1
a1 (γ) + a2 (γ)
Pos[A ≥ a2 (γ)]
+
− a2 (γ)
dγ
2
0
Z
2
1 1
γ a2 (γ) − a1 (γ) dγ.
=
2 0
Carlsson and Fullér [A14] defined the variance of a fuzzy number A as the expected value of
the squared deviations between the arithmetic mean and the endpoints of its level sets. (pages
778-779)
A14-c230 Vercher E, Bermudez JD, Segura JV Fuzzy portfolio optimization under downside risk measures,
FUZZY SETS AND SYSTEMS, 158 (7): 769-782 APR 1 2007
http://dx.doi.org/10.1016/j.fss.2006.10.026
Alternatively, Carlsson and Fullér [A14] define an interval-valued possibilistic mean of fuzzy
numbers, their definition being consistent with the extension principle and also based on the set of
level-cuts. (page 770)
Since the power reference functions are continuous and strictly decreasing, it follows that the
interval-valued possibilistic mean is a subset of the interval-valued probabilistic mean [A14].
(page 772)
A14-c229 Thiagarajah, K., Appadoo, S.S., Thavaneswaran, A. Option valuation model with adaptive fuzzy
numbers, COMPUTERS AND MATHEMATICS WITH APPLICATIONS, 53 (5), pp. 831-841. 2007
http://dx.doi.org/10.1016/j.camwa.2007.01.011
A14-c228 D.H. Hong and K.T. Kim, A note on the maximum entropy weighting function problem, JOURNAL
OF APPLIED MATHEMATICS AND COMPUTING, 23(2007), No. 1-2, pp. 547-552. 2007
http://www.mathnet.or.kr/mathnet/thesis_file/DHHong0613F.pdf
2006
A14-c227 Helical Wan-Sheng Tang, Application of Fuzzy Real Option Theory to the Venture Investment Project
Decision, JOURNAL OF CHINA UNIVERSITY OF GEOSCIENCES (SOCIAL SCIENCES EDITION),
6(2006), number 1, pp. 60-62 (in Chinese). 2006
http://www.cqvip.com/qk/85217x/2006001/21029273.html
A14-c226 Guohua Chen, Shou Chen, Yong Fang, Shouyang Wang, Rate of return based on fuzzy portfolio
model, MATHEMATICS IN ECONOMICS, 23(2006), number 1, pp. 19-25 (in Chinese). 2006
http://www.cqvip.com/qk/91594x/2006001/22043049.html
A14-c225 Helical Wan-Sheng Tang, The Application of Fuzzy Real Option Theory in the Venture Investment
Value Evaluation, JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY (SOCIAL SCIENCES EDITION), 8(2006), number 1, pp. 49-51 (in Chinese). 2006
http://www.cqvip.com/qk/84427X/200601/21274359.html
A14-c224 K. Thiagarajah; A. Thavaneswaran, Fuzzy random-coefficient volatility models with financial applications, THE JOURNAL OF RISK FINANCE, Vol. 7 Issue: 5, pp. 503-524. 2006
http://dx.doi.org/10.1108/15265940610712669
A14-c223 Guohua Chen, Shou Chen, Yong Fang, Shouyang Wang, A Possibilistic Mean VaR Model for Portfolio Selection, ADVANCED MODELING AND OPTIMIZATION, Volume 8, Number 1, pp. 99-107.
2006
http://www.ici.ro/camo/journal/vol8/v8a8.pdf
175
Carlsson et al [A14] introduced the notation of crisp possibilitic mean value of continuous possibility distributions, which are consistent with the extension principle. (page 104)
A14-c222 Fang Y, Lai KK, Wang SY, Portfolio rebalancing model with transaction costs based on fuzzy decision
theory, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 175 (2): 879-893 DEC 1 2006
http://dx.doi.org/10.1016/j.ejor.2005.05.020
Carlsson and Fullér [A14] introduced the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions, which are consistent with the extension
principle. The crisp possibilistic mean value of A is
Z 1
γ(a1 (γ) + a2 (γ)) dγ
EA) =
0
(page 883)
A14-c221 Yoshida Y, Yasuda M, Nakagami J -i, Kurano M, A new evaluation of mean value for fuzzy numbers
and its application to American put option under uncertainty, FUZZY SETS AND SYSTEMS 157 (19):
2614-2626 OCT 1 2006
http://dx.doi.org/10.1016/j.fss.2003.11.022
A14-c220 Dubois D, Possibility theory and statistical reasoning, COMPUTATIONAL STATISTICS & DATA
ANALYSIS 51 (1): 47-69 NOV 1 2006
http://dx.doi.org/10.1016/j.csda.2006.04.015
Fullér and colleagues (Carlsson and Fullér, 2001; Fullér and Majlender, 2003) consider introducing a weighting function on [0, 1] in order to account for unequal importance of cuts when
computing upper and lower expectations.
..
.
The notion of variance has been extended to fuzzy random variables (Koerner, 1997), but little
work exists on the variance of a fuzzy interval. Fullér and colleagues (Carlsson and Fullér, 2001;
Fullér and Majlender, 2003) propose a definition as follows:
Z 1
sup Mγ − inf Mγ 2
V̄ (M ) =
f (γ)dγ
2
0
where f is a weight function. However, appealing this definition may sound, it lacks proper
interpretation in the setting of imprecise probability. In fact, the very idea of a variance of a
possibility distribution is somewhat problematic. A possibility distribution expresses information
incompleteness, and does not so much account for variability. The variance of a constant but
ill-known quantity makes little sense. The amount of incompleteness is then well-reflected by
the area under the possibility distribution, which is a natural characteristics of a fuzzy interval.
Other indices of information already mentioned in Section 4.2 are variants of this simpler index.
Additionally, it is clear that the expression of V̄ (M ) depends upon the area under the possibility
distribution (suffices to let f (λ) = 1). So it is not clear that the above definition qualifies as a
variance: the wider a probability density, the higher the variability of the random variable, but the
wider a fuzzy interval, the more imprecise. However, if the possibility distribution π = µM stands
for subjective knowledge about an ill-known random quantity, then it is interesting to compute the
range V̄ (M ) of variances of probability functions consistent with M , (pages 63-64)
A14-c219 Stefanini L, Sorini L, Guerra ML, Parametric representation of fuzzy numbers and application to
fuzzy calculus, FUZZY SETS AND SYSTEMS, 157(18): 2423-2455 SEP 16 2006
http://dx.doi.org/10.1016/j.fss.2006.02.002
A second example is the interval valued possibilistic mean M (u) and the level-weighted average
u∗GW (see Goetschel and Voxman [25] and Carlsson and Fullér [A14]) given by (page 2436)
A14-c218 Beynon MJ, Munday M, The elucidation of multipliers and their moments in fuzzy closed Leontief
input-output systems, FUZZY SETS AND SYSTEMS 157 (18): 2482-2494 SEP 16 2006
http://dx.doi.org/10.1016/j.fss.2006.02.005
176
A further development demonstrated here is a definition of a number of moments associated with
the fuzzy multipliers. These include mean and standard deviation values originally identified in
non-fuzzy stochastic input-output systems (see [10,15,17]). Their evaluation is a consequence
of the non-linearity of the Leontief inversion (see later). Therefore, mean values of multipliers
will, in general, be different from the observed values. Here, the possibilistic mean value and
variance of fuzzy numbers (multipliers) introduced in [A14] are evaluated, over different levels of
incumbent imprecision (fuzziness). (page 2483)
Motivation for the investigation of the moments of the fuzzy multipliers comes from the work
on stochastic input-output systems [10,15]. The notion of a stochastic input-output system implies that the values for the technical coefficients are evaluated from known distributions. Briefly,
amongst these studies it was found the mean multiplier values were larger than their observed
values (using actual non-fuzzy technical coefficients). Here, for each type of multiplier their possibilistic mean and variance values are found over their respective β domains. The expressions for
these moments were reported in [A14] and are amongst the most recently defined on the general
issue of identifying moments on fuzzy numbers (see also [8]). (page 2489)
A14-c217 Hashemi SM, Modarres M, Nasrabadi E, et al., Fully fuzzified linear programming, solution and
duality, JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 17(3): 253-261 2006
http://iospress.metapress.com/content/0u06cbgmkvqr2pb5/
A14-c216 Facchinetti G, Pacchiarotti N, Evaluations of fuzzy quantities, FUZZY SETS AND SYSTEMS,
157(7): 892-903 APR 1 2006
http://dx.doi.org/10.1016/j.fss.2005.08.003
The basic definition of evaluation we utilize for fuzzy numbers is the weighted average value
(WAV [3,8]), which is very general and depends on two parameters, the real number λ and the
additive measure S. The first one may be connected with an optimistic or pessimistic point of view
of the decision maker; the second one may be regarded as a way for the decision maker to choose
evaluations only into particular subsets of the support, according to his preference. For particular
choices of λ and S, WAV coincides with known comparison indexes (Adamo [1], Carlsson-Fullér
[A14], Facchinetti et al. [10], Fortemps-Roubens [11], Heilpern [13], Yager [20], and a review by
Wang-Kerre [18,19]). (page 893)
A14-c215 Bodjanova S, Median alpha-levels of a fuzzy number, FUZZY SETS AND SYSTEMS, 157(7): 879891 APR 1 2006
http://dx.doi.org/10.1016/j.fss.2005.10.015
A14-c214 Sheen, J.N. Generalized fuzzy numbers comparison by geometric moments, WSEAS Transactions
on Systems, 5(6), pp. 1237-1242. 2006
http://www.wseas.us/e-library/conferences/2006hangzhou/papers/531-135.pdf
A14-c213 Xinwang Liu, On the maximum entropy parameterized interval approximation of fuzzy numbers,
FUZZY SETS AND SYSTEMS, 157(2006), pp. 869-878. 2006
http://dx.doi.org/10.1016/j.fss.2005.09.010
Representing fuzzy numbers by proper intervals is an interesting and important problem. In [1,2],
the level sets are used for ranking fuzzy numbers. The main drawback of the level sets method is
that the level sets may be not continuous [10]. In [5,12,13], the level sets are replaced with expected intervals. Ralescu [17] recently defined the interval approximation of fuzzy number as the
Aumann integral of the set-valued mapping, which is equivalent to the expected interval method.
Chanas [4] and Grzegorzewski [10] analyzed the properties of the expected intervals of fuzzy numbers. Carlsson and Fullér [A14] extended this expectation concept to possibilistic mean. Fullér
and Majlender [A9] further extended these results to the notion of weighted possibilistic mean
with the weighting function method. The purposes of this paper are to extend the fuzzy number
weighting function method introduced in [9] to a general form with the aggregation techniques,
and to propose a parameterized fuzzy number interval approximation method. As a fuzzy number
is determined by the level set intervals with different membership grades, it can be regarded as a
series of intervals with the membership degree as its parameter. (pages 869-870)
177
2005
A14-c212 Xu Weijun; Yin-Feng Xu; Wang Xun; Zhang Weiguo, Fuzzy weighted yield portfolio selection
model, JOURNAL OF SYSTEMS ENGINEERING, 20(2005), number 1, pp. 6-11 (in Chinese). 2005
http://www.cqvip.com/qk/96188x/2005001/15221192.html
A14-c211 G. Wang, C. Wu, C. Zhao, Representation and Operations of Discrete Fuzzy Numbers, SOUTHEAST
ASIAN BULLETIN OF MATHEMATICS, 28(2004), pp. 1003-1010. 2005
http://www.scnu.edu.cn/seam-bulletin/vol29no5/p19.pdf
A14-c210 Yoshida, Y., Yasuda, M., Nakagami, J.-I., Kurano, M. A discrete-time American put option model
with fuzziness of stock prices, FUZZY OPTIMIZATION AND DECISION MAKING, 4 (3), pp. 191-207.
2005
http://dx.doi.org/10.1007/s10700-005-1889-9
A14-c209 Zhihuang Dai and Michael J. Scott, Product Platform Design With Consideration of Uncertainty,
SAE 2005 Transactions Journal of Passenger Cars: Mechanical Systems, vol. 114, pp. 301-309. 2005
A14-c208 Cheng CB, Fuzzy process control: construction of control charts with fuzzy numbers, FUZZY SETS
AND SYSTEMS, 154 (2): 287-303 SEP 1 2005
http://dx.doi.org/10.1016/j.fss.2005.03.002
Carlsson and Fullér [A14] defined the possibilistic variance of a fuzzy number F as (page 291)
In Eq. (4), the mode of the fuzzy number, m, replaces the arithmetic mean of the γ-level set used
in the definition of Carlsson and Fullér [A14]. (page 292)
A14-c207 Ayala G, Leon T, Zapater V, Different averages of a fuzzy set with an application to vessel segmentation, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 13 (3): 384-393 JUN 2005
http://dx.doi.org/10.1109/TFUZZ.2004.839667
A number of authors have studied how to define the average of a fuzzy set, mainly for fuzzy
numbers. Dubois and Prade [8] defined an interval-valued expectation of fuzzy numbers, viewing
them as consonant random sets. Carlsson and Fullér [A14] defined an interval-valued mean of
fuzzy numbers considering them as possibility distributions, a definition which is generalized in
[A9]. (page 384)
2004
A14-c206 Teresa León, Vicente Liern, Paulina Marco, José Vicente Segura, Enriqueta Vercher González, A
downside risk approach for the portfolio selection problem with fuzzy returns, FUZZY ECONOMIC REVIEW, vol. 9, pp. 61-77. 2004
A14-c205 Zhihuang Dai, Michael J. Scott, and Zissimos P. Mourelatos, Propagation of epistemic uncertainty
for design reuse, SAE 2004 Transactions Journal of Materials and Manufacturing, vol. 5, pp. 536-550,
2004.
Dubois & Prade [1987] present a definition of interval- valued expectation of fuzzy numbers,
by viewing them as constant random sets. Based on those principles, Carlsson & Fullér [2001]
proposed the possibilistic mean value (E(A)) and variance (σ 2 (A)) of a fuzzy number.
A14-c204 Hong DH, Kim KT, A note on weighted possibilistic mean, FUZZY SETS AND SYSTEMS, 148
(2): 333-335 DEC 1 2004
http://dx.doi.org/10.1016/j.fss.2004.04.011
A14-c203 Jahanshahloo GR, Soleimani-damaneh M, Nasrabadi E, Measure of efficiency in DEA with fuzzy
input-output levels: a methodology for assessing, ranking and imposing of weights restrictions, APPLIED
MATHEMATICS AND COMPUTATION, 156 (1): 175-187 AUG 25 2004.
http://dx.doi.org/10.1016/j.amc.2003.07.036
178
Carlsson and Fullér [A14] defined possibilistic mean value (M) and variance (Var) of fuzzy number ã as follows:
Z 1
M (ã) =
α(inf[ã]α + sup[ã]α ) dα
0
Var(ã)
1
=
2
Z
1
(inf[ã]α − sup[ã]α )2 dα
0
(page 177)
A14-c202 Gisella Facchinetti, Roberto Ghiselli Ricci, A characterization of a general class of ranking functions
on triangular fuzzy numbers, FUZZY SETS AND SYSTEMS, vol. 146, pp. 297-312. 2004
http://dx.doi.org/10.1016/j.fss.2003.10.023
Further, when we use the Lebesgue measure, corresponding to s(t) = t, we get ρ = σ = 1/2.
Actually, the list of different RFs which reduce to a special case (or generate the same ordering) of CG, not only when applied to (normal) TFNs, but also in more general cases, is very
long: see, for instance, the indexes proposed by Adamo [1], Carlsson-Fullér [A14], ChoobinehLi [7], Delgado- Vila-Voxman [8], Dubois-Prade [11], Facchinetti-Ghiselli Ricci-Muzzioli [12],
Fortemps-Roubens [13], Heilpern [15,16], Liou-Wang [19], Yager [23,24], Yao-Wu [26] and a
review of Wang-Kerre [21,22] for a careful comparison. (page 303)
2003
A14-c201 Eugene Roventa and Tiberiu Spircu, Averaging procedures in defuzzification processes, FUZZY
SETS AND SYSTEMS, 136(2003) 375-385. 2003
http://dx.doi.org/10.1016/S0165-0114(02)00218-X
A14-c200 Gisella Facchinetti, Ranking Functions Induced by Weighted Average of Fuzzy Numbers, FUZZY
OPTIMIZATION AND DECISION MAKING, 1(2002), pp. 313-327. 2002
http://dx.doi.org/10.1023/A:1019692914431
In this paper we present two definitions of possibilistic weighted average of fuzzy numbers, and
by them we introduce two different rankings on the set of real fuzzy numbers. The two methods
are dependent on several parameters. In the first case, the parameter is constant and the results
generalize what Carlsson and Fullér have obtained in (2001) [A14]. In the second case, the parameter is a function, not fixed a priori by the decision maker, but it depends on the position of the
interval on the real axe. In all the two cases we call the parameter degree of risk, which takes into
account of a risk-tendency or aversion of the decision maker.
..
.
Following the idea of Campos and Gonzalez (1989) we start with the introduction of two different
evaluation functions on the set of real intervals, we will call I-evaluation functions. They contain
a parameter we call degree of risk, which takes into account of a risk-tendency or aversion of
the decision maker, that is constant in the first case, a function in the second, and then, using the
definition of a fuzzy numbers by its α-cuts, we introduce two average values (AV) as F-evaluation
functions. Using these two, we obtain several results. One is to generalise the results of Carlsson
and Fullér. They, in a paper of 2001, starting from a particular AV, have introduced the notations of
lower and upper possibilistic mean value and consequently defined the interval-valued possibilistic
mean, crisp possibilistic mean value and crisp variance of a continuous possibility distribution.
(page 313)
Using the previous notations, the next results generalise what Carlsson and Fullér (2001) have
introduced. Their definitions are particular cases in which s(x) = xr with r = 2 and λ = 1/2.
(page 318)
in proceedings and edited volumes
2016
179
A14-c172 S Rajaprakash, R Ponnusamy, Ranking Business Scorecard Factor Using Intuitionistic Fuzzy Analytical Hierarchy Process with Fuzzy Delphi Method in Automobile Sector, In: Rajendra Prasath, Anil Kumar
Vuppala, T. Kathirvalavakumar eds., Mining Intelligence and Knowledge Exploration, Lecture Notes in
Computer Science, vol. 9468/2016, Springer, (ISBN 978-3-319-26831-6) pp. 437-448. 2016
http://dx.doi.org/10.1007/978-3-319-26832-3 41
2015
A14-c171 Ku Muhammad Naim Ku Khalif, Alexander Gegov, Bayesian Logistic Regression using Vectorial
Centroid for Interval Type-2 Fuzzy Sets, In: Proceedings of the 7th International Joint Conference on
Computational Intelligence (IJCCI 2015), SCITEPRESS, (ISBN 978-989-758-157-1) pp. 69-79. 2015
http://dx.doi.org/10.5220/0005614400690079
The concept of possibility mean value for interval fuzzy sets was introduced by Carlsson and Fuller
(2001) where the notations of lower possibilistic and upper possibilistic mean values is defined
the interval-valued possibilistic mean. From probabilistic viewpoint, the possibility mean value of
fuzzy sets can be represented as expected values which is same function as direct defuzzification
method where it doesn’t need type-reduction stage to get the outputs. (page 70)
A14-c170 Jun Cai, Xiaolian Meng, Multi-period portfolio selection model with transaction cost, In: International Conference on Social Science and Higher Education (ICSSHE 2015), Atlantis Press, Advances in
Social Science, Education and Humanities Research, (ISBN 978-94-6252-126-1) pp. 355-360.
http://dx.doi.org/10.2991/icsshe-15.2015.68
A14-c169 I Georgescu, J Kinnunen, Precautionary saving with possibilistic background risk, 16th IEEE International Symposium on Computational Intelligence and Informatics (CINTI), IEEE, 2015. (ISBN 978-14673-8520-6) pp. 165-169. 2015
http://dx.doi.org/10.1109/CINTI.2015.7382903
A14-c168 Jianna Zhao, Yuanyuan Zhao, Research on the Post Evaluation for Thermal Power Construction
Project Based on Entropy Weight Fuzzy Comprehensive Evaluation, Proceedings of the 2015 International
Conference on Computer Science and Intelligent Communication (CSIC 2015), Atlantic Press, [ISBN 97894-62520-84-4], pp. 252-255. 2015
http://dx.doi.org/10.2991/csic-15.2015.60
A14-c167 Mariia Kozlova, Mikael Collan, Pasi Luukka, Comparing Datar-Mathews and fuzzy pay-off approaches to real option valuation, In: Mikael Collan, Pasi Luukka eds., Proceedings of the ROW15 ? Real
Option Workshop, LUT Scientific and Expertise Publications, (ISBN 978-952-265-834-0) pp. 29-34. 2015
The definition and derivation of the fuzzy mean is given in [Carlsson and Fullér]. Practically, the
fuzzy mean of the positive side of the distribution and the success ratio are calculated differently
depending on the position of the distribution with relation to zero. (page 30)
A14-c166 Hai-bin Xie, Trapezoidal approximations by preserving the interval-valued possibilistic mean of
fuzzy numbers with restrictions on support and core, In: Proceedings of the 27th Chinese Control and
Decision Conference (CCDC), (ISBN 978-1-4799-7016-2) pp. 2833-2838. 2015
http://dx.doi.org/10.1109/CCDC.2015.7162410
A14-c165 Marcus Rocha, Lucelia Lima, Helida Santos, Benjamin Bedrega, Fuzzy probability distribution with
VaR constraint for portfolio selection, In: Proceedings of the 16th World Congress of the International
Fuzzy Systems Association (IFSA) and the 9th Conference of the European Society for Fuzzy Logic and
Technology (EUSFLAT), Atlantis Press, (ISBN 978-94-62520-77-6) pp. 1479-1485. 2015
http://dx.doi.org/10.2991/ifsa-eusflat-15.2015.210
Carlsson and Fuller [2] introduced the notations of upper and lower possibilistic mean values,
and introduced the notation of crisp possibilistic mean values and crisp possibilistic variance of
continuous distributions. (page 1479)
A14-c164 Sushil Kumar Bhuiya, Debjani Chakraborty, A Fuzzy Random Periodic Review Inventory Model
Involving Controllable Back-Order Rate and Variable Lead-Time, In: Mathematics and Computing, Proceedings in Mathematics & Statistics, vol. 139, Springer, (ISBN 978-81-322-2451-8), pp. 307-320. 2015
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A14-c163 Luca Anzilli, Gisella Facchinetti, A general fuzzy set representation for decision making, In: Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and the 9th
Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Atlantis Press, (ISBN
978-94-62520-77-6), pp. 857-864. 2015
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A14-c162 A Rubio, J D Bermudez, E Vercher, Comparative analysis of forecasting portfolio returns using Soft
Computing technologies, In: Proceedings of the 16th World Congress of the International Fuzzy Systems
Association (IFSA) and the 9th Conference of the European Society for Fuzzy Logic and Technology
(EUSFLAT), Atlantis Press, (ISBN 978-94-62520-77-6), pp. 617-623. 2015
http://dx.doi.org/10.2991/ifsa-eusflat-15.2015.88
A14-c161 Irina Georgescu, Jani Kinnunen, Ana Maria Lucia-Casademunt, Possibilistic Models of Risk Management, In: Intelligent Techniques in Engineering Management, Intelligent Systems Reference Library,
vol. 87/2015, Springer, (ISBN 978-3-319-17905-6) pp. 21-44. 2015
http://dx.doi.org/10.1007/978-3-319-17906-3_2
A14-c160 Andrea Barbazza, Mikael Collan, Mario Fedrizzi, Pasi Luukka, Consensus Modeling in Multiple
Criteria Multi-expert Real Options-Based Valuation of Patents, In: Intelligent Systems’2014, Proceedings
of the 7th International Conference Intelligent Systems IEEE IS’2014, September 24?26, 2014, Warsaw,
Poland, Volume 1: Mathematical Foundations, Theory, Analyses, Advances in Intelligent Systems and
Computing vol. 322, Springer, (ISBN 978-3-319-11312-8) pp. 269-278. 2015
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2014
A14-c151 Collan Mikael, Fedrizzi Mario, Luukka Pasi, Group possibilistic risk aversion in fuzzy pay-off
method, In: Talasova J, Stoklasa J, Talasek T eds., MATHEMATICAL METHODS IN ECONOMICS
(MME 2014). OLOMOUC: PALACKY UNIV, 2014. 6 p. (ISBN 978-80-244-4209-9) pp. 139-144. 2014
WOS: 000356417900025
A14-c150 S S Appadoo, Y Gajpal, R S Bhatti, A Gaussian Fuzzy Inventory EOQ Model Subject to Inaccuracies In Model Parameters. A Supply Chain Management Application, In: II International Conference on
Business and Management. Mumbai: Academic Research Publishers, 2014. [ISBN 978-0-9895150-3-0],
pp. 7-15. 2014
A14-c149 Leandro Maciel, Fernando Gomide, Rosangela Ballini, Minimum Variance Fuzzy Possibilistic Portfolio, XVII SEMEAD Seminarios em Administracao. Sao Paulo, Brasil, October 29-31, 2014, pp. 1-14,
ISSN: 2177-3866. 2014
http://semead6.tempsite.ws/17semead/resultado/trabalhosPDF/976.pdf
As an extension of fuzzy sets theory, L. Zadeh (Zadeh, 1978) introduced possibilistic theory for
dealing with incomplete information. In Zadehs view, possibilistic distributions were meant to
provide a graded semantics to natural language statements. Some studies have investigated possibilistic theory within the realm of fuzzy sets theory (Dubois & Prade, 1987; Carlsson & Fullér,
2001). (page 2)
A14-c148 M P C Rocha, L M Costa, B R C Bedregal, Fuzzy Laplace Distribution with VaR Applied in Investment Portfolio, Proceedings of the 11th International FLINS Conference, World Scientific, World Scientific
Proceedings Series on Computer Engineering and Information Science, vol. 9/2014, [ISBN 978-981-461996-7], pp. 30-35. 2014
http://dx.doi.org/10.1142/9789814619998 0008
A14-c147 Zhou Jianli, Li Jun, An improved multi-objective particle swarm optimization for constrained portfolio selection model, Proceedings of the 11th International Conference on Service Systems and Service
Management (ICSSSM), [ISBN 978-1-4799-3133-0], pp. 1-5. 2014
http://dx.doi.org/10.1109/ICSSSM.2014.6874155
181
A14-c146 Francisco Campuzano-Bolarin, Josefa Mula, David Peidro, Fuzzy Estimations and System Dynamics
for Improving Manufacturing Orders in VMI Supply Chains in: Supply Chain Management Under Fuzziness, Studies in Fuzziness and Soft Computing, vol. 313/2014, [ISBN 978-3-642-53938-1], pp. 227-241.
2014
http://dx.doi.org/10.1007/978-3-642-53939-8_10
Based on the principles introduced into Dubois and Prade (1987) and the possibilistic interpretation of the ordering proposed by Goetschel and Voxman (1986), Carlsson and Fullér (2001) introduce the notations of lower possibilistic and upper possibilistic mean values, and they define the
interval-valued possibilistic mean, the crisp possibilistic mean value and the crisp (possibilistic)
variance of a continuous possibility distribution, which are consistent with the extension principle
and the definitions of expectation and variance in probability theory. The authors prove that the
proposed concepts ”behave properly” (similarly to their probabilistic counterparts). (page 233)
2013
A14-c145 Wang Dabuxilatu, A soft control chart based on weighted measurement of fuzzy data, In: Proceedings
of the 2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE
Computer Society Press, 2013. (ISBN 978-1-4673-5253-6) pp. 299-303. 2013
http://dx.doi.org/10.1109/FSKD.2013.6816211
Possibility theory has received much attention in the area of uncertainty modelling [15] [17].
Carlsson et al. [A14] proposed the possibilistic mean and possibilistic variance for fuzzy numbers,
these concepts behave properly in measuring central tendency of fuzzy numbers based on a ranking
of fuzzy numbers by the desire to give less importance to the lower levels of fuzzy numbers. (page
299)
A14-c144 Bayaraa S-O, Delgersaikhan U, Dalaisaikhan N, Utility maximization problem using curve trapezoidal fuzzy number, Proceedings of the 8th International Forum on Strategic Technology 2013, IFOST
2013, Ulaanbaatar, [ISBN 978-1-4799-0931-5], pp. 393-395. 2013
http://dx.doi.org/10.1109/IFOST.2013.6616992
A14-c143 Grujic Gabrijela, Stajner-Papuga Ivana, Grbic Tatjana, Medic Slavica, A note on interval-valued
estimations for fuzzy quantities In: 2013 IEEE 11th International Symposium on. Intelligent Systems and
Informatics (SISY), [ISBN 978-1-4799-0303-0], pp. 187-190. 2013
http://dx.doi.org/10.1109/SISY.2013.6662567
A14-c142 Yoshida Yuji, Optimization of value-at-risk portfolios in uncertain lognormal models, Proceedings of
the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), IEEE, [ISBN 978-14799-0348-1], pp. 263-268. 2013
http://dx.doi.org/10.1109/IFSA-NAFIPS.2013.6608410
A14-c141 Xue-jun Ma, Huai-qiang Zhang, A method and application to index design and decision making
based on Takagi-Sugeno fuzzy inference Proceedings of the 2013 International Conference on Management
Science and Engineering (ICMSE), [ISBN 978-1-4799-0473-0], pp. 463-468. 2013
http://dx.doi.org/10.1109/ICMSE.2013.6586322
A14-c140 Meng-rong Sun, Wei Chen, An artificial bee colony algorithm for fuzzy portfolio model with concave transaction costs, 2013 International Conference on Management Science and Engineering (ICMSE),
[ISBN 978-1-4799-0473-0 ], pp. 400-405. 2013
http://dx.doi.org/10.1109/ICMSE.2013.6586312
A14-c139 Cheng Sri, Wei Cren, OPF: A novel framework for fuzzy portfolio selection, In: Proceedings of
the 2013 International Conference on Management Science and Engineering (ICMSE), [ISBN 978-1-47990473-0 ], pp. 1739-1744. 2013
http://dx.doi.org/10.1109/ICMSE.2013.6586501
182
A14-c138 He L, Huang H-Z, Xu H, Zhu S, Ling D, Uncertainty quantification in fatigue lifetime data analysis: A possibilistic approach, 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and
Materials Conference, April 8-11, 2013, Boston, MA, [ISBN: 978-162410223-3]. 2013
http://dx.doi.org/10.2514/6.2013-1606
A14-c137 Casademunt Ana Maria Lucia, Georgescu Irina, Optimal Saving and Prudence in a Possibilistic
Framework, in: Distributed Computing and Artificial Intelligence, Advances in Intelligent Systems and
Computing, vol. 217/2013, Springer, [ISBN: 978-3-319-00550-8 (Print) 978-3-319-00551-5 (Online)], pp.
61-68. 2013
http://dx.doi.org/10.1007/978-3-319-00551-5_8
A14-c136 Alfred M Mbairadjim, Jules Sadefo Kamdem, Michel Terraza, Hedge Funds Risk-Adjusted Performance Evaluation: A Fuzzy Set Theory-Based Approach, In: Virginie Terraza, Hery Razafitombo eds., Understanding Investment Funds: Insights from Performance and Risk Analysis, Palgrave Macmillan, 2013,
[ISBN 9781137273604], pp. 57-71. 2013
A14-c135 Dutta P, Nagare M, A fuzzy-stochastic inventory model without backorder under uncertainty in customer demand, in: Proceedings of the 2nd International Conference on Operations Research and Enterprise
Systems, February 16-18, 2013, Barcelona, Spain, [ISBN 978-989856540-2], pp. 109-114. 2013
Scopus: 84877954718
A14-c134 Rupak Bhattacharyya, POSSIBILISTIC SHARPE RATIO BASED NOVICE PORTFOLIO SELECTION MODELS, in: Rupak Bhattacharyya and Arup Kr. Bhaumik eds., Computer Science & Information
Technology, National Conference on Advancement of Computing in Engineering Research (ACER 13),
MArch 22-23, 2013, Krishnagar, West Bengal, INDIA, [ISBN 978-1-921987-11-3], pp. 33-45. 2013
http://dx.doi.org/10.5121/csit.2013.3204
2012
A14-c133 Irina Georgescu, Combining probabilistic and possibilistic aspects of background risk, 2012 IEEE
13th International Symposium on Computational Intelligence and Informatics (CINTI), 20-22 Nov. 2012,
Budapest, [ISBN 978-1-4673-5205-5], pp. 225,229. 2012
http://dx.doi.org/10.1109/CINTI.2012.6496765
A14-c132 Irina Georgescu, Possibility of risk aversion and coinsurance problem, 2nd World Conference on
Innovation and Computer Sciences 2012, May 10-14, 2012, Ephesus, Turkey, AWERProcedia Information
Technology & Computer Science, 2(2012), pp. 4-8. 2012
http://www.world-education-center.org/index.php/P-ITCS/article/viewFile/565/234
A14-c131 Andreea Iluzia Iacob, Costin Ciprian Popescu, An optimization model with quasi S shape fuzzy data,
2nd World Conference on Innovation and Computer Sciences 2012, May 10-14, 2012, Ephesus, Turkey,
AWERProcedia Information Technology & Computer Science, GLOBAL JOURNAL ON TECHNOLOGY,
2(2012), pp. 132-136. 2012
http://www.world-education-center.org/index.php/P-ITCS/article/view/634/263
A14-c130 Mikael Collan, Simple fuzzy input scorecard for intellectual property rights evaluation, in: Proceedings of the 4th International Conference on Applied Operational Research, 25-27 July 2012, Bangkok,
Thailand, pp. 21-29. 2012
http://www.tadbir.ca/lnms/archive/v4/lnmsv4p21.pdf
Sometimes we are faced with situations where an asset offers high potential, however the most
likely expectation (score) is below the acceptable level. In these cases managers sometimes override policy (cut-off) and declare the asset ”strategically important”, and accept it based on ”gut
feeling”. Such decisions may be based on intuitive understanding of the value of potential, but
suffer from a lack of structured support for the decision. Using fuzzy numbers can help; we can
calculate a ”smart” mean value, a possibilistic mean value (Carlsson and Fullér, 2001), for the
asset score that takes into consideration the downside and the asset potential, defined in Definition
1. (page 27)
183
A14-c129 Luca Anzilli, A Possibilistic Approach to Evaluating Equity-Linked Life Insurance Policies, in: Advances in Computational Intelligence, 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, July 9-13, 2012, Catania, Italy, Communications in Computer and Information Science, vol. 300/2012, Springer, [ISBN 978-3-642-31724-8,
pp. 44-53. 2012
http://dx.doi.org/10.1007/978-3-642-31724-8_6
A14-c128 Enriqueta Vercher, José D Bermúdez, Fuzzy Portfolio Selection Models: A Numerical Study, in:
Financial Decision Making Using Computational Intelligence, Springer Optimization and Its Applications
Ser, [ISBN 978-1-4614-3773-4], pp. 253-280. 2012
A14-c127 Przemyslaw Grzegorzewski, On the Interval Approximation of Fuzzy Numbers, 14th International
Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems,
IPMU 2012, July 9-13, 2012, Catania, Italy, Communications in Computer and Information Science, vol.
299, Springer, [ISBN: 978-3-642-31718-7], pp. 59-68. 2012
http://dx.doi.org/0.1007/978-3-642-31718-7_7
A14-c126 Lee Chung-Chuan, Chen Huei-Ping, A heuristic pricing formula of fuzzy lookback options in uncertain environment, 9th International Conference on Fuzzy Systems and Knowledge Discovery, Chongqing,
China, [ISBN 978-1-4673-0025-4], pp. 515-519. 2012
http://dx.doi.org/10.1109/FSKD.2012.6233717
A14-c125 Irina Georgescu, Jani Kinnunen, Possibilistic Risk Aversion and Its Indicators, 11th WSEAS International Conference on APPLIED COMPUTER and APPLIED COMPUTATIONAL SCIENCE (ACACOS’12), April 18-20, 2012, Rovaniemi, Finland, [ISBN: 978-1-61804-084-8], pp. 178-183. 2012
http://www.wseas.us/e-library/conferences/2012/Rovaniemi/ACACOS/ACACOS-29.pdf
A14-c124 M Collan, K Kyläheiko, Strategic Patent Portfolios: Valuing the Bricks of the Road to the Future,
17th International Working Seminar on Production Economics, February 20-24, 2012, Innsbruck, Austria,
12 pages. 2012
http://www.medifas.net/IGLS/Papers2012/Paper029.pdf
A14-c123 I Georgescu, J Kinnunen, A Mixed Portfolio Selection Problem, 9th International Conference on
Distributed Computing and Artificial Intelligence, March 28-30, 2012, Salamanca, Spain, Advances in
Intelligent and Soft Computing, vol. 151/2012, Springer, [ISBN: 978-3-642-28764-0], pp. 95-102. 2012
http://dx.doi.org/10.1007/978-3-642-28765-7_13
A14-c122 I Georgescu, J Kinnunen, Mixed Multidimensional Risk Aversion, R. Precup, Sz. Kovács, S. Preitl,
E. M. Petriu eds., Applied Computational Intelligence in Engineering and Information Technology: Revised
and Selected Papers from the 6th IEEE International Symposium on Applied Computational Intelligence
and Informatics SACI 2011, Topics in Intelligent Engineering and Informatics, vol. 1/2012, Springer,
[ISBN 978-3-642-28305-5], pp. 39-50. 2012
http://dx.doi.org/10.1007/978-3-642-28305-5_3
A14-c121 I Georgescu, J Kinnunen, A Generalized 3-Component Portfolio Selection Model, 11th WSEAS
International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (AIKED ’12),
February 22-24, 2012, Cambridge, England, [ISBN: 978-1-61804-068-8], pp. 142-147.
http://www.wseas.us/e-library/conferences/2012/CambridgeUK/AIKED/AIKED-22.pdf
2011
A14-c120 Chuan-Sheng Wang, Wei Chen, A Fuzzy Model for R&D Project Portfolio Selection, International
Conference on Information Management, Innovation Management and Industrial Engineering, November
26-27, 2011, Shenzhen, China, [ISBN: 978-0-7695-4523-3], pp. 100-104. 2011
http://dx.doi.org/10.1109/ICIII.2011.30
184
A14-c119 Irina Georgescu, Comparing Possibilistically Multidimensional Risk Aversions, 12th IEEE International Symposium on Computational Intelligence and Informatics, November 21-22, 2011, Budapest,
Hungary, [ISBN: 978-1-4577-0045-3], pp. 183-188. 2011
http://dx.doi.org/10.1109/CINTI.2011.6108496
A14-c118 Andreea Iluzia Iacob, Costin-Ciprian Popescu, Regression Using Partially Linearized Gaussian Fuzzy
Data, International Conference on Informatics Engineering and Information Science, November 14-16,
2011, Kuala Lumpur, Malaysia, [ISBN: 978-3-642-25453-6], pp. 584-595. 2011
http://dx.doi.org/10.1007/978-3-642-25453-6_48
A14-c117 Xiaoxia Huang, Chen Yao, Uncertain portfolio selection for insurer, 8th International Conference on
Fuzzy Systems and Knowledge Discovery, FSKD 2011, July 2-28, 2011, Shanghai, China, [ISBN: 978161284181-6], pp. 760-764. Paper 6019684. 2011
http://dx.doi.org/10.1109/FSKD.2011.6019684
A14-c116 Irina Georgescu, Jani Kinnunen, Multidimensional risk aversion with mixed parameters, In: 6th
IEEE International Symposium on Applied Computational Intelligence and Informatics, May 19-21, 2011,
Timisoara, Romania, [ ISBN: 978-1-4244-9108-7], pp. 63-66. 2011
http://dx.doi.org/10.1109/SACI.2011.5872974
A14-c115 Irina Georgescu, Mixed risk aversion: Probabilistic and possibilistic aspects, 2011 IEEE 9th International Symposium on Applied Machine Intelligence and Informatics (SAMI), January 27-29, 2011,
Smolenice, Slovakia, [ISBN: 978-1-4244-7429-5], pp. 279-283. Paper 11883948. 2011
http://dx.doi.org/10.1109/SAMI.2011.5738889
2010
A14-c114 Alessandro Buoni, Mario Fedrizzi, Jozsef Mezei, A Delphi-based approach to fraud detection using attack trees and fuzzy numbers, International Association for the Scientific Knowledge, Teaching and
Learning 2010, November 29-December 1, 2010, Seville, Spain, pp. 21-28.
A14-c113 Wu Yi, Qiu Wanhua, Zhou Peng, Lin Jian, Project delay risk analysis in aviation manufacturing
enterprise, July 29-31, 2010, 29th Chinese Control Conference, CCC’10. Beijing, China, [ISBN: 978-14244-6263-6], pp. 1763-1767. Paper 5573960. 2010
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5573960&tag=1
A14-c112 Irina Georgescu, A possibilistic Pratt theorem, 8th International Symposium on Intelligent Systems
and Informatics (SISY), 10-11 September 2010, Subotica, Serbia, [ISBN 978-1-4244-7394-6], pp. 193196. 2010
http://dx.doi.org/10.1109/SISY.2010.5647299
A14-c111 Irina Georgescu, Jani Kinnunen, Multidimensional Possibilistic Risk Aversion, 11th International
Symposium on Computational Intelligence and Informatics (CINTI), November 18-20, 2010, Budapest,
Hungary, [ISBN 978-1-4244-9279-4], pp. 163-168. 2010
http://dx.doi.org/10.1109/CINTI.2010.5672253
A14-c110 Shu-Hsien Liao, Shiu-Hwei Ho, Investment Project Valuation Based on the Fuzzy Real Options Approach, 2010 International Conference on Technologies and Applications of Artificial Intelligence, November 18-20, 2010, Hsinchu City, Taiwan, [ISBN 978-0-7695-4253-9], pp. 94-101. 2010
http://dx.doi.org/10.1109/TAAI.2010.26
In essence, identical results are obtained in the case of possibilistic distribution which is adopted
by this study to characterize the NPV of an investment project. In other words, the characteristic
of right-skewed distribution also appears in the FENPV of an investment project when the parameters (such as cash flows) are characterized with fuzzy numbers. Although many studies have
proposed a variety of methods to compute the mean value [A14, A9] and median value [31] of
fuzzy numbers, these works did not consider the right-skewed characteristic present in the FENPV.
(page 98)
185
A14-c109 Zhaoxia Shang, Hong Liu, Xiaoxian Ma, Yanmin Liu, Fuzzy Value-at-Risk and Fuzzy Conditional
Value-at-Risk: Two risk measures under fuzzy uncertainty, IEEE 2nd Symposium on Web Society (SWS),
16-17 Aug. 2010, Beijing , China, [ISBN 978-1-4244-6356-5], pp. 282-290. 2010
http://dx.doi.org/10.1109/SWS.2010.5607440
Recently, a few authors, such as Ramaswamy [15], Tanaka and Guo [19] and Carlsson and Fuller
[A14] studied fuzzy financial optimization problem. Inuiguchi and Ramik [9] surveyed the advantages and disadvantages of fuzzy mathematical programming approaches compared with stochastic programming, and reviewed the newly developed ideas and techniques in fuzzy mathematical
programming. Wang and Zhu [21] summarized on fuzzy portfolio selection. One can refer to Bellman and Zadeh [4] and Zimmermann [24] for a detailed discussion on the fuzzy decision theory.
(page 282)
A14-c108 Ying-yu He, Portfolio selection model with transaction costs based on fuzzy information, 2nd IEEE
International Conference on Information and Financial Engineering (ICIFE), 17-19 Sept. 2010, Chongqing,
China, [ISBN 978-1-4244-6927-7], pp. 148-152. 2010
http://dx.doi.org/10.1109/ICIFE.2010.5609270
A14-c107 Tohid Erfani, Sergei V.Utyuzhnikov, Handling Uncertainty and Finding Robust Pareto Frontier in
Multiobjective Optimization Using Fuzzy Set Theory, 51st AIAA/ASME/ASCE/AHS/ASC Structures,
Structural Dynamics, and Materials Conference, 12-15 April 2010, Orlando, Florida, USA, [ISBN 978160086742-2], article number 2010-3092. 2010
http://pdf.aiaa.org/preview/2010/CDReadyMSDM10_2336/PV2010_3092.pdf
A14-c106 Shu-Hsien Liao, Shiu-Hwei Ho, Investment Appraisal under Uncertainty - A Fuzzy Real Options Approach, Neural Information Processing. Models and Applications 17th International Conference, ICONIP
2010. Sydney, Australia, November 22-25, 2010, LNCS 6444/2010, Springer, [ISBN 978-3-642-17533-6],
pp. 716-726. 2010
http://dx.doi.org/10.1007/978-3-642-17534-3_88
In essence, identical results are obtained in the case of possibilistic distribution which is adopted
by this study to characterize the NPV of an investment project. In other words, the characteristic
of right-skewed distribution also appears in the FENPV of an investment project when the parameters (such as cash flows) are characterized with fuzzy numbers. Although many studies have
proposed a variety of methods to compute the mean value [A14, A9] and median value [14] of
fuzzy numbers, these works did not consider the right-skewed characteristic present in the FENPV.
(page 720)
A14-c105 Shu-Hsien Liao, Shiu-Hwei Ho, A fuzzy real options approach for investment project valuation,
Proceedings of the 5th WSEAS International Conference on Economy and Management Transformation,
October 24-26, 2010, Timisoara, Romania, vol. I, pp. 86-91. 2010
http://www.wseas.us/e-library/conferences/2010/TimisoaraW/EMT/EMT1-12.pdf
A14-c104 Guixiang Wang; Zhenju Mu, The fuzzy degrees of fuzzy n - cell numbers, Seventh International
Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 10-12 August 2010, Yantai, Shandong,
[ISBN 978-1-4244-5931-5 ], pp. 349-353. 2010
http://dx.doi.org/10.1109/FSKD.2010.5569651
A14-c103 Hiroshi Inoue, Masatoshi Miyake, A Default Risk Model in a Fuzzy Framework, International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU
2010), June 28-July 2, 2010, Dortmund, Germany, Springer, [ISBN 978-3-642-14057-0], pp. 280-288.
2010
http://dx.doi.org/10.1007/978-3-642-14058-7_28
A14-c102 Shu-Hsien Liao, Shiu-Hwei Ho, Investment project valuation using a fuzzy real options approach,
Proceedings of the 10th WSEAS international conference on Systems theory and scientific computation, N.
E. Mastorakis, V. Mladenov, and Z. Bojkovic eds., Mathematics And Computers In Science Engineering,
186
August 20-22, 2010, Taipei, Taiwan, World Scientific and Engineering Academy and Society (WSEAS),
[ISBN 978-960-474-218-9], pp. 172-177. 2010
A14-c102 Honghai Liu, David J. Brown, and George M. Coghill, Geometrical Representation of Quantity Space
and Its Application to Robot Motion Description, in: Bruno Apolloni, Robert J. Howlett, Lakhmi C. Jain
(Eds.): Knowledge-Based Intelligent Information and Engineering Systems, 11th International Conference,
KES 2007, XVII Italian Workshop on Neural Networks, Vietri sul Mare, Italy, September 12-14, 2007. Proceedings, Part II., Lecture Notes in Computer Science, Sublibrary: Lecture Notes in Artificial Intelligence,
vol. 4693, Springer, [ISBN 978-3-540-74826-7], pp. 18-25. 2010
http://dx.doi.org/10.1007/978-3-540-74827-4_3
For the conversion of any fuzzy number to that in its MR representation, say A is a fuzzy set,
[A]α is a compact subset of R, and M (A) is a closed interval bounded by the lower and upper
possibilistic mean values [M∗ (A), M ∗ (A)] of A [A14]. (page 21)
A14-c101 Zhu Danmei, Wang Xingtong, Ren Rongrong, A heuristics R&D projects portfolio selection decision system based on data mining and fuzzy logic, International Conference on Intelligent Computation
Technology and Automation, May 11-12, 2010, Changsha, Hunan, China, [ISBN 978-0-7695-4077-1], pp.
118-121. 2010
http://doi.ieeecomputersociety.org/10.1109/ICICTA.2010.257
A14-c100 Mikael Collan; Mario Fedrizzi, Real asset appraisal based on multi-expert approach using the pay-off
method for real option valuation, in: Mikael Collan ed., Proceedings of the 2nd International Conference
on Applied Operational Research - ICAOR’10, Lecture Notes in Management Science, vol. 2/2010, August
25-27, 2010 Turku, Finland, [ISBN: 978-952-12-2414-0], pp. 407-417. 2010
A14-c99 Irina Georgescu; Jani Kinnunen, Credibility measures in portfolio analysis, in: Mikael Collan ed.,
Proceedings of the 2nd International Conference on Applied Operational Research - ICAOR’10, Lecture
Notes in Management Science, vol. 2/2010, August 25-27, 2010 Turku, Finland, [ISBN: 978-952-12-24140], pp. 6-18. 2010
A14-c98 Javan Tan and Chai Quek, Online Self-reorganizing Neuro-fuzzy Reasoning in Interval-Forecasting for
Financial Time-Series, in: PRICAI 2010: Trends in Artificial Intelligence 11th Pacific Rim International
Conference on Artificial Intelligence, Daegu, Korea, August 30 - September 2, 2010, Lecture Notes in
Computer Science, vol. 6230/2010, Springer, [ISBN 978-3-642-15245-0], pp. 523-534. 2010
http://dx.doi.org/10.1007/978-3-642-15246-7_48
The approach is based on the BCM theory of neurological learning via metaplasticity principles
(Bienenstock et al., 1982), which addresses the stability limitations imposed by the monotonic
behavior in Hebbian theory for online learning (Rochester et al., 1956). In this paper, we examine
an adapted version called iSeroFAM for interval-forecasting of financial time-series that follows a
computational efficient approach adapted from Lalla et al. (2008) and Carlsson and Fullér (2001).
(page 523)
This paper proposes iSeroFAM, a modified interpretation of SeroFAM [22], which is computationallybased on the BCM-theory of meta-plasticity for on-line self-reorganizing fuzzy-associative learning. Here, the objective is to realize interval-forecasting capabilities as conceptualized by Carlsson
and Fullér [6]. (page 524)
A14-c97 Sibo Ding, Valuation of Reverse Logistics Company Based on FRO and FMADM, in: 2nd International Conference on e-Business and Information System Security (EBISS), Wuhan, China, May 22-23,
2010, [ISBN 978-142445895-0], pp. 1-4. 2010, pp. 256-259. 2010
http://dx.doi.org/10.1109/EBISS.2010.5473406
A14-c96 Ying-yu He, The comparison of the optimal portfolio corresponding to different weight functions, The
Third International Conference on Business Intelligence and Financial Engineering, August 13-15, 2010,
Hong Kong, pp. 196-200. 2010
http://dx.doi.org/10.1109/BIFE.2010.54
187
A14-c95 P. Majlender, Fuzziness in Supply Chain Management, in: Cengiz Kahraman, Mesut Yavuz eds.,
Production Engineering and Management under Fuzziness, Studies in Fuzziness and Soft Computing series,
vol. 252/2010, Springer, Berlin/Heidelberg, pp. 201-247. 2010
http://www.springerlink.com/content/162882N375G73688Zhang Wanjun
2009
A14-c94 Q Wang, K W Hipel, D M Kilgour, Using fuzzy real options in a brownfield redevelopment decision
support system, IEEE International Conference on Systems, Man and Cybernetics, October 11-14, 2009,
San Antonio, USA, [ISBN: 978-1-4244-2793-2], pp. 1545-1550. 2009
http://dx.doi.org/10.1109/ICSMC.2009.5346312
Soft-computing techniques have demonstrated their advantages in intelligent behavior. Fuzzy theory is especially suitable for situations in which expert knowledge is required. Hence, fuzzy real
options are proposed for dealing with private risks that are hard to objectively estimate based on
possibility theory as claimed by Carlsson and Fuller [A8] [A14]. If private risks are represented as
fuzzy variables, possibility theory can be used. In this case, both subjective and objective uncertainties are integrated into the fuzzy real options model. However, Carlsson’s fuzzy real options
are limited to the exercise price and current value in the options model [A8]. Hence, the transformation method is employed to generalize fuzzy variable representation to any parameter, which
overcomes the multiple outputs problem [22]. The idea underlying the transformation method
follows three steps: firstly, decompose fuzzy numbers into discrete form; then use an α-cut for
calculation purposes as a traditional function; and finally, search the coordinates of the points in
the hypersurfaces of the cube [22]. (page 1547)
A14-c93 X Deng, R Li, Y Wan, Linear efficacy method for a portfolio selection with bounded assets based
on possibility theory, 4th International Conference on Computer Sciences and Convergence Information
Technology, November 24-26, 2009, Seoul, South Korea, [ISBN: 978-1-4244-5244-6], pp. 602-607. Paper
5367882. 2009
ISI:000280705700120
A14-c92 Lin Gao, Xu Huixin, Fuzzy weights with the minimum spanning tree problem limits the possibility of
opportunity for planning mode, 17th Symposium on Fuzzy Theory and Its Applications. Kaohsiung City,
Taiwan, pp. 1187-1194. 2009
A14-c90 Qiansheng Zhang, Baoguo Jia, Shengyi Jiang, Interval-Valued Intuitionistic Fuzzy Probabilistic Set
and Some of Its Important Properties, in: 1st International Conference on Information Science and Engineering (ICISE), December 26-28, 2009, Nanjing, China, [ISBN 978-1-4244-4909-5], pp. 4038-4041.
2009
http://dx.doi.org/10.1109/ICISE.2009.692
A14-c89 Daniel E. Salazar Aponte; Claudio M. Rocco S.; Blas Galván, On Uncertainty and Robustness in
Evolutionary Optimization-Based MCDM, in: Evolutionary Multi-Criterion Optimization, Lecture Notes
in Computer Science, vol. 5467/2009, Springer, Berlin / Heidelberg, [ISBN 978-3-642-01019-4], pp. 5165. 2009
http://dx.doi.org/10.1007/978-3-642-01020-0_9
A14-c88 Takashi Hasuike and Hiroaki Ishii, A Type-2 Fuzzy Portfolio Selection Problem Considering Possibility Measure and Crisp Possibilistic Mean Value, in: J. P. Carvalho, D. Dubois, U. Kaymak and J. M. C.
Sousa eds., Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and
2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009,
[ISBN: 978-989-95079-6-8], pp. 1120-1125. 2009
www.eusflat.org/publications/proceedings/
IFSA-EUSFLAT_2009/pdf/tema_1311.pdf
A14-c87 Zhong-Xing Wang, Jian Li, The Method for Ranking Fuzzy Numbers Based on the Approximate Degree and the Fuzziness, 6th International Conference on Fuzzy Systems and Knowledge Discovery, FSKD
2009, Tianjin, China, 14 -16 August 2009, Volume 3, [ISBN 978-076953735-1], pp. 335-339. 2009
http://dx.doi.org/10.1109/FSKD.2009.32
188
A14-c86 Gisella Facchineti, Nicoletta Pacchiarotti, Evaluation of fuzzy quantities by means of a weighting functions, In: Bruno Apolloni, Simone Bassis, Maria Marinaro eds., New Directions in Neural Networks - 18th
Italian Workshop on Neural Networks: WIRN 2008, Frontiers in Artificial Intelligence and Applications,
Volume 193, 2009, IOS Press, pp. 194-204. 2009
http://dx.doi.org/10.3233/978-1-58603-984-4-194
A14-c85 J. Tan; C. Quek, ACPOP: Ambiguity correction-based pseudo-outer-product fuzzy rule identification
algorithm, IEEE International Conference on Fuzzy Systems, art. no. 5277388, pp. 74-79. 2009
http://dx.doi.org/10.1109/FUZZY.2009.5277388
A14-c84 W. Chen; S. Tan, Fuzzy portfolio selection problem under uncertain exit time, IEEE International
Conference on Fuzzy Systems, art. no. 5277181, pp. 550-554. 2009
http://dx.doi.org/10.1109/FUZZY.2009.5277181
In [A14], Carlsson and Fullér introduced possibilistic mean value, variance and covariance, which
are important tools for solving fuzzy portfolio selection problem. Then they applied possibilistic
mean value to built portfolio model with highest utility score [A12]. (page 550)
A14-c83 T. Hasuike; H. Ishii, A portfolio selection problem with type-2 fuzzy return based on possibility
measure and interval programming, IEEE International Conference on Fuzzy Systems, art. no. 5277134,
pp. 267-272. 2009
http://dx.doi.org/10.1109/FUZZY.2009.5277134
A14-c82 Wei Chen; Ling Yang; Fasheng Xu, PSO-based possibilistc mean-variance model with transaction
costs, 2009 Chinese Control and Decision Conference, CCDC 2009, 17-19 June, 2009, Guilin, China, art.
no. 5195275, pp. 5993-5997. 2009
http://dx.doi.org/10.1109/CCDC.2009.5195275
In this paper, we will discuss the portfolio selection problem with transaction costs based on
the possibilistic theory. The rest of the paper is organized as follows. In Section 2, based on
the Carlsson and Fullérs’ notations, we will discuss some properties as in probability theory. In
section 3, a possibilistic portfolio model with transaction cost is proposed, in which transaction
cost is assumed as a no-convex-no-concave function instead of V-Shaped function. (page 5993)
A14-c81 Yong Shi, Shouyang Wang, Yi Peng, Jianping Li and Yong Zeng, Compromise Approach-Based Genetic Algorithm for Constrained Multiobjective Portfolio Selection Model, in: Yong Shi, Shouyang Wang,
Yi Peng, Jianping Li, Yong Zeng eds., Cutting-Edge Research Topics on Multiple Criteria Decision Making,
Communications in Computer and Information Science series, vol. 35/2009, Springer, [ISBN 978-3-64202297-5], pp. 697-704. 2009
http://dx.doi.org/10.1007/978-3-642-02298-2_104
A14-c80 S. S. Appadoo; S. K. Bhatt; C.R.Bector, Phi-lambda Mixed Strategy for Group Multi-attribute TOPSIS
Model with Application to Supplier Selection Problem, in: Mehran Hojati ed., Proceedings of the Annual
Conference of the Administrative Sciences Association of Canada, Management Science Division, Niagara
Fallas, Ontario, Canada, June 6-9, 2009, vol. 30, 17 pages. 2009
http://libra.acadiau.ca/library/ASAC/v30/ManagementScience/Papers/AppadooBhattBectorSharma.pdf
A14-c79 S. S. Appadoo; A. Dua; V. N. Sharma, On fuzzy economic order quantity using possibilistic approach,
in: Mehran Hojati ed., Proceedings of the Annual Conference of the Administrative Sciences Association
of Canada, Management Science Division, Niagara Fallas, Ontario, Canada, June 6-9, 2009, vol 30, 11
pages. 2009
http://libra.acadiau.ca/library/ASAC/v30/ManagementScience/Papers/AppaddooDuaSharma.pdf
A14-c78 Qian-Sheng Zhang; Sheng-Yi Jiang, Statistical correlation of intuitionistic fuzzy sets, 2009 International Conference on Machine Learning and Cybernetics, Volume 2, 12-15 July 2009, [ISBN 978-1-42443702-3], pp. 817-821. 2009
http://dx.doi.org/10.1109/ICMLC.2009.5212459
189
A14-c77 G.-X. Wang; Y.-L. Liu; X.-N. Gao, The means of fuzzy n-cell numbers and the pre-orders on fuzzy ncell number space, 2009 International Conference on Machine Learning and Cybernetics, Volume 2, 12-15
July 2009, [ISBN 978-1-4244-3702-3], pp. 866-870. 2009
http://dx.doi.org/10.1109/ICMLC.2009.5212360
A14-c76 Jihui Zhang, Junqin Xu, Fuzzy Entropy Method for Quantifying Supply Chain Networks Complexity, in: Jie Zhou ed., Complex Sciences, Lecture Notes of the Institute for Computer Sciences, Social
Informatics and Telecommunications Engineering, Springer, [ISBN 978-3-642-02468-9], vol. 5(2009), pp.
1690-1700. 2009
http://dx.doi.org/10.1007/978-3-642-02469-6_47
A14-c75 Barbara Gladysz and Dorota Kuchta, Least Squares Method for L-R Fuzzy Variables, in: Fuzzy
Logic and Applications, Lecture Notes in Computer Science, Springer, [ISBN 978-3-642-02281-4], vol.
5571/2009, pp. 36-43. 2009
http://dx.doi.org/10.1007/978-3-642-02282-1_5
A14-c74 T. Joronen, Computational theory of meaning articulation: A human estimation approach to fuzzy
arithmetic, in: Views on Fuzzy Sets and Systems from Different Perspectives, Studies in Fuzziness and
Soft Computing series, vol. 243/2009, pp. 115-127. 2009
http://dx.doi.org/10.1007/978-3-540-93802-6_6
A14-c73 Juan Guillermo Lazo Lazo, Alexandre Anozé Emerick, Dan Posternak, Thiago Souza Mendes Guimaraes,
Marco Aurélio Cavalcanti Pacheco and Marley Maria Bernardes Rebuzzi Vellasco, Analysis of Alternatives
for Oil Field Development under Uncertainty, in: Intelligent Systems in Oil Field Development under Uncertainty, Studies in Computational Intelligence Series, vol. 183/2009, pp. 187-225. 2009
http://dx.doi.org/10.1007/978-3-540-93000-6_6
A14-c72 Juan Guillermo Lazo Lazo, Marco Antonio G. Dias, Marco Aurélio Cavalcanti Pacheco and Marley
Maria Bernardes Rebuzzi Vellasco, Real Option Value Calculation by Monte Carlo Simulation and Approximation by Fuzzy Numbers and Genetic Algorithms, in: Intelligent Systems in Oil Field Development
under Uncertainty, Studies in Computational Intelligence Series, vol. 183/2009, pp. 139-186. 2009
http://dx.doi.org/10.1007/978-3-540-93000-6_5
2008
A14-c71 P. Majlender, Soft decision support systems for evaluating real and financial investments, in: Fuzzy
Engineering Economics with Applications, Studies in Fuzziness and Soft Computing series, 233/2008, pp.
307-338. 2008
http://dx.doi.org/10.1007/978-3-540-70810-0_17
A14-c70 Y. Yoshida, A Perception-Based Estimation of Uncertainty and its Application to Financial Portfolios,
7th WSEAS International Conference on Computational Intelligence Man-Machine Systems and Cybernetics, December 29-31, 2008, Cairo, Egypt, [ISBN: 978-960-474-049-9 ], pp. 59-64. 2008
ISI:000264086100009
A14-c69 G H Chen, S Chen, Y Fang, S Y Wang, A possibilistic mean variance portfolio selection model, 2nd
International Conference on Management Science and Engineering Management, November 3-8, 2008,
Chongqing, China, [ISBN: 978-1-84626-002-5], pp. 365-372. 2008
A14-c68 S S Appadoo, S K Bhatt, C R Bector, V N Sharma, A POSSIBILITY ASSISTED FUZZY EOQ
INVENTORY MODEL, in: Annual Conference of the Administrative Sciences Association of Canada,
Halifax, Canada, May 24-27, 2008, pp. 76-96. 2008
http://ojs.acadiau.ca/index.php/ASAC/article/view/702/610
190
Carlsson and Fuller introduced possibilistic moments of fuzzy numbers. In this paper, we extend
some of those results to economic order quantity inventory model (EOQ) using nonlinear type of
fuzzy numbers. We combine fuzzy technique assisted by possibility theory to deal with uncertainty
and derive some important results. A numerical example is provided and concluding remarks are
made. (page 76)
A14-c67 W. Chen, A possibilistic portfolio model with borrowing and bounded constraints and its application,
Chinese Control and Decision Conference, CCDC 2008, Yantai, China, July 2-4, 2008, art. no. 4597424,
pp. 804-808. 2008
http://dx.doi.org/10.1109/CCDC.2008.4597424
A14-c66 Gong Yanbing; Zhang Jiguo, Two new optimal aggregation approaches of fuzzy opinions in group
decision environment, 3rd International Conference on Intelligent System and Knowledge Engineering,
(ISKE 2008), University Convention Center, Xiamen, China, 17-19 Nov. 2008, vol. 1, pp. 389-394. 2008
http://dx.doi.org/10.1109/ISKE.2008.4730961
A14-c65 Irina Georgescu, Risk Aversion through Fuzzy Numbers, First International Conference on Complexity
and Intelligence of the Artificial and Natural Complex Systems. Medical Applications of the Complex
Systems. Biomedical Computing, November 08-10, 2008, Targu Mures, Romania, [ISBN 978-0-76953621-7], pp. 174-182. 2008
http://doi.ieeecomputersociety.org/10.1109/CANS.2008.27
A14-c64 A Saeidifar, Point and interval estimators of fuzzy numbers, 9th Iranian Statistics Conference, 20-22
August 2008, Isfahan, Iran, pp. 574-584. 2008
http://www.irstat.ir/Files/ISC/ISC9/ISC9%20-%20Proceedings
%20(English).pdf#page=583
A14-c63 Mohammad Hossein Fazel Zarandi and Mohammad Mehdi Fazel Zarandi, Fuzzy Multiple Agent
Decision Support Systems for Supply Chain Management, in: Vedran Kordic ed., Supply Chain, Theory
and Applications, I-Tech Education and Publishing, Vienna, Austria, pp. 177-204. 2008
http://journals.i-techonline.com/downloadpdf.php?id=741
A14-c62 X.-C. Liang, L. Dai, Credit rating of small business with trapezoid fuzzy linguistic variables, Proceedings of the International Conference on Information Management, Innovation Management and Industrial
Engineering, ICIII 2008 1, art. no. 4737493, pp. 46-49. 2008
http://dx.doi.org/10.1109/ICIII.2008.189
A14-c60 Y. Yoshida, A risk-sensitive portfolio with mean and variance of fuzzy random variables, Lecture
Notes in Artificial Intelligence, Springer, [ISBN 978-3-540-85983-3], vol. 5227/2008, pp. 358-366. 2008
http://dx.doi.org/10.1007/978-3-540-85984-0_44
A14-c59 G. Yanbing, Z.Jiguo, A method for fuzzy multi-attribute decision making with preference information
in the form of fuzzy complementary judgment matrix (2008) Proceedings - 5th International Conference on
Fuzzy Systems and Knowledge Discovery, FSKD 2008, 3, art. no. 4666265, pp. 336-340. 2008
http://dx.doi.org/10.1109/FSKD.2008.108
A14-c58 Y. Gong, J. Zhang, A new method for assessing the weights of fuzzy opinions in group decision environment, Proceedings - International Conference on Intelligent Computation Technology and Automation,
ICICTA 2008, 1, art. no. 4659604, pp. 836-839. 2008
http://dx.doi.org/10.1109/ICICTA.2008.104
A14-c57 H.-W. Hsu, H.-F. Wang, Closed-loop green supply chain logistics model with uncertain reverse parameters, 2008 International Conference on Wireless Communications, Networking and Mobile Computing,
WiCOM 2008, art. no. 4679358. 2008
http://dx.doi.org/10.1109/WiCom.2008.1450
A14-c56 Y. Yoshida, A risk-minimizing portfolio model with fuzziness, IEEE International Conference on
Fuzzy Systems (FUZZ-IEEE 2008), 1-6 June 2008, pp. 909-914. 2008
http://dx.doi.org/10.1109/FUZZY.2008.4630478
191
A14-c55 Y.J. Tupac, J.G Lazo., L. Faletti, M.A. Pacheco, M.M.B.R. Vellasco, Decision support system for
economic analysis of E& P projects under uncertainties, in: Society of Petroleum Engineers - Intelligent
Energy Conference and Exhibition: Intelligent Energy 2008, vol. 2, pp. 1115-1124. 2008
2007
A14-c54 Ming Zeng, He Wang, Ting Zhang, Baozhu Li, Shulin Huang, Research and Application of Power
Network Investment Decision-making Model based on Fuzzy Real Options, International Conference on
Service Systems and Service Management, pp.1-5, 9-11 June 2007
http://dx.doi.org/10.1109/ICSSSM.2007.4280151
A14-c53 Chen, Tao; Zeng, Yurong; Wang, Lin; Zhang, Jinlong, Evaluating IT Investment Using a Hybrid
Approach of Fuzzy Risk Analysis and Real Options, Fourth International Conference on Fuzzy Systems
and Knowledge Discovery (FSKD 2007), vol.1, pp.135-139, 24-27 Aug. 2007
http://dx.doi.org/10.1109/FSKD.2007.276
A14-c52 Guerra, Maria Letizia; Sorini, Laerte; Stefanini, Luciano, Parametrized Fuzzy Numbers for Option
Pricing, IEEE International on Fuzzy Systems Conference, (FUZZ-IEEE 2007), 23-26 July 2007, pp.1-6.
2007
http://dx.doi.org/10.1109/FUZZY.2007.4295456
A14-c51 Mendel, J.M.; Dongrui Wu, Cardinality, Fuzziness, Variance and Skewness of Interval Type-2 Fuzzy
Sets, IEEE Symposium on Foundations of Computational Intelligence (FOCI 2007), 1-5 April 2007, pp.
375-382. 2007
http://dx.doi.org/10.1109/FOCI.2007.371499
One popular dénition of the (possibilistic) variance of a T1 FS A is given by Carlsson and Fullér
[A14] as ”the expected value of the squared deviations between the arithmetic mean and the endpoints of its level sets,” i.e., (page 379)
A14-c50 Chen Tao, Zhang Jinlong, Liu Shan, and Yu Benhai, Fuzzy Real Option Analysis for IT Investment
in Nuclear Power Station, Y. Shi et al. (Eds.): ICCS 2007, Part III, Lecture Notes in Computer Science,
Volume 4489/2007, Springer, [978-3-540-72587-9], pp. 953-959, 2007. 2007
http://dx.doi.org/10.1007/978-3-540-72588-6_152
Supposing A = (a1 , aM , a2 ) be a triangular fuzzy number then the possibilistic expected value of
A is [A14] (page 955)
A14-c49 Lan, Yuping; Lv, Xuanli; Zhang, Weiguo A Linear Programming Model of Fuzzy Portfolio Selection
Problem, IEEE International Conference on Control and Automation, (ICCA 2007), May 30 2007-June 1
2007, Guangzhou, China, [ISBN: 978-1-4244-0818-4], pp. 3116 - 3118. 2007
http://www.ieeexplore.ieee.org/iel5/4376306/4376307/04376935.pdf?
Zadeh [6] proposed possibility theory based on possibilistic distributions. Carlsson and Fullér
[A14] defined the notions of possibilistic mean value and variance of fuzzy numbers. (page 3116)
Carlsson and Fullér [A14] introduced the possibilistic mean value of A as
Z
1
M (A) =
γ[a1 (γ) + a2 (γ)] dγ
0
(page 3116)
Carlsson and Fullér [A14] also introduced the possibilistic variance and covariance of fuzzy numbers as
Z
1 1
γ[a2 (γ) − a1 (γ)]2 dγ
Var(A) =
2 0
(page 3116)
192
A14-c48 Yuji Yoshida, Fuzzy Extension of Estimations with Randomness: The Perception-Based Approach,
in: Vicenc Torra, Yasuo Narukawa, Yuji Yoshida (Eds.): Modeling Decisions for Artificial Intelligence,
4th International Conference, MDAI 2007, Kitakyushu, Japan, August 16-18, 2007, Proceedings. Springer,
Lecture Notes in Computer Science, Sublibrary: Lecture Notes in Artificial Intelligence, vol. 4617, [ISBN
978-3-540-73728-5], pp. 295-306. 2007
http://dx.doi.org/10.1007/978-3-540-73729-2_28
We can find other approaches regarding variance in Carlsson and Fullér [A14], Feng et al. [3],
Körner [4] and Yoshida [15]. (page 306)
A14-c47 Chen Tao, Zhang Jinlong, Yu Benhai, and Liu Shan A Fuzzy Group Decision Approach to Real Option
Valuation, in: Aijun An, Jerzy Stefanowski, Sheela Ramanna, Cory J. Butz, Witold Pedrycz, Guoyin Wang
(Eds.): Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, 11th International Conference,
RSFDGrC 2007, Toronto, Canada, May 14-16, 2007, Lecture Notes in Computer Science, Sublibrary:
Lecture Notes in Artificial Intelligence, vol. 4482, Springer, [ISBN 978-3-540-72529-9], pp. 103-110.
2007
http://dx.doi.org/10.1007/978-3-540-72530-5_12
[A14] introduced the possibilistic expected value of triangular fuzzy number A = (a1 , aM , a2 ) as
1
2
E(A) = aM + (a1 + a2 ).
3
6
And the possibilistic variance of fuzzy figure A as
(page 106)
A14-c46 Bermudez, J.D.; Segura, J.V.; Vercher, E.; A fuzzy ranking strategy for portfolio selection applied to
the Spanish stock market, Fuzzy Systems Conference, (FUZZ-IEEE 2007) 23-26 July 2007, London, UK,
pp. 787-790. 2007
http://dx.doi.org/10.1109/FUZZY.2007.4295466
Vercher et al. [19] develop a detailed study of the above approach to the portfolio selection problem. They also worked with the definition of possibilistic mean value of a fuzzy number introduced
by Carlsson and Fullér [A14]. With that possibilistic mean value, the crisp expected return and
downside risk are respectively given by:
A14-c45 Yuji Yoshida, A Risk-Minimizing Model Under Uncertainty in Portfolio, in: Melin, P.; Castillo, O.;
Aguilar, L.T.; Kacprzyk, J.; Pedrycz, W. (Eds.) Foundations of Fuzzy Logic and Soft Computing 12th International Fuzzy Systems Association World Congress, IFSA 2007, Cancun, Mexico, Junw 18-21, 2007,
Proceedings Series: Lecture Notes in Computer Science, Sublibrary: Lecture Notes in Artificial Intelligence, Vol. 4529, Springer, [ISBN: 978-3-540-72917-4], 2007 pp. 381-391. 2007
http://dx.doi.org/10.1007/978-3-540-72950-1_38
We can find other approaches in (Carlsson and Fullér 2001; Feng et al. 2001), which discuss the
variance of fuzzy numbers by possibility theory. (page 386)
A14-c44 Y. Yoshida, Mean value and variance of fuzzy random variables by evaluation measures, 3rd IEEE
International Conference on Intelligent Systems, September 4-6, 2006, London, England, [ISBN: 978-14244-0195-6], pp. 227-232. 2006
ISI:000244714800042
A14-c43 Jinlong Zhang; Guodong Cong; Yugang Yu; Yeming Gong, A Fuzzy Rough Group Decision-making
Model for Rating and Ranking IT Outsourcing Aggressive Risk, International Conference on Service Systems and Service Management, 25-27 October 2006, vol.2, pp.1050-1056. 2006
http://dx.doi.org/10.1109/ICSSSM.2006.320653
A14-c42 Zhang WG, Chen QQ, Lan HL, A portfolio selection method based on possibility theory, in: Algorithmic Aspects in Information and Management, Series: Lecture Notes in Computer Science, vol. 4041,
[ISBN 978-3-540-35157-3], pp. 367-374. 2006
193
http://dx.doi.org/10.1007/11775096_34
Carlsson and Fullér [A14] defined the notions of possibilistic mean value and variance of fuzzy
numbers. (page 368)
Carlsson and Fullér [A14] introduced the possibilistic mean value of A as
Z 1
M (A) =
γ(a(γ) + b(γ)) dγ
0
(page 368)
A14-c41 Yoshida Y, A defuzzification method of fuzzy numbers induced from weighted aggregation operations,
in: Modeling Decisions for Artificial Intelligence, Series: Lecture Notes in Computer Science, Sublibrary:
Lecture Notes in Artificial Intelligence, vol. 3885, pp. 161-171. 2006
http://dx.doi.org/10.1007/11681960_17
A14-c40 Yoshida, Y. Mean values of fuzzy numbers with evaluation measures and the measurement of fuzziness, Proceedings of the 9th Joint Conference on Information Sciences, JCIS 2006, art. no. 298. 2006
http://dx.doi.org/10.2991/jcis.2006.298
A14-c39 Yoshida, Y. Mean values of fuzzy numbers and the measurement of fuzziness by evaluation measures,
2006 IEEE Conference on Cybernetics and Intelligent Systems, art. no. 4017804, pp. 1-6. 2006
http://dx.doi.org/10.1109/ICCIS.2006.252245
A14-c38 Zarandi, M.H.F., Pourakbar, M., Turksen, I.B. An intelligent agent-based system for reduction of
bullwhip effect in supply chains, IEEE International Conference on Fuzzy Systems, art. no. 1681782, pp.
663-670. 2006
http://dx.doi.org/10.1109/FUZZY.2006.1681782
. . . are equal to variance and mean of a fuzzy number proposed by Carlsson and Fullér [A14] as
equation (18) for mean and (19) for variance: (page 666)
A14-c37 Liu, H., Brown, D.J., An extension to fuzzy qualitative trigonometry and its application to robot
kinematics, IEEE International Conference on Fuzzy Systems, art. no. 1681849, pp. 1111-1118. 2006
http://dx.doi.org/10.1109/FUZZY.2006.1681849
Say A is a fuzzy set, [A]α is a compact subset of R, and M(A) is a closed interval bounded by the
lower and upper possibilistic mean values [M∗ (A), M ∗ (A)] of A [A14]. Then we can give the
following dénition, (page 1114)
A14-c36 S S Appadoo, C R Bector, Binomial Option Pricing Model Using O(2, 2) - Trapezoidal Type Fuzzy
Numbers In: ASAC 2005 Conference, Toronto, Canada, pp. 46-58.
http://luxor.acadiau.ca/library/ASAC/v26/02/02_index.html
A14-c35 Wenyi Zeng, Hongxing Li, Weimin Ye On the weighted interval approximation of a fuzzy number In:
10th International Conference on Fuzzy Theory and Technology (FTT 2005), 2005.
http://fs.mis.kuas.edu.tw/˜cobol/JCIS2005/papers/44.pdf
A14-c34 Wang, X., Xu, W., Zhang, W., Hu, M. Weighted possibilistic variance of fuzzy number and its application in portfolio theory, Fuzzy Systems and Knowledge Discovery, Lecture Notes in Artificial Intelligence,
vol. 3613, [ISBN 978-3-540-28312-6], Springer, pp. 148-155. 2005
http://dx.doi.org/10.1007/11539506_18
In 1987, Dubois and Prade déned an interval-valued expectation of fuzzy num- bers as a closed
interval bounded by the expectations calculated from its upper and lower distribution funtions.
They also showed that this expectation remains additive in the sense of addition of fuzzy numbers
[3]. In 2001, Carlsson and Fullér introduced an interval-valued mean value of fuzzy numbers,
viewing them as possibility distributions [A14]. (page 148)
194
A14-c33 B. Blankenburg and M. Klusch, Fuzzy Bilateral Shapley Value Stable Coalition Forming Among
Agents, GTDT 2005: Workshop on Game Theoretic and Decision Theoretic Agents at IJCAI-2005, Edinburgh, Scotland.
A14-c32 Dubois, D., Fargier, H., Fortin, J., The empirical variance of a set of fuzzy intervals, in: proceedings
of the 2005 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2005, May 22-25 2005, Reno,
USA. pp. 885-890. 2005
http://dx.doi.org/10.1109/FUZZY.2005.1452511
In the scope of fuzzy random variables, an interesting question is to define the counterpart of a
variance. The mean value of a set of fuzzy intervals is already known for a long time, but the
notion of variance has received less attention. Yet, several definitions already exist by Körner
[13], Feng et al [14], Carlsson and Fullér [A14]. (page 887)
We have defined the potential variance of a symmetric fuzzy interval based on these results. The
obtained definition is an interval of the form [0, Vmax ]. Interestingly the expression of Vmax is
similar to Carlsson and Fulleér variance [A14]. Two questions remain: is this expression valid
for asymmetric fuzzy intervals? Is Vmax equal to the upper bound of the variance of all random
variables included in the probability family induced by the fuzzy interval? (page 890)
A14-c30 Zhang WG, Wang YL, Using fuzzy possibilistic mean and variance in portfolio selection model, Computational Intelligence and Security, LECTURE NOTES IN ARTIFICIAL INTELLIGENCE, vol. 3801,
[ISBN 978-3-540-30818-8], pp. 291-296. 2005
http://dx.doi.org/10.1007/11596448_42
Zhang and Nie [7] introduced the admissible efficient portfolio model under the assumption that
the expected returns and risks of assets have admissible errors. Zadeh [9] proposed possibility
theory based on possibilistic distributions. Carlsson and Fullér [A14 defined the notions of possibilistic mean value and variance of fuzzy numbers. In this paper, we consider the portfolio
selection problem based on the possibilistic mean and variance under the assumption that the returns of assets are fuzzy numbers. The possibilistic mean value corresponds to the return, while
the possibilistic variance corresponds to the risk. Especially, we obtain a linear programming
model when returns of assets are symmetric triangular fuzzy numbers. (page 292)
A14-c29 Wei-Guo Zhang, Wen-An Liu and Ying-Luo Wang, A Class of Possibilistic Portfolio Selection Models
and Algorithms, in: Deng, Xiaotie; Ye, Yinyu (Eds.) Internet and Network Economics, First International
Workshop, WINE 2005, Hong Kong, China, December 15-17, 2005, Proceedings Series: Lecture Notes in
Computer Science , Vol. 3828, Sublibrary: Information Systems and Applications, incl. Internet/Web, and
HCI, Springer, [ISBN: 978-3-540-30900-0], 2005 pp. 464-472. 2005
http://dx.doi.org/10.1007/11600930_46
In this paper, a crisp possibilistic variance and a crisp possibilistic covariance of fuzzy numbers
are defined, which is different from the ones introduced by Carlsson and Fullér. (page 464)
A14-c28 T. Sato, S. Takahashi, C, Huang and H. Inoue, Option pricing with fuzzy barrier conditions, in: Y. Liu,
G. Chen and M. Ying eds., Proceedings of the Eleventh International Fuzzy systems Association World
Congress, July 28-31, 2005, Beijing, China, 2005 Tsinghua University Press and Springer, [ISBN 7-30211377-7] 380-384. 2005
A14-c27 Zhang, J.-P., Li, S.-M. Portfolio selection with quadratic utility function under fuzzy envirornment,
2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005, pp. 2529-2533. 2005
http://dx.doi.org/10.1109/ICMLC.2005.1527369
A14-c26 Yoshida, Y. Mean values of fuzzy numbers by evaluation measures and its measurement of fuzziness,
Proceedings - International Conference on Computational Intelligence for Modelling, Control and Automation, CIMCA 2005 and International Conference on Intelligent Agents, Web Technologies and Internet, 2,
art. no. 1631462, pp. 163-169. 2005
http://ieeexplore.ieee.org/iel5/10869/34212/01631462.pdf?
195
A14-c25 Blankenburg, B., Klusch, M. BSCA-F: Efficient fuzzy valued stable coalition forming among agents,
Proceedings - 2005 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT’05,
2005, art. no. 1565632, pp. 732-738. 2005
http://dx.doi.org/10.1109/IAT.2005.48
To achieve this, we utilize the fuzzy bilateral Shapley value which, however, implies that, in
general, only subgame-stability can be achieved. We show that it is reasonable to utilize the possibilistic mean value [A14] for defuzzifying the negotiated fuzzy payoffs to implement unambiguous
coalition contracts among the agents. (page 732)
A14-c24 Lazo, J.G.L., Vellasco, M.M.B.R., Pacheco, M.A.C. Determination of real options value by Monte
Carlo simulation and fuzzy numbers Proceedings - HIS 2005: Fifth International Conference on Hybrid
Intelligent Systems, 2005, art. no. 1587794, pp. 488-493. 2005
http://dx.doi.org/10.1109/ICHIS.2005.35
Therefore, the final crisp real option value is the mean of the fuzzy number obtained from the
simulation process (VF). This mean value is calculated according to the method described in [13A14].
A14-c23 E. Nasibov, S. Senol, A. Mert, New Approaches To Determine The WABL Parameters In Fuzzy
Aggregation, IJSIT Lecture Notes of First International Conference on Informatics, Vol.1, No.2, 173-178.
2004
A14-c22 Yoshida Y, A mean estimation of fuzzy numbers by evaluation measures,in: Mircea Gh. Negoita,
Robert J. Howlett, Lakhmi C. Jain eds., Knowledge-Based Intelligent Information and Engineering Systems: 8th International Conference, KES 2004, Wellington, New Zealand, September 20-25, 2004, Proceedings, LECTURE NOTES IN COMPUTER SCIENCE, 3214, pp. 1222-1229. 2004
http://www.springerlink.com/content/le6q7rq5lrrwfycv/
. . . which has been studied by Goetshel and Voxman [4] and Carlsson and Fullér [A14], is different
from our method (3) since . . . (page 1225)
A14-c21 F. Augusto Alcaraz Garcia, Fuzzy real option valuation in a power station reengineering project Soft
Computing with Industrial Applications - Proceedings of the Sixth Biannual World Automation Congress,
June 28 - July 1, 2004, Seville, Spain, [ISBN 1-889335-21-5], vol. 17, pp. 281-287. 2004
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1439379
A14-c20 Collan, M. Fuzzy real investment valuation model for very large industrial real investments, Soft
Computing with Industrial Applications - Proceedings of the Sixth Biannual World Automation Congress,
pp. 379-384. 2004
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1439395
The yearly standard deviation is calculated separately for IC and FCF using possibilistic mean
value and variance of fuzzy numbers as they are presented in [A14]. (page 382)
A14-c19 L. Spircu and T. Spircu, Fuzzy Treatment of American Call Options, Proceedings of the Tenth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based
Systems IPMU’2004, July 4-9, 2004, Perugia, Italy, 1841-1846. 2004
A14-c18 Wang, X., Xu, W.-J., Zhang, W.-G. A class of weighted possibilistic mean-variance portfolio selection
problems Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 4, pp. 20362040. 2004
http://ieeexplore.ieee.org/iel5/9459/30104/01382130.pdf?arnumber=1382130
In 1987, Duhois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them
as consonant random sets. They also showed that this expectation remains additive in the sense of
addition of fuzzy numbers [4]. In 2001, Carlsson and Fullér introduced an interval-valued mean
value of fuzzy numbers, viewing them as possibility distributions [A14]. In 2003, Fullér and
Majlender proposed an weighted possibility mean of fuzzy numbers, viewing them as weighted
possibility distributions [A9]. (page 2036)
196
A14-c17 Wang, G.-X., Zhao, C.-H. Characterization of discrete fuzzy numbers and application in adaptive filter
algorithm, Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 3, pp.
1850-1854. 2004
http://dx.doi.org/10.1109/ICMLC.2004.1382078
A14-c16 Péter Majlender, Strategic Investment Planning by Using Dynamic Decision Trees, in: Proceedings of
the 36th Annual Hawaii International Conference on System Sciences (HICSS’03), Track 3, p. 85a. 2003
http://dx.doi.org/10.1109/HICSS.2003.1174208
A14-c15 Fang Y, Lai KK, Wang SY, A fuzzy approach to portfolio rebalancing with transaction costs, COMPUTATIONAL SCIENCE - ICCS 2003, PT II, PROCEEDINGS, LECTURE NOTES IN COMPUTER
SCIENCE, Springer-Verlag, Heidelberg, Vol. 2658, 10-19. 2003
http://dx.doi.org/10.1007/3-540-44862-4_2
Carlsson and Fullér [A14] introduced the notation of crisp possibilistic mean (expected) value and
crisp possibilistic variance of continuous possibility distributions, which are consistent with the
extension principle. (page 12)
A14-c14 Wei-Guo Zhang, Zan-Kan Nie, On Possibilistic Variance of Fuzzy Numbers, in: G. Wang, Q. Liu, Y.
Yao, A. Skowron eds, Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing: 9th International
Conference, RSFDGrC 2003, Chongqing, China, May 26-29, 2003, LECTURE NOTES IN COMPUTER
SCIENCE, Volume 2639/2003, Springer, 398-402. 2003
http://dx.doi.org/10.1007/3-540-39205-X_66
In 2001 Carlsson and Fullér [A14] defined the concepts of lower possibilistic and upper possibilistic mean values. Furthermore, they also introduced a crisp variance of continuous possibility
distributions. This paper introduces the concepts of lower and upper possibilistic variances based
on the lower and upper possibilistic mean values of fuzzy numbers introduced by Carlsson and
Fullér. We also define a crisp possibilistic variance which is different from [A14]. These concepts are consistent with the extension principle and with the well-known definition of variance in
probability theory. (page 398)
A14-c13 Zhihuang Dai, Michael J. Scott, Zissimos P.Mourelatos, Incorporating epistemic uncertainty in robust design, in: Proceedings of the 2003 ASME Design Engineering Technical Conferences (DETC 2003),
September 2-6, 2003, Chicago, Illinois, USA, (DAC-48713.pdf), pp. 85-95. 2003
http://design.me.uic.edu/mjscott/papers/dac48713.pdf
A14-c12 G.M. Peschland and H.F. Schweiger, Reliability Analysis in Geotechnics with Finite Elements – Comparison of Probabilistic, Stochastic and Fuzzy Set Methods, in: Proceedings of the 3rd International Symposium on Imprecise Probabilities and Their Applications (ISIPTA ’03), Carleton Scientific Proceedings in
Informatics 18, University of Lugano, Lugano, Switzerland, 14-17 July 2003, pp. 437-451. 2003
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.582
For defuzzication a method based on weighted possibilistic mean and variance of fuzzy numbers
is used in this paper. Carlsson and Fullér [A14] suggested the notations of weighted possibilistic
mean value and variance of fuzzy numbers, which are consistent with the extension principle.
Furthermore, they showed that the weighted variance of linear combinations of fuzzy numbers
can be computed in a similar manner as in probability theory: (pages 445-446)
A14-c11 Zhang, W.-G., Zhang, Q.-M., Nie, Z.-K. A class of fuzzy portfolio selection problems, International
Conference on Machine Learning and Cybernetics, 5, pp. 2654-2658. 2003
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1259982
A14-c10 Y Yoshida, M Yasuda, JI Nakagami, M Kurano, The mean value with evaluation measures and a zerosum stopping game with fuzzy values, Workshop on Networking Games and Resource Allocation, July
12-15, 2002, Petrozavodsk, Russia, [ISBN: 1-59033-843-X], pp. 219-225. 2002
ISI:000221613900017
197
A14-c9 Yuji Yoshida, Masami Yasuda, Jun-ichi Nakagami, Masami Kurano, American Options with Uncertainty of the Stock Prices : The Discrete-Time Model in: Mathematical Decision Making under Uncertainty,
Kyoto University Research Information Repository, vol. 1252, pp. 174-180. 2002
http://hdl.handle.net/2433/41835
A14-c8 Dı́az-Hermida, F., Carinena, P., Bugarı́n, A., Barro, S. Modelling of task-oriented vocabularies: An
example in fuzzy temporal reasoning, IEEE International Conference on Fuzzy Systems, pp. 43-46. 2001
http://dx.doi.org/10.1109/FUZZ.2001.1007241
in books
A14-c6 Marek Gagolewski, DATA FUSION THEORY, METHODS, AND APPLICATIONS, Institute of Computer Science, Polish Academy of Sciences, 2015. INFORMATION TECHNOLOGIES: RESEARCH
AND THEIR INTERDISCIPLINARY APPLICATIONS; vol 7, (ISBN 978-83-63159-20-7). 2015
A14-c5 Jiuping Xu, Ziqiang Zeng, Fuzzy-Like Multiple Objective Multistage Decision Making, Studies in
Computational Intelligence, Volume 533(2014), [ISBN: 978-3-319-03397-6 (Print) 978-3-319-03398-3
(Online)]. 2014
http://dx.doi.org/10.1007/978-3-319-03398-3
A14-c4 Mikael Collan, The Pay-Off Method: Re-Inventing Investment Analysis - With numerical application
examples from different industries, CreateSpace Inc., 2012. 128 p. [ISBN 978-14-782-3842-3]. 2012
https://www.createspace.com/3936428
A14-c3 Jiuping Xu and Xiaoyang Zhou, Fuzzy-Like Multiple Objective Decision Making, Studies in Fuzziness
and Soft Computing, Volume 263/2011, Springer, [ISBN 978-3-642-16894-9], 2011.
http://dx.doi.org/10.1007/978-3-642-16895-6
A14-c2 Rudolf Seising, Views on Fuzzy Sets and Systems from Different Perspectives Philosophy and Logic,
Criticisms and Applications, Studies in Fuzziness and Soft Computing Series, Vol. 243/2009, Springer,
[ISBN 978-3-540-93801-9]. 2009
A14-c1 Fang Yong, Lai Kin Keung, Wang Shouyang, Fuzzy Portfolio Optimization: Theory and Methods,
Lecture Notes in Economics and Mathematical Systems, vol. 609/2008, Springer, Berlin; Heidelberg,
[ISBN 978-3-540-77925-4 ], pp. 131-141. 2008
http://dx.doi.org/10.1007/978-3-540-77926-1
Carlsson and Fullér introduced the notation of crisp possibilistic mean value and crisp possibilistic
variance of continuous possibility distributions. (page 27)
in Ph.D. dissertations
• Alessandro Buoni, Fraud Detection in the Banking Sector: A Multi-Agent Approach, Åbo Akademi University,Department of Information Technologies, [ISBN 978-952-12-2801-8]. 2012
http://www.doria.fi/handle/10024/84911
To obtain the connection degree for the pair li, vj , we calculate the f-weighted possibilistic mean
value of Aij, defined in Carlsson and Fuller (2001). (page 63)
• József Mezei, A quantitative view on fuzzy numbers, Department of Information Technologies (TUCS), Åbo
Akademi University, Åbo, Finland, [ISBN 978-952-12-2670-0]. 2011
http://www.doria.fi/handle/10024/72548
In 2001, Carlsson and Fullér defined the possibilistic mean value and variance of a fuzzy number
[9] and their definition only uses the concepts of possibility theory independently of probabilities.
These concepts have been studied and applied in many fields since their introduction. In the
following years, Carlsson, Fullér and Majlender introduced the notion of possibilistic covariance
and correlation [13, 39] using the same approach. (page 4)
• Qian Wang, Facilitating Brownfield Redevelopment Projects: Evaluation, Negotiation, and Policy. University
of Waterloo, Canada, 2011.
198
http://uwspace.uwaterloo.ca/bitstream/10012/5948/1/Wang_Qian.pdf
• Takashi Hasuike, Studies on Mathematical Methods for Asset Allocation Problems with Randomness and
Fuzziness. Graduate School of Information Science and Technology Osaka University, Japan. 2009
http://ir.library.osaka-u.ac.jp/metadb/up/LIBCLK003/f_2008-23046h.pdf
• Markku Heikkilä, R&D investment decisions with real options - Profitability and Decision Support. Åbo
Akademi University, Åbo, Finland, [ISBN 978-952-12-2379-2]. 2009
• Patrick Meyer, Progressive Methods in Multiple Criteria Decision Analysis, Faculte de Droit, d’Economie et
de Finance. Universite du Luxembourg. 2007
http://citeseerx.ist.psu.edu/
viewdoc/download?doi=10.1.1.124.9749&rep=rep1&type=pdf
Let us first introduce the concept of possibilistic mean (see [Carlsson and Fullér, DP87] for further
details). Recall that in Section 6.3.1 we considered the membership function of a fuzzy number x̃
as a possibility distribution. (page 123)
• Fokrul Alom Mazarbhuiya, Mining temporal patterns in datasets, Department of Computer Science and Application, Gauhati University, India. 2007
http://hdl.handle.net/10603/69139
• Elcin Kentel, Uncertainty Modeling Health Risk Assessment and Groundwater Resources Management. Georgia Institute of Technology, August 2006
http://hdl.handle.net/1853/11584
Many new theories are emerging in the area of uncertainty modeling with non-probabilistic and
hybrid methods (Carlsson and Fullér 2001; Ferson and Ginzburg 1996; Fortemps and Roubens
1996; Guyonnet et al. 2005; Helton 2004; Moens and Vandepitte 2005; Oberkampf et al. 2004;
Tonon et al. 2001). When the source and nature of available information is appropriate using these
emerging methods in modeling natural systems is the future goal of our research. (page 280)
• Péter Majlender, A Normative Approach to Possibility Theory and Soft Decision Support, Turku Centre for
Computer Science, Institute for Advanced Management Systems Research, Åbo Akademi University, No
54, [ISBN 952-12-1409-0]. 2004
A fundamental approach, based on the view of fuzzy numbers as possibility distributions instead
of probability distributions, has been presented by Carlsson and Fullér in 2001, where they déned
the interval-valued mean of fuzzy numbers [9]. Introducing the concept of interval-valued possibilistic mean as a closed interval bounded by the lower and upper possibilistic mean values of
a fuzzy number, they proved that it is always a proper subset of the interval-valued probabilistic
mean. This relationship shows that points with small membership degrees are considered less important in possibilis- tic sense than in probabilistic sense. More importantly, Carlsson and Fullér
introduced the notations of crisp possibilistic mean value and crisp possibilistic variance of possibility distributions and showed that they are consistent with the extension principle. (pages 32-33)
• Mikael Collan, Giga-Investments: Modelling the Valuation of Very Large Industrial Real Investments Institute
for Advanced Management Systems Research, Ph.D. Dissertation, Turku Centre for Computer Science
(TUCS), Dissertations, No. 57, [ISBN 952-12-1441-4], November 2004
http://mpra.ub.uni-muenchen.de/4328/1/MPRA_paper_4328.pdf
We use the possibilistic mean value of S0 and X (crisp), as defined in (Carlsson and Fullér, 2001a),
within the model for calculation of d1 and d2 . (page 52)
• Vincent Labatut, RESEAUX CAUSAUX PROBABILISTES A GRANDE ECHELLE : UN NOUVEAU
FORMALISME POUR LA MODELISATION DU TRAITEMENT DE L’INFORMATION CEREBRALE,
UNIVERSITE TOULOUSE III - PAUL SABATIER. 2003
http://tel.archives-ouvertes.fr/docs/00/04/64/26/PDF/tel-00005190.pdf
199
[A15] Christer Carlsson and Robert Fullér, Optimization under fuzzy if-then rules, FUZZY SETS AND SYSTEMS,
119(2001) 111-120. [MR1810565]. doi 10.1016/S0165-0114(98)00465-5
in journals
2016
A15-c38 Edit Toth-Laufer, Andras Rövid, Marta Takacs, Error calculation of the HOSVD-based rule base
reduction in hierarchical fuzzy systems, FUZZY SETS AND SYSTEMS (to appear). 2016
http://dx.doi.org/10.1016/j.fss.2015.12.018
The usage of the fuzzy approach is limited in the real time and adaptive systems, because the
number of the input parameters (consequently, the number of the rules) increases the complexity
exponentially [16]. While the usage of fuzzy approach is justified for medical-related applications,
because it is well-suited for these tasks, due to the fact that medicine uses linguistic descriptions,
which can be well represented by the fuzzy linguistic variables [17, A15].
2014
A15-c37 XI Yong-sheng, LIU Zhen-juan, LI Hong-guang, Operational Optimization of Distillation Columns
Based on Fuzzy Mathematical Programming, Computer Simulation, 31(2014), number 1, pp. 378-382.
2014
http://dx.doi.org/10.3969/j.issn.1006-9348.2014.01.085
A15-c36 Keyvan Shahgholian, Davoud Jafari, Hossein Kalantari, Saeid Kalantari, Seyed Farshad Forghani,
Investigation of Regional Development Level with Fuzzy Approach ( Case Study: Sistan and Baluchistan
Province, Iran ), Reef Resources Assessment and Management Technical Paper, 40(2014), number 2, pp.
18-23. 2014
http://behaviorsciences.com/wrramt/wp-content/uploads/2014/03/3-Forghani.pdf
A15-c35 Lurong W, Lin J, Bizhi W, Qidi W, Development of fuzzy controller of intelligent traffic light based
on BP neutral network, International Journal of Control and Automation, 7(2014), number 9, pp. 247-256.
2014
http://dx.doi.org/10.14257/ijca.2014.7.9.21
A15-c34 Xi Y, Liu Z, Li H, An approach for mathematical programming with fuzzy rules and its engineering
applications, Beijing Huagong Daxue Xuebao (Ziran Kexueban)/Journal of Beijing University of Chemical
Technology (Natural Science Edition) 41: (1) pp. 101-105. 2014
Scopus: 84893589584
A15-c33 David Philip McArthur, Sylvia Encheva, Inge Thorsen, Predicting with a small amount of data: An
application of fuzzy reasoning to regional disparities, Journal of Economic Studies, 41(2014), number 1,
pp. 12-28. 2014
Scopus: 84893277826
2013
A15-c32 ZENG Shengda, WU Lurong, JING Lin, WU Bizhi, Study on Monte Carlo Simulation of Intelligent
Traffic Lights Based on Fuzzy Control Theory Sensors & Transducers, 156(2013, Number 9, pp. 211-216.
2013
Firstly, through the theoretical analysis and construction of traffic light fuzzy neural network of
traffic flow, we establish the expert fuzzy control rule library; and by constant adjustment and
learning in the MATLAB fuzzy system (FIS) [11]-[A15], we achieve the queue length membership function and green light delay membership function value and map out the corresponding
membership function diagram [4], as shown in Fig. 4: (page 214)
2012
200
A15-c31 Sylvia Encheva, Reasoning With Non-Binary Logics, World Academy of Science, Engineering and
Technology, 67(2012), pp. 143-146. 2012
https://waset.org/journals/waset/v67/v67-25.pdf
A15-c30 R. Ramkumar, A. Tamilarasi, T. Devi, Intelligent Control for Job Shop Scheduling using Soft Computing, EUROPEAN JOURNAL OF SCIENTIFIC RESEARCH, 71(2012), number 3, pp. 364-373. 2012
http://www.europeanjournalofscientificresearch.com/ISSUES/EJSR_71_3_06.pdf
Fuzzy Logic incorporates a simple, rule-based IF . . . THEN . . . approach to a solving control problem rather than attempting to model a system mathematically [Christer Carlsson et al., 2001].
The Fuzzy Logic model is empirically-based, relying on an operator’s experience rather than their
technical understanding of the system. (page 365)
2011
A15-c29 Sanjay Jain, Adarsh Mangal, P R Parihar, Solution of fuzzy linear fractional programming problem,
OPSEARCH, 48(2011), number 2, pp. 129-135. 2011
http://dx.doi.org/10.1007/s12597-011-0043-4
2010
A15-c28 Mohammad H. Sabour; Mohammad F. Foghani, Design of Semi-composite Pressure Vessel using
Fuzzy and FEM, APPLIED COMPOSITE MATERIALS, 17(2010), issue 2, pp. 175-182. 2010
http://dx.doi.org/10.1007/s10443-009-9114-6
2009
A15-c27 Sylvia Encheva, Sharil Tumin, Problem Identification Based on Fuzzy Functions, WSEAS TRANSACTIONS ON ADVANCES IN ENGINEERING EDUCATION, 6(2009), pp. 111-120. 2009
http://www.wseas.us/e-library/transactions/education/2009/29-490.pdf
2008
A15-c26 Sanjay Jain and Kailash Lachhwani, Sum of Linear and Fractional Multiobjective Programming Problem under Fuzzy Rules Constraints, AUSTRALIAN JOURNAL OF BASIC AND APPLIED SCIENCES,
2(2008), number 4, pp. 1204-1208. 2008
http://www.insinet.net/ajbas/2008/1204-1208.pdf
2006
A15-c25 RETNO KUSWANDARI, M ALI SHARIFI, M BUCE SALEH, AGGREGATION METHODS FOR
ASSESING THE SUSTAINABILITY OF FOREST MANAGEMENT, TROPICAL FOREST MANAGEMENT JOURNAL, 12(2006), issue 2, pp. 1-14. 2006
http://katalog.perpustakaan.ipb.ac.id/jurnale/files/MHT061202rku.pdf
In Fuzzy Reasoning method knowledge is represented by IF-THEN linguistic rules. Real values
are transformed into linguistic values by an operation called fuzzification. Then simulation of
the evolution of the overall system is represented by rules of the form of IF (antecedents) - THEN
(consequent), where the implication operator THEN and the connectives AND among antecedents
are fuzzy. The antecedent part of the rules contains some linguistic values of the decision variables,
and the consequence part consists of a linguistic value of the objective function (Carlsson and
Fuller, 2001). (page 4)
2005
A15-c24 Jorge R Rodrı́guez, Mara R Méndez, Eugenio F Carrasco, Optimization Under Fuzzy If-Then Rules
Using Stochastic Algorithms COMPUTER AIDED CHEMICAL ENGINEERING, 20(2005), pp. 181-186.
2005
http://dx.doi.org/10.1016/S1570-7946(05)80152-X
201
More recently, Carlsson and Fullér (2001) suggested the use of Tsukamoto’s fuzzy reasoning
method to determine the crisp functional relationship between the objective function and the decision variables, and solved the resulting non-linear programming problem (NLP) to find and
optimal solution. (pages 181-182)
Fuzzy optimization problems can be stated and solved in many different ways. Usually, the authors
consider optimization problems of the form (Carlsson and Fullér, 2001):
min f (x) subject to x ∈ X,
where f or/and X are defined by fuzzy terms. Then they are searching for a crisp x∗ which (in
certain) sense minimizes f under the fuzzy constraints X. (page 182)
Let us take a particular example, recently studied by Carlsson and Fullér (2001), which considers
the following optimization problem: (page 183)
A15-c23 Deng-Feng Li, An approach to fuzzy multiattribute decision making under uncertainty, INFORMATION SCIENCES, 169 (2005) 97-112. 2005
http://dx.doi.org/10.1016/j.ins.2003.12.007
A15-c22 D.R. Pavel, Optimisation with Fuzzy Linguistic Rules, Annals of ”Dunarea de Jos” University of
Galati. Fascicle II, Mathematics, Physics, Theoretical Mechanics. Vol. XXVIII, no. XXIII, pp. 77-80.
2005
http://www.phys.ugal.ro/Annals_Fascicle_2/year2005/Annals2005Abstract.pdf
2004
A15-c21 Ho Jung et al, Intelligent Fault Diagnosis System of Aircraft Electrommunication Based on Compensated Neural Network and Its Applications, COMPUTER MEASUREMENT & CONTROL, 12(2004),
number 4, pp. (in Chinese). 2004
http://d.wanfangdata.com.cn/Periodical_jsjzdclykz200404008.aspx
A15-c20 Chen Q, Li S -Y, Xi Y -G, Optimization of production process under if-then rules and its application to
reheating furnace CONTROL AND DECISION, 19(2004), number 10, pp. 1097-1100 (in Chinese). 2004
in proceedings and edited volumes
2014
A15-c13 Stefan Preitl, Radu-Emil Precup, Zsuzsa Preitl, Alexandra-Iulia Stinean, Mircea-Bogdan Radac,
Claudia-Adina Dragos, Control Algorithms for Plants Operating Under Variable Conditions, Applications,
in: Advances in Soft Computing, Intelligent Robotics and Control, vol 8/2014, Topics in Intelligent Engineering and Informatics, Springer Verlag, [ISBN 978-3-319-05944-0], pp. 3-39. 2014
http://dx.doi.org/10.1007/978-3-319-05945-7_1
2013
A15-c12 Song Fuchao, Hou Wenkui, Shi Long, The information-enhanced fault diagnosis system design of
avionics power supply module, 2013 International Conference on Quality, Reliability, Risk, Maintenance,
and Safety Engineering (QR2MSE), [Print ISBN: 978-1-4799-1014-4], pp. 1758-1761. 2013
http://dx.doi.org/10.1109/QR2MSE.2013.6625916
A15-c11 Chakraborty Debjani, Guha Debashree, Multi-objective optimization based on fuzzy if-then rules,
2013 IEEE International Conference on Fuzzy Systems (FUZZ), IEEE Computer Society Press, [Print
ISBN 978-1-4799-0020-6], pp. 1-7. 2013.
http://dx.doi.org/10.1109/FUZZ-IEEE.2013.6622519
2012
202
A15-c10 Sylvia Encheva, Individual Paths in Self-evaluation Processes, Computational Intelligence and Intelligent Systems, Communications in Computer and Information Science, Springer, [ISBN 978-3-642-342899], pp. 425-431. 2012
http://dx.doi.org/10.1007/978-3-642-34289-9_47
2011
A15-c9 Sylvia Encheva, Approximate Reasoning and Conceptual Structures, Second International Conference
on Ubiquitous Computing and Multimedia Applications, April 13-15, 2011, Daejeon, South-Korea, Communications in Computer and Information Science, vol. 150/2011, Springer, [ISBN: 978-3-642-20974-1],
pp. 100-109. 2011
http://dx.doi.org/10.1007/978-3-642-20975-8_11
A15-c8 S. Encheva, Some Fuzzy Logic Based Predictions, 10th WSEAS International Conference on Artificial
Intelligence, Knowledge Engineering and Data Bases., February 20-22, 2011, Cambridge, England, pp.
176-180. 2011
http://www.wseas.us/e-library/conferences/2011/Cambridge/AIKED/AIKED-30.pdf
2010
A15-c7 Sylvia Encheva and Sharil Tumin, Fuzzy Knowledge Processing for Unveiling Correlations between
Preliminary Knowledge and the Outcome of Learning New Knowledge, in: Magued Iskander, Vikram
Kapila and Mohammad A. Karim eds., Technological Developments in Education and Automation, Springer,
[ISBN 978-90-481-3655-1], pp. 179-182. 2010
http://dx.doi.org/10.1007/978-90-481-3656-8_34
2009
A15-c6 Sylvia Encheva, Frequent Sets Mining for Problem Identification, Proceedings of the 5th WSEAS/IASME
International Conference on Educational Technologies, July 01-03, 2009, Trenerife, Spain, Recent Advances in Computer Engineering Series, [ISBN 978-960-474-092-5], pp. 33-37. 2009
ISI:000268848000003
http://www.wseas.us/e-library/conferences/2009/lalaguna/EDUTE/EDUTE-03.pdf
A15-c5 Sylvia Encheva, Concepts in fuzzy logics, in: Proceedings of the 10th WSEAS international Conference
on Automation & information, Prague, Czech Republic, March 23 - 25, 2009, N. E. Mastorakis, A. Croitoru,
V. E. Balas, E. Son, and V. Mladenov, Eds. Recent Advances In Electrical Engineering. World Scientific
and Engineering Academy and Society (WSEAS), Stevens Point, Wisconsin, pp. 300-304. 2009
A15-c4 Sylvia Encheva, Sharil Tumin, Progress Evaluation Based on Fuzzy Relationships, in: New Directions
in Intelligent Interactive Multimedia Systems and Services - 2, Studies in Computational Intelligence series,
vol. 226/2009, Springer, [ISBN 978-3-642-02936-3], pp. 201-210. 2009
http://dx.doi.org/10.1007/978-3-642-02937-0_18
2007
A15-c3 S. Ari, H.E. Khalifa, J.F. Dannenhoffer, P. Wilcoxen, C. Isik, Generating a fuzzy logic system from
optimized numerical models, Annual Conference of the North American Fuzzy Information Processing
Society - NAFIPS, art. no. 4271105, pp. 452-457. 2007
http://dx.doi.org/10.1109/NAFIPS.2007.383882
in books
203
A15-c2 Eleytherios Mantelas, CaFe: Cellular Automata - Fuzzy Engine, LAP Lambert Academic Publishing,
(ISBN 978-3-8443-2996-4). 2011
This type of fuzzy systems provides an intuitive form of knowledge base which easy to maintain
and (Castellano et al. 2003). Another approach is the Sugeno system (Takagi & Sugeno 1985,
Sugeno & Kang 1986) also known as TSK. These systems return an output in numerical form
rather than fuzzy sets providing thus a more simple syntax that appears to perform better for
linear phenomena (Carlsson & Fuller 2001). Regardless the approach, a fuzzy system includes the
following stages (Cox 1994, Kirschfink 1999, Hatzichristos & Potamias 2004):
A15-c1 Plamen P. Angelov, Evolving Rule-Based Models: A Tool for Design of Flexible Adaptive Systems,
Series: Studies in Fuzziness and Soft Computing , Vol. 92, Springer, [ISBN: 978-3-7908-1457-6], 2002.
in Ph.D. dissertations
• Purshottam Kumar, AN ECO - FRIENDLY AND AFFORDABLE MELTING TECHNIQUE FOR CAST
IRON FOUNDRIES, Faculty of Engineering, Dayalbagh Educational Institute, India. 2014
http://hdl.handle.net/10603/42326
[A16] Christer Carlsson and Robert Fullér, Multiobjective linguistic optimization, FUZZY SETS AND SYSTEMS,
115(2000) 5-10. [Zbl.0978.90081]. doi 10.1016/S0165-0114(99)00020-2
in journals
2016
A17-c59 Sahu AK, Datta S, Mahapatra SS, Evaluation and selection of resilient suppliers in fuzzy environment:
Exploration of fuzzy-VIKOR, BENCHMARKING: AN INTERNATIONAL JOURNAL, 23: (3) pp. 651673. 2016
http://dx.doi.org/10.1108/BIJ-11-2014-0109
A16-c42 Hsin-Cheng Lin, Chen-Song Wang, Juei Chao Chen, Berlin Wu, New statistical analysis in marketing
research with fuzzy data, JOURNAL OF BUSINESS RESEARCH, 69: (6), pp. 2176-2181. 2016
http://dx.doi.org/10.1016/j.jbusres.2015.12.026
After the study of fuzzy graphic rating scale (FGRS) by Hesketh, Pryor, Gleitzman, and Hesketh
(1988); Costas, Maranon, and Cabrera (1994) chose 100 university students as a sample of the
research. They found that FGRS fits in the feature of human psychology. Herrera and HerreraViedma (2000) present the steps of linguistic decision analysis under linguistic information. Building on fuzzy number, their statements show different degrees of possibilities to express linguistics;
however, studies must consider whether the response will produce the same fuzzy number. Building on the similarity of the linguistic concept, they present a formula of fuzzy association degree.
Carlsson and Fuller (2000a); Carlsson and Fuller (2000b); Chiang, Chow, and Wang (2000), and
Herrera and Herrera-Viedma (2000) discussed many concepts regarding the computation of fuzzy
linguistic worthy broadcasting. (page 2177)
2014
A16-c41 Manfeng Liu, Haiping Ren, A New Intuitionistic Fuzzy Entropy and Application in Multi-Attribute
Decision Making, Information 5(2014), number 4, pp. 587-601. 2014
http://dx.doi.org/10.3390/info5040587
For multi-attributes decision problems, such as supplier selection, material selection in manufactory and evaluation of firms safety performance, it is necessary to consider many factors simultaneously. This makes the problem become complex and it is difficult to find the best solution.
We often notice that, in many situations, crisp data are inadequate or insufficient for setting up a
model of realistic decision problems [A16,2], because the problems are vague or fuzzy in nature
and could not be represented by crisp numbers. (page 587)
204
A16-c40 Berlin Wu, Hung T Nguyen, New Statistical Analysis on the Marketing Research and Efficiency
Evaluation with Fuzzy Data, Management Decision, 52(2014), number 2. Paper 17111910. 2014
http://www.emeraldinsight.com/journals.htm?articleid=17111910
A16-c39 Beggas M, Médini L, Laforest F, Laskri MT, Towards an ideal service QoS in fuzzy logic-based
adaptation planning middleware, Journal of Systems and Software 92: (1) pp. 71-81. 2014
http://dx.doi.org/10.1016/j.jss.2013.07.023
Classical fuzzy control system, which is a fuzzy expert control system (Pernici and Siadat, 2011;
Carlsson and Fullér, 2000) that deduces the satisfaction degree of a given service variant in a given
context condition. For that, it has five inputs: three context parameters and two QoS parameters
and one output: satisfaction degree. Context parameters are: bandwidth, battery level and video
zone size. QoS parameters are: image quality and sequence rate. (page 78)
A16-c38 Zhen-Hua Che, Tzu-An Chiang, Y C Kuo, Zhihua Cui, Hybrid Algorithms for Fuzzy Reverse Supply
Chain Network Design, The Scientific World Journal, 2014(2014). Article ID 497109. 2014
http://dx.doi.org/10.1155/2014/497109
Carlsson & Fuller [A16] suggested that, the fuzzy reasoning method could be used to determine
the relationship between decision variables and objective functions in order to determine the optimal solution of fuzzy multi-objective linguistics.
2013
A16-c37 Fang Y, An approach to evaluating the effectiveness of customer relationship management with interval
grey linguistic variables, INTERNATIONAL JOURNAL OF DIGITAL CONTENT TECHNOLOGY AND
ITS APPLICATIONS, 7(2013), number 2, pp. 372-378. 2013
http://dx.doi.org/10.4156/jdcta.vol7.issue2.45
A16-c36 Adel Hatami-Marbini, Madjid Tavana, Saber Saati, Fatemeh Kangi, A fuzzy group linear programming technique for multidimentional analysis of preference, JOURNAL OF INTELLIGENT AND FUZZY
SYSTEMS, 25(2013), number 3, pp. 723-735. 2013
http://dx.doi.org/10.3233/IFS-120678
2012
A16-c35 Berlin Wu, Mei Fen Liu, Zhongyu Wang, EFFICIENCY EVALUATION IN TIME MANAGEMENT
FOR SCHOOL DMINISTRATION WITH FUZZY DATA, International Journal of Innovative Computing,
Information and Control, 8(2012), number 8, pp. 5787-5895. 2012
http://www.ijicic.org/isme10-15.pdf
Liu and Song [11] developed one type of measurement whose linguistic is similar to semantic
proximity. Based on the similarity of linguistic concept, they presented a formula of fuzzy association degree. Liu and Song [11] used the information of botany as an example to illustrate and
analyze the categorical similarity of rare plant in the ecology. Carlsson and Fuller [A17], Carlsson and Fuller [A16], Chiang, Chow and Wang [14], Herrera and Herrera-Viedma [10], Dubois
and Prade [15] had discussed many concepts about the computation of fuzzy linguistic and these
concepts are worthy to broadcast. (page 5788)
A16-c34 Yan Ch, iDong-hong Wang, An Approach to Evaluating the Computer Practice Course Reform Based
on Computer Multi-media Network Technique with 2-tuple Linguistic Information, INTERNATIONAL
JOURNAL OF ADVANCEMENTS IN COMPUTING TECHNOLOGY, 4(2012), number 7, pp. 102-109.
2012
http://dx.doi.org/10.4156/ijact.vol4.issue7.11
A16-c33 Hsieh C -S, Chen Y -W, Wu C -H, Huang T, Characteristics of fuzzy synthetic decision methods for
measuring student achievement, QUALITY AND QUANTITY, 46(2012), number 2, pp. 523-543. 2012
http://dx.doi.org/10.1007/s11135-010-9384-y
205
Carlsson and Fuller (2000) suggest using the fuzzy reasoning method to determine the relationship
between decision variables and objective function in discovering the best solution to fuzzy multiobjective linguistic problems. (page 527)
A16-c32 Ana X Halabi, Jairo R Montoya-Torres, Nelson Obregón, A Case Study of Group Decision Method
for Environmental Foresight and Water Resources Planning Using a Fuzzy Approach, GROUP DECISION
AND NEGOTIATION, 21(2012), number 2, pp. 205-232. 2012
http://dx.doi.org/10.1007/s10726-011-9269-z
2009
A16-c31 Deng-Feng Li, Relative ratio method for multiple attribute decision making problems, INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY AND DECISION MAKING, 8(2009), pp.
289-311. 2009
http://dx.doi.org/10.1142/S0219622009003405
A16-c30 Ching Min Sun, Cynthia H.F. Wu, To choose or not? That is the question of memberships: Fuzzy
statistical analysis as a new analytical approach in child language research, JOURNAL OF MODELLING
IN MANAGEMENT, 4(2009), pp. 55-71. 2009
http://dx.doi.org/10.1108/17465660910943757
A16-c29 Zeshui Xu, An Interactive Approach to Multiple Attribute Group Decision Making with Multigranular Uncertain Linguistic Information, GROUP DECISION AND NEGOTIATION, 18(2009) pp. 119-145.
2009
http://dx.doi.org/10.1007/s10726-008-9131-0
2008
A16-c28 Zhang Ling, Multi-attribute decision making based on association theory research, MANAGEMENT
REVIEW, 20(2008), number 5, pp. 51-57 (in Chinese). 2008
http://www.cqvip.com/qk/96815a/2008005/27274741.html
A16-c27 Deng-Feng Li, Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment, FUZZY OPTIMIZATION AND DECISION MAKING, 7(2008) 17-34. 2008
http://dx.doi.org/10.1007/s10700-007-9022-x
In the LINMAP, all the decision data are known precisely or given as crisp values. However, under
many conditions, crisp data are inadequate or insufficient to model real-life decision problems
(Carlsson and Fullér 2000; Delgado et al. 1992; Li 2005a; Li and Yang 2004). (page 18)
2007
A16-c26 Li DF, Sun T, Fuzzy linear programming approach to multi-attribute decision-making with linguistic
variables and incomplete information, ADVANCES IN COMPLEX SYSTEMS, 10: (4), pp. 505-525. 2007
A16-c25 D.-F. Li, A fuzzy closeness approach to fuzzy multi-attribute decision making, FUZZY OPTIMIZATION AND DECISION MAKING, 6 (3), pp. 237-254. 2007
http://dx.doi.org/10.1007/s10700-007-9010-1
Indeed, human judgments are vague or fuzzy in nature and thus it may not be appropriate to
represent them by precise numerical values. A more realistic approach could be to use linguistic
variables to model human judgments (Carlsson and Fullér 2000). (page 238)
A16-c24 D.-F. Li, Compromise ratio method for fuzzy multi-attribute group decision making, APPLIED SOFT
COMPUTING JOURNAL, 7(3), pp. 807-817. 2007
http://dx.doi.org/10.1016/j.asoc.2006.02.003
A16-c23 D.-F. Li, T. Sun, Fuzzy linmap method for multiattribute group decision making with linguistic
variables and incomplete information, INTERNATIONAL JOURNAL OF UNCERTAINTY, FUZZINESS
AND KNOWLEDGE-BASED SYSTEMS, 5(2), pp. 153-173. 2007
http://dx.doi.org/10.1142/S0218488507004509
206
A fuzzy multiattribute group decision making (FMGADM) problem is to find a best compromise
solution from all feasible alternatives assessed on multiple attributes, both quantitative and qualitative [10, 19, A16, 34]. (page 155)
A16-c22 Y.-H Lin., B. Wu, The comparisons and applications of traditional mode and fuzzy mode in quantitative research, WSEAS TRANSACTIONS ON MATHEMATICS, 6 (1), pp. 145-150. 2007
2006
A16-c21 Jianzhong Chen, Ying Liu A model and its application for uncertainly group decision making WORLD
JOURNAL OF MODELLING AND SIMULATION, 2: (1) pp. 45-54. 2006
http://www.worldacademicunion.com/journal/1746-7233WJMS/WJMSvol2no1paper5.pdf
A16-c20 Z. Xu, A practical procedure for group decision making under incomplete multiplicative linguistic
preference relations, Group Decision and Negotiation 15 (6), pp. 581-591. 2006
http://dx.doi.org/10.1007/s10726-006-9034-x
A16-c19 M.R. Gholamian, S.M.T. Fatemi Ghomi M. Ghazanfari, A hybrid intelligent system for multiobjective
decision making problems, Computers and Industrial Engineering, 51 (1), pp. 26-43. 2006
http://dx.doi.org/10.1016/j.cie.2006.06.011
Fuzzy rule bases are also used to extract unstructured objective functions of decision maker (Carlsson & Fullér, 2000). (page 27)
A16-c18 H.-C. Xia, D.-F. Li, J.-Y., Zhou, J.-M. Wang, Fuzzy LINMAP method for multiattribute decision
making under fuzzy environments, Journal of Computer and System Sciences, 72 (4), pp. 741-759. 2006
http://dx.doi.org/10.1016/j.jcss.2005.11.001
A16-c17 M.R. Gholamian, S.M.T. Fatemi Ghomi M. Ghazanfari, A hybrid computational intelligent system
for multiobjective supplier selection problem, International Journal of Management and Decision Making,
7 (2-3), pp. 216-233. 2006
http://dx.doi.org/10.1016/j.cie.2006.06.011
A16-c16 Bogdana Pop and Ioan Dzitac, On choosing proper linguistic description for fractional functions in
fuzzy optimization, ACTA UNIVERSITATIS APULENSIS, 12(2006) 63-72. 2006
http://www.emis.de/journals/AUA/acta12/Bogdana Pop gata/art_extins.pdf
In [A16] Carlsson et al. considered a mathematical programming problem in which the functional
relationship between the decision variables and the objective function is not completely known
and built a knowledge-base which consists of a block of fuzzy if-then rules, where the antecedent
part of the rules contains some linguistic values of the decision variables, and the consequence
part is a linear combination of the crisp values of the decision variables. (page 64)
2005
A16-c15 B. Pop, I. Dzitac, On a fuzzy linguistic approach to solving multiple criteria fractional programming problem, INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL,
1(2005) 381-385. 2005
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A16-c14 M.S.A. Osman et al, Multiple criteria decision-making theory applications and software: A literature
review, Advances in Modelling and Analysis, B 48 (1-2), pp. 1-35. 2005
A16-c13 Deng-Feng Li, An approach to fuzzy multiattribute decision making under uncertainty, INFORMATION SCIENCES, 169 (2005) 97-112. 2005
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A16-c12 Deng-Feng Li, Jian-Bo Yang, Fuzzy linear programming technique for multiattribute group decision
making in fuzzy environments, INFORMATION SCIENCES, 158(2004) 263-275. 2004
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A16-c11 Liu MeiFen, Wu Berlin, All Work and No Play Makes Jack a Dull Leader? Impact Evaluation with
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A16-c10 Ching-Sen Hsieh, Chih-Hung Wu, Tao Huang, Yu-Wen Chen, Analyzing the Characteristics of Fuzzy
Synthetic Decision Methods on Evaluating Student’s Academic Achievement - An empirical investigation
of junior high school students in Taiwan, International Conference on Artificial Intelligence and Computational Intelligence, November 07-November 08, 2009, Shanghai, China, [ISBN 978-0-7695-3816-7], pp.
491-495. 2009
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A16-c9 Yuan-Horng Lin and Berlin Wu, Fuzzy mode and its applications in survey research, in: G. R. Dattatreya
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A16-c8 Tatjana Petkovic and Risto Lahdelma, Multi-source multi-attribute data fusion, in: Timo Honkela,
Ville Könönen, Matti Pöllä, and Olli Simula, editors, Proceedings of AKRR’05, International and Interdisciplinary Conference on Adaptive Knowledge Representation and Reasoning, pp. 26-32, Espoo, Finland,
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Conference of the North American Fuzzy Information Processing Society - NAFIPS 2005, art. no. 1548631,
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A16-c1 Z. Xu, Linguistic Decision Making: Theory and Methods, Springer,[ISBN 978-3-642-29439-6]. 2013
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in Ph.D. dissertations
• Anoop Kumar Sahu, Supply Chain Performance Appraisement and Benchmarking for Manufacturing Industries:
Emphasis on Traditional, Green, Flexible and Resilient Supply Chain along with Supplier Selection. Department
of Mechanical Engineering National Institute of Technology, India. 2015
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[A17] Christer Carlsson and Robert Fullér, Benchmarking in linguistic importance weighted aggregations, FUZZY
SETS AND SYSTEMS, 114(2000) 35-41. [Zbl.0963.91028]. doi 10.1016/S0165-0114(98)00047-5
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2016
A17-c58 Hajlaoui Sonia, Halouani Nesrin, Habib Chabouchoub, Development of some linguistic aggregation
operators with conservation of interaction between criteria and their application in multiple attribute group
decision problems, TOP: AN OFFICIAL JOURNAL OF THE SPANISH SOCIETY OF STATISTICS AND
OPERATIONS RESEARCH (to appear). 2016
http://dx.doi.org/10.1007/s11750-016-0412-5
Dealing now with linguistic information, a great number of approaches have been proposed, which
can be classified into three categories according to Bonissone and Decker (1986). The first one
is based on the extension principle (Bonissone and Decker 1986; Degani and Bortolan 1988)
that basically supports the semantics of the linguistic terms, through making operations on the
fuzzy numbers, so that a numerical result can be obtained. But, it is hard for the DM to interpret
its involvement according to the pre-determined linguistic term set. The second approach is the
symbolic method (Delgado et al. 1993) that uses the indexes of the linguistic terms to make
computations. Therefore, the initial linguistic terms usually can not exactly be equivalent to the
results. Accordingly, an approximation process has to be developed to express the result in the
initial domain. This leads not only to the consequent loss of information but also to the lack of
precision (Carlsson and Fuller 2000).
A17-c57 Hsin-Cheng Lin, Chen-Song Wang, Juei Chao Chen, Berlin Wu, New statistical analysis in marketing
research with fuzzy data, JOURNAL OF BUSINESS RESEARCH, Volume 69, Issue 6, Pages 2176-2181.
2016
http://dx.doi.org/10.1016/j.jbusres.2015.12.026
After the study of fuzzy graphic rating scale (FGRS) by Hesketh, Pryor, Gleitzman, and Hesketh
(1988); Costas, Maranon, and Cabrera (1994) chose 100 university students as a sample of the
research. They found that FGRS fits in the feature of human psychology. Herrera and HerreraViedma (2000) present the steps of linguistic decision analysis under linguistic information. Building on fuzzy number, their statements show different degrees of possibilities to express linguistics;
however, studies must consider whether the response will produce the same fuzzy number. Building on the similarity of the linguistic concept, they present a formula of fuzzy association degree.
Carlsson and Fuller (2000a); Carlsson and Fuller (2000b); Chiang, Chow, and Wang (2000), and
Herrera and Herrera-Viedma (2000) discussed many concepts regarding the computation of fuzzy
linguistic worthy broadcasting. (page 2177)
A17-c56 Wen-Tao Guo, Van-Nam Huynh, Yoshiteru Nakamori, A proportional 3-tuple fuzzy linguistic representation model for screening new product projects, JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS
ENGINEERING, 25: (1) pp. 1-22. 2016t
http://dx.doi.org/10.1007/s11518-015-5269-x
2015
A17-c55 José M Merigó, Daniel Palacios-Marqués, Shouzhen Zeng, Subjective and objective information in linguistic multi-criteria group decision making, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH,
248(2015), number 2, pp. 522-531. 2015
http://dx.doi.org/10.1016/j.ejor.2015.06.063
Weighted aggregation functions are those functions that weight the aggregation process by using
the weighted average. That is, aggregations that considers different degrees of importance for the
available information. Some examples are the aggregation with the weighted average (Carlsson
& Fuller, 2000; Grabisch et al. 2011), belief structures that use the weighted average (Merigó et
al. 2010) and the weighted OWA (WOWA) operator (Torra, 1997). The weighted average can be
defined as follows. (page 524)
209
A17-c54 Changhui Yang, Qiang Zhang, Shuai Ding, An evaluation method for innovation capability based on
uncertain linguistic variables, Applied Mathematics and Computation 256(2015), pp. 160-174. 2015
http://dx.doi.org/10.1016/j.amc.2014.12.154
2014
A17-c53 Yang W-E, Wang X-F, Wang J-Q, Counted linguistic variable in decision-making, International Journal
of Fuzzy Systems, 16: (2) pp. 196-203. 2014
Scopus: 84904993617
However, a considerable problem in the existing CWW is that aggregating linguistic variables
sometimes does not result in a pre-identified linguistic term [2], especially when we aggregate
linguistic variables without normalized weights. The CWW result would be hard to understand in
these cases. This issue will decrease the efficiency of a linguistic decision model, because helping
decision-makers to better understand the decision procedure and consequence is a major objective
of decision analysis. But if we retranslate the CWW result to a pre-identified linguistic variable
approximately, the information will be lost unavoidably [A17]. (page 196)
A17-c52 Lee AS, The investigation into the influence of the features of furniture product design on consumers’
perceived value by fuzzy semantics, South African Journal of Business Management, 45: (1) pp. 79-93.
2014
Scopus: 84898762606
A17-c51 Wu Dongrui, A reconstruction decoder for computing with words, INFORMATION SCIENCES,
255(2014), number 10, pp. 1-15. 2014
http://dx.doi.org/10.1016/j.ins.2013.08.050
2013
A17-c50 Jin F-X, Huang T-M, Method for regulating consistency of linguistic judgment matrix, Xi Tong Gong
Cheng Yu Dian Zi Ji Shu/Systems Engineering and Electronics, 35(2013), number 7, pp. 1472-1476. 2013
http://dx.doi.org/10.3969/j.issn.1001-506X.2013.07.20
A17-c49 Yejun Xu, Panfeng Shi, Jose M Merigo, Huimin Wang, Some proportional 2-tuple geometric aggregation operators for linguistic decision making, JOURNAL OF INTELLIGENT AND FUZZY SYSTEMS,
25(2013), number 3, pp. 833-843. 2013
http://dx.doi.org/10.3233/IFS-130774
A17-c48 Y Ju, A Wang, Extension of VIKOR method for multi-criteria group decision making problem with
linguistic information, APPLIED MATHEMATICAL MODELLING, 37(2013), number 5, pp. 3112-3125.
2013
http://dx.doi.org/10.1016/j.apm.2012.07.035
The available approaches for dealing with linguistic terms can be classified into three categories
[23,24]: (1) The extension principle [25]; (2) The symbolic method [26]; and (3) The 2-tuple fuzzy
linguistic representation model [23]. In the former two approaches, an approximation process must
be developed to express the result in the initial expression domain, for the computation results
usually do not exactly match any of the initial linguistic terms. This produces the consequent loss
of information and hence the lack of precision [A17]. (page 3113)
2012
A17-c47 Berlin Wu, Mei Fen Liu, Zhongyu Wang, EFFICIENCY EVALUATION IN TIME MANAGEMENT
FOR SCHOOL ADMINISTRATION WITH FUZZY DATA, International Journal of Innovative Computing, Information and Control, 8(2012), number 8, pp. 5787-5895. 2012
http://www.ijicic.org/isme10-15.pdf
210
Liu and Song [11] developed one type of measurement whose linguistic is similar to semantic
proximity. Based on the similarity of linguistic concept, they presented a formula of fuzzy association degree. Liu and Song [11] used the information of botany as an example to illustrate and
analyze the categorical similarity of rare plant in the ecology. Carlsson and Fuller [A17], Carlsson and Fuller [A16], Chiang, Chow and Wang [14], Herrera and Herrera-Viedma [10], Dubois
and Prade [15] had discussed many concepts about the computation of fuzzy linguistic and these
concepts are worthy to broadcast. (page 5788)
A17-c46 Merigó J M, Gil-Lafuente A M, Zhou L -G, Chen H -Y Induced and Linguistic Generalized Aggregation Operators and Their Application in Linguistic Group Decision Making, Group Decision and
Negotiation 21(2012), number 4, pp. 531-549. 2012
http://dx.doi.org/10.1007/s10726-010-9225-3
A17-c45 Zheng Pei, Da Ruan, Jun Liu, Yang Xu, A linguistic aggregation operator with three kinds of weights
for nuclear safeguards evaluation, KNOWLEDGE-BASED SYSTEMS, 28(2012), pp. 19-26. 2012
http://dx.doi.org/10.1016/j.knosys.2011.10.016
A17-c44 Zhi-Ping Fan, Wei-Lan Suo, Bo Feng, Identifying risk factors of IT outsourcing using interdependent
information: An extended DEMATEL method, EXPERT SYSTEMS WITH APPLICATIONS, 39(2012),
number 3, pp. 3832-3840. 2012
http://dx.doi.org/10.1016/j.eswa.2011.09.092
In the former two approaches, the computation results usually do not exactly match any of the
initial linguistic terms, and then an approximation process must be developed to express the result
in the initial expression domain. This produces the consequent loss of information and hence
the lack of precision (Carlsson & Fuller, 2000). Whereas, the third kind of approach overcomes
the above limitations. The advantage of this approach is that linguistic term is managed as a
continuous range instead of a discrete one. The approach has no loss of information when it is
used to conduct the computation with linguistic terms. Therefore, the approach based on the 2tuple fuzzy linguistic representation model is more convenient and precise to deal with linguistic
terms in risk factor identification. (page 3834)
A17-c43 Ana X Halabi, Jairo R Montoya-Torres, Nelson Obregón, A Case Study of Group Decision Method
for Environmental Foresight and Water Resources Planning Using a Fuzzy Approach, GROUP DECISION
AND NEGOTIATION, 21(2012), number 2, pp. 205-232. 2012
http://dx.doi.org/10.1007/s10726-011-9269-z
2011
A17-c42 Chen Liu, Alejandro Ramirez-Serrano, Guofu Yin, Customer-driven product design and evaluation method for collaborative design environments, JOURNAL OF INTELLIGENT MANUFACTURING,
22(2011), number 5, pp. 751-764. 2011
http://dx.doi.org/10.1007/s10845-009-0334-2
The linguistic approach is an approximate technique, which represents qualitative aspects as linguistic values by means of linguistic variables (Carlsson and Fuller 2000; Xu 2005; Zadeh 1975).
(page 760)
A17-c41 Bo Feng, Wen-Li Li, Zhi-Ping Fan, Yang Liu, Assessing the intention level of service Adoption:
A 2-Tuple fuzzy linguistic Approach, INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING,
INFORMATION AND CONTROL, 7(2011), number 5(B), pp. 2579-2591. 2011
Scopus: 79956151063
A17-c40 Hong-Bin Yan; Van-Nam Huynh; Yoshiteru Nakamori, A probabilistic model for linguistic multiexpert decision making involving semantic overlapping, EXPERT SYSTEMS WITH APPLICATIONS,
38(2011), pp. 8901-8912. 2011
http://dx.doi.org/10.1016/j.eswa.2011.01.105
211
The idea is that the convex combination of linguistic labels resulting from two linguistic labels
should be an element in the set. In these two approaches, however, the results usually do not match
any of the initial linguistic labels, hence an approximation process must be developed to express
the result in the initial expression domain. This produces the consequent loss of information and
lack of precision (Carlsson & Fullér, 2000). (page 8901)
A17-c39 Hong-Bin Yan, Van-Nam Huynh, Yoshiteru Nakamori, Tetsuya Murai, On prioritized weighted aggregation in multi-criteria decision making, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), pp.
812-823. 2011
http://dx.doi.org/10.1016/j.eswa.2010.07.039
Remark. It is of interest noting that in a different context, Carlsson and Fullér (2000) concentrated
on the issue of linguistic importance weighted aggregations, where the importance is interpreted as
benchmarks. In their study, when both importance weights and ratings of criteria are given as crisp
numbers, Łukasiewicz implication is also used to compute the benchmark achievement. In case
of fuzzy numbers, a possibilistic approach is presented to compute the benchmark achievement.
In addition, Carlsson and Fullér’s method only focus on symmetric triangular fuzzy numbers.
The benchmark used in our aggregation operator has similar but different meaning with Carlsson and Fullér’s method (Carlsson & Fullér, 2000). Firstly, as there are various types of fuzzy
numbers, specifying only symmetric triangular fuzzy numbers will not be appropriate in practical
applications. Secondly, instead of the possibility interpretation, the benchmark has a probability
interpretation lying in the philosophical root of Simon’s bounded rationality (Simon, 1955) as well
as represents the S-shaped value function (Kahneman & Tversky, 1979). Finally, benchmark in
Carlsson and Fullér’s work (Carlsson & Fullér, 2000) and ours has different meanings. Carlsson
and Fullér viewed importance weight as benchmark of criteria satisfaction, whereas our method
considered DM’s requirements. (page 820)
2010
A17-c38 Xiaohan Yu, Zeshui Xu, Xiumei Zhang, Uniformization of multigranular linguistic labels and their application to group decision making, JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING, 19(2010), number 3, pp. 257-276. 2010
http://dx.doi.org/10.1007/s11518-010-5137-7
In some multiple attribute decision making problems of real world, decision makers are accustomed to provide their preferences over alternatives expressed in linguistic forms, such as ”good”,
”fair”, ”poor”, etc., because of the complexity and uncertainty of practical things, and fuzzy human thinking. In order to assess alternatives using linguistic information conveniently, linguistic
label sets have been researched in lots of papers (Yager 1995, 1998, Carlsson & Fullér 2000, Herrera & Herrera-Viedma 1995, Torra 1996, Xu 2004a, etc.). In the following, we briefly review
some basic knowledge about linguistic label sets. (page 259)
2009
A17-c37 Zhi-Ping Fan, Bo Feng, Wei-Lan Suo, A fuzzy linguistic method for evaluating collaboration satisfaction of NPD team using mutual-evaluation information, INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS, 122(2009), Issue 2, December 2009, Pages 547-557. 2009
http://dx.doi.org/10.1016/j.ijpe.2009.05.018
In the former two categories of methods, the results usually do not exactly match any of the initial
linguistic terms, and then an approximation process must be developed to express the result in the
initial expression domain. This produces the consequent loss of information and hence the lack of
precision (Carlsson and Fuller, 2000), whereas, the third category of methods overcome the above
limitations. The main advantage of this representation model is to be continuous in its domain. It
can express any counting of information in the universe of the discourse. Therefore, the third one
is more convenient and precise to deal with linguistic terms. (pages 550-551)
212
A17-c36 Ching Min Sun, Cynthia H.F. Wu, To choose or not? That is the question of memberships: Fuzzy
statistical analysis as a new analytical approach in child language research, JOURNAL OF MODELLING
IN MANAGEMENT, 4(2009), pp. 55-71. 2009
http://dx.doi.org/10.1108/17465660910943757
A17-c34 Zeshui Xu, An Interactive Approach to Multiple Attribute Group Decision Making with Multigranular Uncertain Linguistic Information, GROUP DECISION AND NEGOTIATION, 18(2009) pp. 119-145.
2009
http://dx.doi.org/10.1007/s10726-008-9131-0
2008
A17-c33 Sadiq R, Tesfamariam S, Developing environmental indices using fuzzy numbers ordered weighted
averaging (FN-OWA) operators, STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT, 22: (4), pp. 495-505. 2008
http://dx.doi.org/10.1007/s00477-007-0151-0
A17-c32 JIN Wei; FU Chao, A group decision making model with phased feedback based on 2-tuple and
T-OWA operator, JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY (NATURAL SCIENCE),
32(2008), number 6, pp. 851-856 (in Chinese). 2008
http://d.wanfangdata.com.cn/Periodical_hfgydxxb200906020.aspx
A17-c31 Wang, J.-H., Hao, J., An approach to computing with words based on canonical characteristic values
of linguistic labels, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 15(4), pp. 593-604. 2007
http://dx.doi.org/10.1109/TFUZZ.2006.889844
In such approach, it will either result in large-scale increases in computational complexity [14] or
make the results do not exactly match any of the initial linguistic terms (and then an approximation
process must be developed to express the result in the initial expression domain which induces the
consequent loss of information and hence the lack of precision [A17]). (page 593)
A17-c30 Yeh, D.-Y., Cheng, C.-H., Chi, M.-L., A modified two-tuple FLC model for evaluating the performance
of SCM: By the Six Sigma DMAIC process, APPLIED SOFT COMPUTING JOURNAL, 7(3), pp. 10271034. 2007
http://dx.doi.org/10.1016/j.asoc.2006.06.008
A17-c29 Pei, Z., Ruan, D., Xu, Y., Liu, J., Handling linguistic Web information based on a multi-agent system,
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 22 (5), pp. 435-453. 2007
http://dx.doi.org/10.1002/int.v22:5
A17-c28 Herrera-Viedma, E., Lopez-Herrera, A.G., Luque, M., Porcel, C., A fuzzy linguistic IRS model based
on a 2-tuple fuzzy linguistic approach, INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS
AND KNOWLEDGE-BASED SYSTEMS, 15 (2), pp. 225-250. 2007
http://dx.doi.org/10.1142/S0218488507004534
In this approach, the query weights and document scores are ordered linguistic terms. These models of IRSs are affected by the two characteristic problems of ordinal fuzzy linguistic modelling
[25, A17]:
• The loss of precision: The ordinal fuzzy linguistic approach works with discrete linguistic
domains and this implies some limitations in the representation of the linguistic information,
e.g. to represent the relevance degrees.
• The loss of information: Aggregation operators of ordinal linguistic information use approximation operations in their definitions (e.g. rounding operation), and thus this produces the
consequent loss of information.
(page 226)
A17-c27 Lin, Y.-H., Wu, B., The comparisons and applications of traditional mode and fuzzy mode in quantitative research, WSEAS Transactions on Mathematics, 6 (2007), number 1, pp. 145-150. 2007
213
A17-c26 Jiang, Y.-P., Xing, Y.-N., Consistency analysis of two-tuple linguistic judgement matrix, JOURNAL
OF NORTHEASTERN UNIVERSITY (NATURAL SCIENCE) , 28 (1), pp. 129-132 (in Chinese). 2007
http://d.wanfangdata.com.cn/Periodical_dbdxxb200701033.aspx
A17-c25 Xu ZS, A practical procedure for group decision making under incomplete multiplicative linguistic
preference relations GROUP DECISION AND NEGOTIATION 15 (6): 581-591 NOV 2006
http://dx.doi.org/10.1007/s10726-006-9034-x
A17-c24 Xu ZS, A note on linguistic hybrid arithmetic averaging operator in multiple attribute group decision
making with linguistic information, GROUP DECISION AND NEGOTIATION 15 (6): 593-604 NOV
2006
http://dx.doi.org/10.1007/s10726-005-9008-4
A17-c23 Wang JH, Hao JY A new version of 2-tuple. fuzzy linguistic, representation model for computing with
words IEEE TRANSACTIONS ON FUZZY SYSTEMS 14 (3): 435-445 JUN 2006
http://dx.doi.org/10.1109/TFUZZ.2006.876337
In the former two approaches, the results usually do not match any of the initial linguistic terms,
then an approximation process must be developed to express the result in the initial expression
domain. This produces the consequent loss of information and hence the lack of precision [A17].
(page 435)
A17-c22 Xu ZS, A direct approach to group decision making with uncertain additive linguistic preference
relations, FUZZY OPTIMIZATION AND DECISION MAKING, 5 (1), pp. 21-32. 2006
http://dx.doi.org/10.1007/s10700-005-4913-1
A17-c21 Xu ZS, Deviation measures of linguistic preference relations in group decision making, OMEGAINTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 33 (3): 249-254 JUN 2005
http://dx.doi.org/10.1016/j.omega.2004.04.008
A17-c20 Huynh VN, Nakamori Y, A satisfactory-oriented approach to multiexpert decision-making with linguistic assessments, IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS
35 (2): 184-196 APR 2005
http://dx.doi.org/10.1109/TSMCB.2004.842248
The issue of weighted aggregation has been studied extensively in, e.g., [A17], [10], [12], [22][24], [48], [51], and [52]. (page 184)
A17-c19 Xu ZS, EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations, INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED
SYSTEMS 12 (6): 791-810 DEC 2004
http://dx.doi.org/ 10.1142/S0218488504003211
The traditional approaches are mainly as follows: (i) The approach based on extension [21, 22]
principle, which presents the results by means of the fuzzy numbers obtained from the fuzzy
arithmetic computations based on the extension principle, or by means of linguistic labels computed from the fuzzy numbers obtained using a [32, 23] linguistic approximation process. (ii)
The method based on symbols [23], whose results are inherently linguistic labels due to either the
operators used, basically max and min operators [26] or because in the computations on the order
index there exists an approximation by means of the round operator [27, 32]. Both the approaches
develop an approximation process to express linguistic formation and hence the lack of precision
[A17]. (page 792)
A17-c18 Fan, Z.-P., Jiang, Y.-P., Judgment method for the satisfying consistency of linguistic judgment matrix,
CONTROL AND DECISION, 19(2004), number 8, pp. 903-906 (in Chinese). 2004
http://d.wanfangdata.com.cn/Periodical_kzyjc200408014.aspx
A17-c17 Luo XD, Lee JHM, Leung HF, et al. Prioritised fuzzy constraint satisfaction problems: axioms,
instantiation and validation, FUZZY SETS AND SYSTEMS, 136 (2): 151-188 JUN 1 2003.
http://dx.doi.org/10.1016/S0165-0114(02)00385-8
214
A17-c16 F. Herrera, E. Lopez and M.A. Rodrı́guez A linguistic decision model for promotion mix management
solved with genetic algorithms, FUZZY SETS AND SYSTEMS, 131(2002) 47-61. 2002
http://dx.doi.org/10.1016/S0165-0114(01)00254-8
A17-c15 Herrera F, Martinez L, A 2-tuple fuzzy linguistic representation model for computing with words,
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 8(6): 746-752 DEC 2000.
http://ieeexplore.ieee.org/iel5/91/19275/00890332.pdf?arnumber=890332
These computational techniques are as follows.
• The first one is based on the extension principle [2], [6]. It makes operations on the fuzzy
numbers that support the semantics of the linguistic terms.
• The second one is the symbolic method [5]. It makes computations on the indexes of the
linguistic terms.
In both approaches, the results usually do not exactly match any of the initial linguistic terms, then
an approximation process must be developed to express the result in the initial expression domain.
This produces the consequent loss of information and hence the lack of precision [A17]. (page
746)
in proceedings and edited volumes
A17-c14 D Wu, A reconstruction decoder for the perceptual computer, 2012 IEEE International Conference on
Fuzzy Systems, June 10-15, 2012, Brisbane, [ISBN 978-146731506-7], pp. 1-8. Article number 6250766.
2012
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A17-c13 Y Qin, Z Pei, THE PROPERTIES OF WOWA OPERATORS, In: 9th International FLINS Conference
on Computational Intelligence: Foundations and Applications, August 2-4, 2010, Emei, China, [ISBN:
978-981-4324-69-4], pp. 565-570. 2010
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A17-c12 Jiafeng Ji; Zheng Pei, Obtaining complex linguistic rules from decision information system based
genetic algorithms, IEEE International Conference on Granular Computing, 17-19 August 2009, Lushan
mountain/Nanchang, China, art. no. 5255114, pp. 268-273. 2009
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A17-c11 J H Dai, J Li, Judgment and improving of consistency for linguistic judgment matrix, 4th International
Conference on Innovation and Management, December 5-6, 2007, Ube, Japan, [ISBN: 978-7-5629-26108], pp. 2295-2299. 2007
A17-c10 V N Huynh, Y Nakamori, Group decision making with linguistic information using a probabilitybased approach and OWA operators, 2007 IEEE INTERNATIONAL CONFERENCE ON SYSTEMS,
MAN AND CYBERNETICS, October 7-10, 2007, Montreal, Canada, [ISBN: 978-1-4244-0990-7], pp.
2018-2023. 2007
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A17-c9 Van-Nam Huynh; Yoshiteru Nakamori, Group decision making with linguistic information using a
probability-based approach and OWA operators, IEEE International Conference on Systems, Man and Cybernetics, 7-10 Oct. 2007, [doi 10.1109/ICSMC.2007.4413915], pp. 570-575. 2007
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A17-c8 Rakus-Andersson, E. Approximation of clock-like point sets, in: Fuzzy and Rough Techniques in
Medical Diagnosis and Medication, Studies in Fuzziness and Soft Computing, Springer, vol. 212, pp.
155-181+183-189. 2007
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A17-c7 Zheng, P., Liangzhong, Y. A new aggregation operator of linguistic information and its properties, 2006
IEEE International Conference on Granular Computing, art. no. 1635846, pp. 486-489. 2006
215
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The management of linguistic information implies the use of operators of comparison and aggregation. Many researchers have studied operators of comparison and aggregation [7] - [A17]. In
[7], the linguistic weighted averaging (LWA) operator is presented as a tool to aggregate linguistic
weighted information: namely, linguistic information which has associated different linguistic importance degrees. Nowadays, the fuzzy linguistic approach has been successfully applied to many
different problems such as decision, information retrieval, medicine, and education etc [A17] [15]. (page 486)
A17-c6 Yuan-Horng Lin and Berlin Wu, Fuzzy mode and its applications in survey research, in: G. R. Dattatreya
ed., Proceedings of the 10th WSEAS International Conference on Applied Mathematics, 2006, pp. 286-291.
2006
A17-c5 Van-Nam Huynh and Yoshiteru Nakamori, Multi-Expert Decision-Making with Linguistic Information:
A Probabilistic-Based Model, in: Proceedings of the 38th Hawaii International Conference on System
Sciences, [file name: 22680091c]. 2005
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A17-c4 Pei Z, Du YJ, Yi LZ, et al. Obtaining a complex linguistic data summaries from database based on a new
linguistic aggregation operator, in: Computational Intelligence and Bioinspired Systems, 8th International
Workshop on Artificial Neural Networks, IWANN 2005, LECTURE NOTES IN COMPUTER SCIENCE,
vol. 3512, pp. 771-778. 2005
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A17-c3 Huynh, V.N., Nguyen, C.H., Nakamori, Y. MEDM in general multi-granular hierarchical linguistic contexts based on the 2-tuples linguistic model, 2005 IEEE International Conference on Granular Computing,
2005, art. no. 1547338, pp. 482-487. 2005
http://dx.doi.org/10.1109/GRC.2005.1547338
In linguistic decision analysis, irrespective of the membership function based semantics or ordered
structure based semantics of the linguistic term set, one has to face the problem of weighted aggregation of linguistic information. The issue of weighted aggregation has been studied extensively
in, e.g., [A17], [4], [14]. (page 482)
A17-c2 Xu, Z.-S. An ideal point based approach to multi-criteria decision making with uncertain linguistic
information in:) Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 4,
pp. 2078-2082. 2004
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A17-c1 Peneva, V., Popchev, I. Fuzzy decisions in soft computing, 2nd International IEEE Conference on Intelligent Systems - Proceedings, vol. 2, pp. 606-609. 2004
http://dx.doi.org/10.1109/IS.2004.1344821
. . . aggregation operators of linguistic weighted information [2], [21], e.g. the Linguistic Weighted
Averaging (LWA) operator, the Weighted Min and Weighted Max operators [19], [A17]; (page
607)
in Ph.D. dissertations
• Mohammed Amine Abchir, Vers une sémantique oue: application a la geolocalisation, Université Paris 8 Vincennes Saint-Denis. 2013
http://tel.archives-ouvertes.fr/docs/00/90/98/28/PDF/TheseAbchirFinale.pdf
[A18] Christer Carlsson and Robert Fullér, Fuzzy multiple criteria decision making: Recent developments, FUZZY
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in journals
2016
A18-c324 Hong-yu Zhang, Rui Zhou, Jian-qiang Wang, Xiao-hong Chen, An FMCDM approach to purchasing
decision-making based on cloud model and prospect theory in e-commerce, INTERNATIONAL JOURNAL
OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 9: (4) pp. 676-688. 2016
http://dx.doi.org/10.1080/18756891.2016.1204116
A18-c323 L Zhang, Y Xu, C H Yeh, L He, D Q Zhou, Bi-TOPSIS: A New Multicriteria Decision Making
Method for Interrelated Criteria With Bipolar Measurement, IEEE Transactions on Systems, Man, and
Cybernetics Part A: Systems and Humans (to appear). 2016
http://dx.doi.org/10.1109/TSMC.2016.2573582
A18-c322 Hassanali Faraji Sabokbar, Ali Hosseini, Audrius Banaitis, Nerija Banaitiene, A NOVEL SORTING
METHOD TOPSIS-SORT: AN APPLICATION FOR TEHRAN ENVIRONMENTAL QUALITY EVALUATION, E & M EKONOMIE A MANAGEMENT, 2: pp. 87-104. 2016
http://dx.doi.org/10.15240/tul/001/2016-2-006
Multiple Criteria Decision Making (MCDM) is all about making choices in the presence of multiple, generally conflicting criteria. Many real- life problems are multi-objective by nature that
requires evaluation of more than one criterion. Therefore, MCDM has become an important issue and many researches are devoted to help people make better decision (Montibeller & Franco,
2011; Wang et al., 2015). However, there is no consensus between authors on classification and
categorization of MCDM methods. Vincke (1992) suggest the following categories: (1) multiple attribute theory, (2) outranking methods, and (3) interactive methods. Apart from the above,
Carlsson & Fuller (1996) classifies these methods into four quite distinct groups: (1) the outranking methods, (2) the value and utility theory approaches, (3) the interactive multiple objective
programming approach, and (4) the methods based on group decision and negotiation theory.
A18-c321 Fabio De Felice, Antonella Petrillo, Strategic management of the new product development process,
International Journal of Service and Computing Oriented Manufacturing, 2: (2) pp. 124-137. 2016
http://dx.doi.org/10.1504/IJSCOM.2016.076436
A18-c320 Bonnini S, Multivariate Approach for Comparative Evaluations of Customer Satisfaction with Application to Transport Services, COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 45: (5) pp. 1554-1568. 2016
http://dx.doi.org/10.1080/03610918.2014.941685
A18-c320 Hwai-Hui Fu, Shian-Yang Tzeng Applying Fuzzy Multiple Criteria Decision Making approach to
establish safety-management system for hot spring hotels, ASIA PACIFIC JOURNAL OF TOURISM RESEARCH (to appear). 2016
http://dx.doi.org/10.1080/10941665.2016.1175487
A18-c319 A Afsordegan, M Snchez, N Agell, S Zahedi, L V Cremades, Decision making under uncertainty using a qualitative TOPSIS method for selecting sustainable energy alternatives, INTERNATIONAL JOURNAL OF ENVIRONMENTAL SCIENCE AND TECHNOLOGY (to appear). 2016
http://dx.doi.org/10.1007/s13762-016-0982-7
Multi-Criteria Decision-Making (MCDM) approaches, introduced in the early 1970s, are powerful
tools used for evaluating problems and addressing the process of making decisions with multiple
criteria. MCDM involves structuring decision processes, defining and selecting alternatives, determining criteria formulations and weights, applying value judgments and evaluating the results
to make decisions in design, or selecting alternatives with respect to multiple conflicting criteria
(Carlsson and Fuller 1996; Yilmaz and Dadeviren 2011).
A18-c318 Hanratty TP, Allison Newcomb E, Hammell RJ II, Richardson JT, Mittrick MR, A fuzzy-based approach to support decision making in complex military environments, International Journal of Intelligent
Information Technologies, 12(2016), number 1, pp. 1-30. 2016
http://dx.doi.org/10.4018/IJIIT.2016010101
217
A18-c317 Ivana Olivkova, EVALUATION OF QUALITY PUBLIC TRANSPORT CRITERIA IN TERMS OF
PASSENGER SATISFACTION, TRANSPORT AND TELECOMMUNICATION, 17: (1) pp. 18-27. 2016
The situation arises while evaluating urban public transport quality criteria that part of the criteria
is of quantitative nature (quantitative criteria values are expressed in the metric scale) and another part is of qualitative nature (qualitative criteria values are expressed in ordinal metric scale)
(Moreno and Fidelis and Ramos, 2014). Metrization of ordinal scales, i.e. assigning points from
five-point scale as a tool for assessing passengers’ attitudes and opinions, is the way to achieve
possibilities of statistic evaluation, common for metric scales, while using ordinal scales (Carlsson
and Fuller, 1996). (page 19)
http://dx.doi.org/10.1515/ttj-2016-0003
A18-c316 Ankit Gupta, Shruti Kohli, OWA Operator-Based Hybrid Framework for Outlier Reduction in Web
Mining, INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS (to appear). 2016
http://dx.doi.org/10.1002/int.21810
A18-c315 Ankit Gupta, Shruti Kohli, An MCDM approach towards handling outliers in web data: a case study
using OWA operators, ARTIFICIAL INTELLIGENCE REVIEW (to appear). 2016
http://dx.doi.org/10.1007/s10462-015-9456-4
A18-c314 Fatih Cavdur Merve Kose, A Fuzzy Logic and Binary-Goal Programming-Based Approach for Solving the Exam Timetabling Problem to Create a Balanced-Exam Schedule, INTERNATIONAL JOURNAL
OF FUZZY SYSTEMS, 18(2016), issue 1, pp. 119-129. 2016
http://dx.doi.org/10.1007/s40815-015-0046-z
2015
A18-c313 N M Stefano, N Casarotto Filho, L G L Vergara, R U G Rocha, COPRAS (Complex Proportional
Assessment): State of the Art Research and its Applications, IEEE Latin America Transactions, 13: (12)
pp. 3899-3906. 2015
http://dx.doi.org/10.1109/TLA.2015.7404925
A18-c312 Torralvo FA, Sanchez RV, An application of multicriteria decision methodology to religious heritage
conservation: The case of the Cathedral of Jerez de la Frontera (CADIZ), European Journal of Science and
Theology, 11: (2) pp. 95-105. 2015
Scopus: 84934277928
A18-c311 Ta-Chung Chu, Solving Fuzzy MCDM by Subtracting Benefit Criteria from Cost Criteria, Universal
Journal of Management, 3: (8) pp. 337-345. 2015
http://dx.doi.org/10.13189/ujm.2015.030805
Fuzzy multiple criteria decision-making (MCDM) is a powerful tool for evaluation and selection
of alternatives versus different criteria, where ratings of alternatives under different criteria and the
importance weights of criteria are usually assessed in fuzzy numbers or linguistic values (Zadeh,
1975) represented by fuzzy numbers. Numerous fuzzy MCDM methods have been investigated.
A review of many of these methods can be found in Carlsson and Fuller (1996), Ribeiro (1996),
Chu and Varma (2012), and Moghimi and Anvari (2014). (page 317)
A18-c310 Dana Balas-Timar, Sonia Ignat, Conceptual Applicant Screening Model with Fuzzy Logic in Industrial Organizational Contexts, PROCEDIA - SOCIAL AND BEHAVIORAL SCIENCES, 203(2015), pp.
257-263. 2015
http://dx.doi.org/10.1016/j.sbspro.2015.08.291
Since then the number of contributions for more systematic and rational decision making with
multiple criteria, has continued to grow. Along with Bellman, Zadeh, and Zimmermann introducing fuzzy sets into the field, there emerged a new family of methods to deal with problems which
had been unsolvable with standard MCDM techniques (Carlsson, C., & Fullér, R., 1996). (page
258)
218
A18-c309 Enrique Herrera-Viedma, Fuzzy Sets and Fuzzy Logic in Multi-Criteria Decision Making. The 50th
Anniversary of Prof. Lotfi Zadeh’s Theory: Introduction, TECHNOLOGICAL AND ECONOMIC DEVELOPMENT OF ECONOMY, 21(2015), number 5, pp. 677-683. 2015
http://dx.doi.org/10.3846/20294913.2015.1084956
A18-c308 Seema, Darshan Kumar, A decision support system for IMS selection based on fuzzy VIKOR method,
INTERNATIONAL JOURNAL OF SERVICES AND OPERATIONS MANAGEMENT, 22: (1) pp. 86100. 2015
http://dx.doi.org/10.1504/IJSOM.2015.070884
A18-c307 Hamdani Hamdani, Retantyo Wardoyo, A review on fuzzy multi-criteria decision making land clearing for oil palm plantation, International Journal of Advnces in Intelligent Informatics (to appear). 2015
http://www.ijain.org/index.php/IJAIN/article/view/26
A18-c306 Ivana Olivková, Model for Measuring Passenger Satisfaction and Assessing Mass Transit Quality,
JOURNAL OF PUBLIC TRANSPORTATION, 18(2015), number 3, pp. 52-70. 2015
All criteria listed in Table 1 have the same bearing from the passenger viewpoint. A lower nominal
value of the given criteria is preferred (more useful) in the eyes of the passenger than a higher
nominal value, and vice versa. The mass transit quality criteria can be divided into two groups
according to manner of assessment (Carlsson and Fuller 1996):
a) Quantitative criteria - Nominal values were set objectively based on data on the individual
components of transit time listed by passengers in the questionnaire.
b) Qualitative criteria - Nominal values were set subjectively by a passenger opinion survey on a
five-point scale, where 1 is the best score (most desirable) and 5 is the worst score (least desirable).
(page 55)
A18-c305 Chandrashekhar Meshram, Shyam Sundar Agrawal, Multi-criteria Decision Making Using Genetic
Algorithmic Approach in Computer Simulation Models, International Journal of Hybrid Information Technology, 8(2015), number 6, pp. 17-24. 2015
http://dx.doi.org/10.14257/ijhit.2015.8.6.02
A18-c304 Mehrbakhsh Nilashi et al, A knowledge-based expert system for assessing the performance level of
green buildings KNOWLEDGE-BASED SYSTEMS, 86(2015), issue 1, pp. 194-209. 2015
http://dx.doi.org/10.1016/j.knosys.2015.06.009s
A18-c303 Hamdani, Khabib Mustofa, A Review: Clearing Oil Palm Plantation with Multi-Stakeholder Model,
International Journal of Computer Applications, 115: (2) pp. 1-10. 2015
http://dx.doi.org/10.5120/20120-2181
A18-302 Jurate SKUPIENE, Multiple Criteria Decision Methods in Informatics Olympiads, Olympiads in Informatics, 9(2015), pp. 173-191. 2015
http://dx.doi.org/10.15388/ioi.2015.14
Among MCDA approaches explicitly meant for solving group decision making problems there
are techniques which foresee negotiation theory, working with group dynamics, etc. References
to that can be found in (Carlsson and Fullér, 1996; Lu et al., 2007). (page 184)
A18-c301 Juhani Iivari, Making Sense of the History of Information Systems Research 1975-1999: A View of
Highly Cited Papers, COMMUNICATIONS OF THE ASSOCIATION FOR INFORMATION SYSTEMS,
36(2015), number 4, pp. 516-561. 2015
http://aisel.aisnet.org/cais/vol36/iss1/25
A18-c300 Cengiz Kahraman, Sezi Cevik Onar, Basar Oztaysi, Fuzzy Multicriteria Decision-Making: A Literature Review, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE, 8(2015), number
4, pp. 637-666. 2015
http://dx.doi.org/10.1080/18756891.2015.1046325
A18-c299 Peng Wang, Yang Li, Yong-Hu Wang, Zhou-Quan Zhu, A New Method Based on TOPSIS and
Response Surface Method for MCDM Problems with Interval Numbers, MATHEMATICAL PROBLEMS
IN ENGINEERING, 2015(2015), Paper 938535. 11 p. 2015
http://dx.doi.org/10.1155/2015/938535
219
A18-c298 Debdas Ghosh, Debjani Chakraborty, A method for capturing the entire fuzzy non-dominated set of
a fuzzy multi-criteria optimization problem, FUZZY SETS AND SYSTEMS, 272(2015), pp. 1-29. 2015
http://dx.doi.org/10.1016/j.fss.2015.02.005
Excellent surveys of developments in fuzzy decision-making problems can be found in [A18, 27].
A18-c297 Chandrashekhar Meshram, Shyam Sundar Agrawal, Fuzzy Multi-criteria Decision Making associated
with Risk and Confidence Attributes Bulletin of Electrical Engineering and Informatics, 4(2015), number
3, pp. 441-. 2015
http://dx.doi.org/10.12928/eei.v4i3.441
A18-c296 P Georgieva, I Popchev, FUZZY LOGIC AND VISUAL ANALYTICS APPLIED TO CORPORATE
SOCIAL RESPONSIBILITY CASE STUDY MANAGING FINANCIAL INVESTMENTS, Proceedings
of the Bulgarian Academy of Sciences, 68(2015), number 1, pp. 87-94. 2015
http://www.science-bas.org/Comptes%20rendus/Special/2015/No-1/01-12.pdf
A18-c296 Jen-Hsiang Chen, Fahmida Abedin, Kuo-Ming Chao, Nick Godwin, Yinsheng Li, Chen-Fang Tsai,
A hybrid model for cloud providers and consumers to agree on QoS of cloud services, Future Generation
Computer Systems (to appear). 2015
http://dx.doi.org/10.1016/j.future.2014.12.003
A18-c295 Sanjay Kumar Dubey, Sumit Pandey, Measurement of Usability of Office Application Using a Fuzzy
Multi-Criteria Technique, International Journal of Information Technology and Computer Science, 7(2015),
number 4, pp. 64-72. 2015
http://www.mecs-press.org/ijitcs/ijitcs-v7-n4/IJITCS-V7-N4-7.pdf
A18-c294 Hanbin Kuang, D Marc Kilgour, Keith W Hipel, Grey-based PROMETHEE II with application to
evaluation of source water protection strategies, Information Sciences, 294(2015), pp. 376-389. 2015
http://dx.doi.org/10.1016/j.ins.2014.09.035
Handling uncertainty with reasonable and systematic methodologies has been a prominent topic
in MCDA [65] over the past two decades. At the theoretical level, there have been many surveys
of related techniques, such as Chen et al.’s [12] comprehensive survey of fuzzy discrete MCDA
methods; Carlsson and Fuller’s [10] summary of the development of fuzzy MCDA in the 1990s,
focusing on the interdependence of criteria in MCDM; Greco et al.’s [24, 25] proposed MCDA
procedures related to rough set theory; Ian N. Durbach’s [34] review of technical tools used in
uncertain MCDA and simulation experiment to assess some simplified value function approaches.
(pages 377-378)
2014
A18-c293 Mohammadfam I, Nikoomaram H, Lotfi FH, Mansouri N, Rajabi AA, Mohammadfam F, Development of a Decision-Making Model for Selecting and Prioritizing Accident Analysis Techniques in Process
Industries JOURNAL OF SCIENTIFIC & INDUSTRIAL RESEARCH, 73: (8) pp. 517-520. 2014
A18-c292 Eun-Sung Chung, Yeonjoo Kim, Development of fuzzy multi-criteria approach to prioritize locations
of treated wastewater use considering climate change scenarios, Journal of Environmental Management,
146(2014), pp. 505-516. 2014
http://dx.doi.org/10.1016/j.jenvman.2014.08.013
A18-c291 Hossein Safari, Mehdi Ajalli, A Fuzzy TOPSIS Approach for Ranking of Supplier: A Case Study
of ABZARSAZI Company, Social and Basic Sciences Research Review 2(2014), number 10, pp. 429-444.
2014
http://www.absronline.org/journals/index.php/sbsrr/article/viewFile/341/358
A18-c290 Sami A. Moufti, Tarek Zayed, Saleh Abu Dabous, Defect-Based Condition Assessment of Concrete Bridges: Fuzzy Hierarchical Evidential Reasoning Approach, TRANSPORTATION RESEARCH
RECORD: JOURNAL OF THE TRANSPORTATION RESEARCH BOARD, Volume 2431 / Maintenance
and Preservation 2014, pp. 88-96. 2014
http://dx.doi.org/10.3141/2431-12
220
A18-c289 Olalekan S. Akinola, Kazeem A. Nosiru, Factors Influencing Students’ Performance in Computer
Programming: A Fuzzy Set Operations Approach, International Journal of Advances in Engineering &
Technology, 7(2014), issue 4, pp. 1141-1149. 2014
http://www.e-ijaet.org/media/3I22-IJAET0721391_v7_iss4_1141-1149.pdf
A18-c288 Divyajyothi M, G Rachappa, D H Rao, A Scenario Based Approach For Dealing With Challenges In
A Pervasive Computing Environment, International Journal on Computational Sciences & Applications 4:
(2) pp. 31-38. 2014
http://dx.doi.org/10.5121/ijcsa.2014.4204
A18-c287 V Anandan, G Uthra, Defuzzification by Area of Region and Decision Making Using Hurwicz Criteria for Fuzzy Numbers, Applied Mathematical Sciences, 8(2014), number 63, pp. 3145-3154. 2014
http://dx.doi.org/10.12988/ams.2014.44294
A18-c286 Bahir Dar, Contractor Selection for Enhancing the Quality of University Education in Nigeria using
the Hamming Distance, AFRREV IJAH, 3: (10) pp. 272-284. 2014
http://dx.doi.org/10.4314/ijah.v3i2.17
The fuzzy set theory is used to solve the rigorous theory of approximation and vagueness based on
generalization of standard set theory to fuzzy set or numbers (Carlsson and Fuller, 1996). (page
275)
A18-c285 Nogues Soledad, Gonzalez-Gonzalez Esther, Multi-criteria impacts assessment for ranking highway
projects in Northwest Spain, Transportation Research Part A: Policy and Practice, 65(2014), pp. 80-91.
2014
http://dx.doi.org/10.1016/j.tra.2014.04.008
Multi-Criteria Decision-Making (MCDM) includes two categories of decision-making: based on
multiple attributes (MADM), which involves the selection of alternatives according to the significance of the defining attributes; and based on multiple objectives (MODM), which constitutes
mathematically programming the achievement of multiple objectives simultaneously (Almeida
Ribeiro, 1996; Carlsson and Fullér, 1996; Jankwoski, 1995; and Malczewski, 2006). (page 81)
A18-c284 Yashon Ouma, M Kirichu, C Yaban, Ryutaro Tateishi, Optimization of urban highway bypass horizontal alignment: a methodological overview of intelligent spatial MCDA approach using fuzzy AHP and
GIS, Advances in Civil Engineering. Paper 182568. 2014
http://dx.doi.org/10.1155/2014/182568
Carlsson and Fullér [4] classified MCDM methods into four distinct types including: (i) outranking, (ii) utility theory, (iii) multiple objective programming, and (iv) group decision and negotiation theory.
A18-c283 Yu Chen, Longcang Shu, Thomas J Burbey, An Integrated Risk Assessment Model of TownshipScaled Land Subsidence Based on an Evidential Reasoning Algorithm and Fuzzy Set Theory, Risk Analysis,
34: (4) pp. 656-669. 2014
http://dx.doi.org/10.1111/risa.12182
A18-c282 Shashikant Tamrakar, Ajay Tiwari, Praveen Tandon, Application of Analytical HIERARCHY Process
in Industries, International Journal of Modern Engineering Research, 4: (3) pp. 28-32. 2014
http://www.ijmer.com/papers/Vol4_Issue3/Version-3/IJMER-43032832.pdf
A18-c281 L.A. Gardashova Application of DEO Method to Solving Fuzzy Multiobjective Optimal Control
Problem, Volume 2014 (2014), Article ID 971894, 7 pages
http://dx.doi.org/10.1155/2014/971894
A18-c280 A Martin, T Miranda Lakshmi, V Prasanna Venkatesan, An information delivery model for banking
business, International Journal of Information Management, 34(2014), number 2, pp. 139-150. 2014
http://dx.doi.org/10.1016/j.ijinfomgt.2013.12.003
221
A18-c279 Ahmed Ali Baig, Risza Ruzli, Estimation of Failure Probability Using Fault Tree Analysis and Fuzzy
Logic for CO2 Transmission, International Journal of Environmental Science and Development, 5(20014),
number 1, pp. 26-30. 2014
http://dx.doi.org/10.7763/IJESD.2014.V5.445
A18-c278 Chang L, Ouzrout Y, Nongaillard A, Bouras A, Jiliu Z, Multi-criteria decision making based on trust
and reputation in supply chain, International Journal of Production Economics, 147: (PART B) 362-372.
2014
http://dx.doi.org/10.1016/j.ijpe.2013.04.014
When multiple indicators satisfy requirements at the same time, human always feel confused and
do not know how to make a decision. As a useful tool, the research on multi-criteria decision
making has covered many scientific domains (Carlsson and Fullér, 1996) and a large number of
multi-criteria decision making approaches have been proposed. (page 366)
A18-c277 Mohsen Varmazyar, Behrouz Nouri, A fuzzy AHP approach for employee recruitment, Decision
Science Letters, 3(2014), pp. 27-36. 2014
http://dx.doi.org/10.5267/j.dsl.2013.08.006
Carlsson and Fuller (1996) apply fuzzy set theory in the decision making process under multicriteria with incomplete or vague information. The primary objective of this work is that many
real world problems have more to do with fuzziness than randomness as the major source of
imprecision (Zimmerman, 1992). In such situations, it is more suitable to manage uncertainty by
fuzzy set theory than by probability theory (Whalen, 1993). (page 28)
A18-c276 LLAMAS B, MAZADIEGO L F, ELIO J, ORTEGA M F, GRANDIA F, RINCONES M, SYSTEMATIC APPROACH FOR THE SELECTION OF MONITORING TECHNOLOGIES IN CO2 GEOLOGICAL STORAGE PROJECTS. APPLICATION OF MULTICRITERIA DECISION MAKING, Global
NEST Journal 16: (1) 36-42. 2014
Analytical Hierarchy Process (AHP) is one of the most extended and powerful MCDM. Nowadays it has become a method used by several companies in solving various multi-criteria problems, ranking these in the following categories: selection, prioritization and assessment, provision
of resources against a standard assessment, management and quality management and strategic
planning (Saaty, 1980; 1986; Carlsson and Fullér 1996). (pages 38-39)
A18-c275 Debdas Ghosh, Debjani Chakraborty, A new method to obtain fuzzy Pareto set of fuzzy multi-criteria
optimization problems, JOURNAL OF INTELLIGENT AND FUZZY SYSTEMS, Volume 26, Issue 3,
2014, Pages 1223-1234. 2014
http://dx.doi.org/10.3233/IFS-130808
2013
A18-c274 Aishwarya Singh and Sanjay Kumar Dubey, Evaluation of Usability Using Soft Computing Technique, International Journal of Scientific & Engineering Research, 4(2013), issue 12, pp. 162-166. 2013
http://www.ijser.org/researchpaper
%255CEvaluation-of-Usability-Using-Soft-Computing-Technique.pdf
A18-c273 Kua-Hsin Peng, Gwo-Hshiung Tzeng, A hybrid dynamic MADM model for problem-improvement
in economics and business, Technological and Economic Development of Economy, 19(2013), number 4,
pp. 638-660. 2013
http://dx.doi.org/10.3846/20294913.2013.837114
A18-c272 Lazim Abdullah, Fuzzy Multi Criteria Decision Making and its Applications: A Brief Review of
Category, Procedia - Social and Behavioral Sciences, 67(2013), pp. 131-136. 2013
http://dx.doi.org/10.1016/j.sbspro.2013.10.213
The fusion of MCDM and fuzzy set theory strengthen a new decision theory which was later being
known as Fuzzy MCDM. Carlsson and Fuller [A18] reinforced the role of fuzzy sets in decision
making. Fuzzy MCDM methods have been found in many practical applications in the real word.
However, the fusion has not comes without critics and pessimistic view. (page 131)
222
As MCDM developed to its maturity state, Carlson and Fuller [A18] propose the categorization of
MCDM into four major families. Outranking approach based on the pioneering work by Bernard
Roy and implemented in the ELECTRE and PROMETHEE methods was categorized as the first.
The second category is value and utility theory approaches. These approaches mainly started by
Keeney and Raiffa and then implemented in a number of methods. Of these methods, a special
and very well known method in this family is the Analytic Hierarchy Process (AHP) developed by
Saaty and then implemented in the Expert Choice software package. The third category and the
largest group is the interactive multiple objective programming (MOLP) approach with pioneering
work done by Yu Stanley Zionts, Milan Zeleny, Ralph Steuer and a number of others. The fourth
category of MCDM that classified by Carlsson and Fuller [A18] is group decision and negotiation
theory. (page 133)
A18-c271 Chu T-C, A mean of removals-based fuzzy MCDM method for the evaluation and selection of suppliers, International Journal of Management and Enterprise Development, 12(2013), numbers 4-6, pp. 349362. 2013
http://dx.doi.org/10.1504/IJMED.2013.056444
A18-c270 Ta-Chung Chu, Peerayuth Charnsethikul, Ordering Alternatives under Fuzzy Multiple Criteria Decision Making via a Fuzzy Number Dominance Based Ranking Approach, International Journal of Fuzzy
Systems, 15(2013), number3, pp. 263-273. 2013
http://www.ijfs.org.tw/ePublication/
2013_paper_3/ijfs13-3-r-1-Ordering%2520Alternatives%2520und.pdf
A18-c269 B Naderi, A Arshadi, Scheduling a variant of flowshop problems to minimize total tardiness, TECHNICAL JOURNAL OF ENGINEERING AND APPLIED SCIENCES, 3(2013), number 22, pp. 3142-3149.
2013
A18-c268 D P Singh, Abhishake Chaudhary, Vijayant Maan, Selection of Heat Exchanger for Heat Operation
by Multiple Attribute Decision Making (MADM) Approach, International Journal of Engineering Research
& Technology, 2(2013), number 10, pp. 3072-3080. 2013
A18-c267 Ibadov N, Wielokryterialna ocena procesów budowlanych z uwzglȩdnieniem rozmytego modelowania niepewności aspektów technologicznych, Autobusy : technika, eksploatacja, systemy transportowe,
14(2013), number 3, pp. 1183-1191. 2013
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.baztech-article-BWA0-0059-0016
A18-c266 Mei Li Wang, Long Long Li, Dong Jian He, A Teaching Evaluation Model Based on Fuzzy Multiple
Attribute Decision Making, Applied Mechanics and Materials, 333-335(2013), pp. 2197-2201. 2013
http://dx.doi.org/10.4028/www.scientific.net/AMM.333-335.2197
A18-c265 Wei Z, Lv J, Fuzzy linear programming solution with elastic constraints Liaoning Gongcheng Jishu
Daxue Xuebao (Ziran Kexue Ban)/Journal of Liaoning Technical University (Natural Science Edition),
32(2013), number 6, pp. 844-847. 2013
http://dx.doi.org/10.3969/j.issn.1008-0562.2013.06.027
A18-c264 Hossein Safari, Abdol Hossein Jafarzadeh, Alireza Faghih, Mohammad Reza Fathi, Ranking of Iran’s
Informatics Companies Based on EFQM and Fuzzy System, World Applied Programming 3(2013), number
3, pp. 101-107. 2013
http://www.waprogramming.com/download.php?download=5174c9a76dc1d2.78694493.pdf
A18-c263 ABHISHAKE CHAUDHARY, VIJAYANT MAAN, BHARAT SINGH CHITTORIYAN, PARDEEP
GAHLOT, SELECTION OF ROBOT FOR WELDING OPERATION BY MULTIPLE ATTRIBUTE DECISION MAKING (MADM) APPROACH, JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN MECHANICAL ENGINEERING, 2(2013), number 2, pp. 536-544. 2013
http://www.ejournal.aessangli.in/ASEEJournals/MECH74.pdf
Christer Carlsson [5] states that Multiple Criteria Decision Making (MCDM) shows signs of becoming a maturing field. There are four quite distinct families of methods: (i) the outranking, (ii)
223
the value and utility theory based, (iii) the multiple objective programming, and (iv) group decision and negotiation theory based methods. Fuzzy MCDM has basically been developed along the
same lines, although with the help of fuzzy set theory a number of innovations have been made
possible; the most important methods are reviewed and a novel approach - interdependence in
MCDM is introduced. (page 537)
A18-c262 Kumar S, Singh B, Qadri MA, Kumar YVS, Haleem A, A framework for comparative evaluation
of lean performance of firms using fuzzy TOPSIS, INTERNATIONAL JOURNAL OF PRODUCTIVITY
AND QUALITY MANAGEMENT, 11(2013), number 4, pp. 371-392. 2013
http://dx.doi.org/10.1504/IJPQM.2013.054267
A18-c261 C Guerra, MJ Metzger, J Honrado, J Alonso, A spatially explicit methodology for a priori estimation of field survey effort in environmental observation networks, INTERNATIONAL JOURNAL OF
GEOGRAPHICAL INFORMATION SCIENCE, (to appear). 2013
http://dx.doi.org/10.1080/13658816.2013.805760
A18-c260 Badawy R, Yassine A, Heßler A, Hirsch B, Albayrak S A novel multi-agent system utilizing quantuminspired evolution for demand side management in the future smart grid, INTEGRATED COMPUTERAIDED ENGINEERING, 20(2013), number 2, pp. 127-141. 2013
http://dx.doi.org/10.3233/ICA-130423
A18-c259 Georgieva P, Popchev I, Fuzzy logic Q-measure model for managing financial investments, COMPTES
RENDUS DE L’ACADEMIE BULGARE DES SCIENCES, 66(2013), number 5, pp. 651-658. 2013
Scopus: 84878457260
A18-c258 Li X, Xiang Z, Li Q, Liu Y, Obtain win-win solutions for multiple criteria decision making based on
extenics and intelligent knowledge, ADVANCES IN INFORMATION SCIENCES AND SERVICE SCIENCES, 5(2013), number 5, pp. 106-115. 2013
http://dx.doi.org/10.4156/AISS.vol5.issue5.13
A18-c257 YK Chiam, M Staples, X Ye, L Zhu, Applying a Selection Method to Choose Quality Attribute
Techniques, INFORMATION AND SOFTWARE TECHNOLOGY 55(2013), number 8, pp. 1419-1436.
2013
http://dx.doi.org/10.1016/j.infsof.2013.02.001
Numerous multicriteria decision making (MCDM) methods have been developed to help with
decision problems by evaluating a set of candidates against pre-specified criteria. Examples of
MCDM include Multi-Attribute Utility Theory (MAUT) [40], AHP [8], outranking techniques
[41], weighting techniques [42], and fuzzy techniques [A18]. In this research, we apply AHP to
evaluate the candidate QATs according to cost/benefit criteria because AHP provides a convenient
way to measure both quantitative and qualitative factors. (page 1421)
A18-c256 Espinoza J, Rojas C, Rodriguez J, Rivera M, Sbarbaro D, Multiobjective Switching State Selector for Finite States Model Predictive Control based on Fuzzy Decision Making in a Matrix Converter,
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, Volume 60, Issue 2, 2013, Article number
6226852, Pages 589-599. 2013
http://dx.doi.org/10.1109/TIE.2012.2206343
A18-c255 Giada La Scalia, Solving type-2 assembly line balancing problem with fuzzy binary linear programming, JOURNAL OF INTELLIGENT AND FUZZY SYSTEMS, 25(2013), number 3, pp. 517-524. 2013
http://dx.doi.org/10.3233/IFS-120656
A18-c254 Jing Tian, Dan Yu, Bing Yu, Shilong Ma, A Fuzzy TOPSIS Model via Chi-square Test for Information
Source Selection, KNOWLEDGE-BASED SYSTEMS, 37(2013), pp. 515-527. 2013
http://dx.doi.org/10.1016/j.knosys.2012.09.010
2012
A18-c253 Nyaruhuma AP, Gerke M, Vosselman G, Mtalo EG, Verification of 2D building outlines using oblique
airborne images, ISPRS JOURNAL OF PHOTOGRAMMETRY AND REMOTE SENSING, 71(2012), pp.
62-75. 2012
WOS:000306722000005
224
A18-c252 Shahriar A, Modirzadeh M, Sadiq R, Tesfamariam S, Seismic induced damageability evaluation of
steel buildings: a Fuzzy-TOPSIS method, EARTHQUAKES AND STRUCTURES, 3: (5) 695-717. 2012
WOS:000309504400004
A18-c251 Z Eslaminasab, T Dokoohaki, A new fuzzy MCDM using non-linear programming, Acta Computare,
1(2012), pp. 216-223. 2012
http://dx.doi.org/10.5899/2012/cjac-001-025
A18-c250 Yatsalo B, Sullivan T, Didenko V, Gritsuk S, Tkachuk A, Mireabasov O, Slipenkaya V, Pichugina
I, Linkov I, Environmental risk management with the use of multi-criteria spatial decision support system
DECERNS, INTERNATIONAL JOURNAL OF RISK ASSESSMENT AND MANAGEMENT, 16(2012),
number 4, pp. 175-198. 2012
http://dx.doi.org/10.1504/IJRAM.2012.051254
A18-c249 Babak Daneshvar Rouyendegh, Turan Erman Erkan, SELECTION OF ACADEMIC STAFF USING THE FUZZY ANALYTIC HIERARCHY PROCESS (FAHP): A PILOT STUDY, Tehnički vjesnik
19(2012), number 4, pp. 923-929. 2012
The MCDM was introduced in the early 1970’s as a promising and important field of study. Since
then, the number of contributions to the theories and models, which could be used as a basis
for more systematic and rational decision-making with multi-criteria, has continued to grow at a
steady rate [A18]. In general, MCDM is a modelling and methodological tool for dealing with
complex engineering problems [13]. Many mathematical programming models have been developed to address MCDM problems. However, in recent years, MCDM methods have gained
considerable acceptance for judging different proposals. (page 923)
A18-c248 Qiu, B.-B., Liu, J.N.K., Ma, W.-M., Novel methods for intuitionistic fuzzy multiple attribute decision
making, JOURNAL OF SOFTWARE, Volume 7, Issue 11, November 2012, Pages 2553-2559. 2012
http://dx.doi.org/10.4304/jsw.7.11.2553-2559
A18-c247 Daud Mohamad, Aidatulsima Abdullah, Siti Shafiqah Razali, Suhaila Zulkifli, FACTORS INFLUENCING STUDENTS’ CHOICE IN PURSUING TO HIGHER INSTITUTIONS: A FUZZY SET OPERATION APPROACH, International Journal of Research and Reviews in Applied Sciences, 12(2012),
number 3, pp. 463-467. 2012
http://www.arpapress.com/Volumes/Vol12Issue3/IJRRAS_12_3_16.pdf
A18-c246 Doraid Dalalah, Mohammad Al-Tahat, Khaled Bataineh, Mutually dependent multi-criteria decision
making, FUZZY INFORMATION AND ENGINEERING, 4(2012), number 2, pp. 195-216. 2012
http://dx.doi.org/10.1007/s12543-012-0111-3
A18-c245 H Sheikhi, A novel approach for solving fuzzy multi-objective zero-one linear programming problems, Int. J. Research in Industrial Engineering, 1(2012), number 1, pp. 43-63. 2012
A18-c244 Pao-Long Chang, Chiung-Wen Hsu, Chiu-Yue Lin, Assessment of hydrogen fuel cell applications
using fuzzy multiple-criteria decision making method, APPLIED ENERGY, Volume 100, December 2012,
Pages 93-99. 2012
http://dx.doi.org/10.1016/j.apenergy.2012.03.051
A18-c243 Y C Chen, H S Huang, P L Yu, EMPOWER MCDM BY HABITUAL DOMAINS TO SOLVE
CHALLENGING PROBLEMS IN CHANGEABLE SPACES, INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING, 11(2012), number 2, pp. 457-490. 2012
http://dx.doi.org/10.1142/S0219622012400111
A18-c242 Bernardo Llamas, Pablo Cienfuegos, Multicriteria Decision Methodology to Select Suitable Areas
for Storing CO2, ENERGY & ENVIRONMENT, 23(2012), number 2-3, pp. 249-264. 2012
http://dx.doi.org/10.1260/0958-305X.23.2-3.249
A18-c241 Jing T, Dan Y, Bing Y, Shilong M, A fuzzy multi-criteria group decision making model for information source selection, ADVANCES IN INFORMATION SCIENCES AND SERVICE SCIENCES, 4(2012),
number 6, pp. 184-192. 2012
http://dx.doi.org/10.4156/AISS.vol4.issue6.22
225
A18-c240 Praveen Ranjan Srivastava, Optimal Software Release Using Time and Cost Benefits via Fuzzy MultiCriteria and Fault Tolerance, JOURNAL OF INFORMATION PROCESSING SYSTEMS, 8(2012), number
1, pp. 21-54. 2012
http://dx.doi.org/10.3745/JIPS.2012.8.1.021
A18-c239 R. Ramkumar, A. Tamilarasi, T. Devi, Intelligent Control for Job Shop Scheduling using Soft Computing, EUROPEAN JOURNAL OF SCIENTIFIC RESEARCH, 71(2012), number 3, pp. 364-373. 2012
http://www.europeanjournalofscientificresearch.com/ISSUES/EJSR_71_3_06.pdf
Fuzzy Logic was conceived as a better method for sorting and handling data but has proven to
be an excellent choice for many control system applications since it mimics human control logic
[Christer Carlsson et al., 1996]. (page 366)
A18-c238 Tsung-Han Chang, A method of fuzzy preference relation to authorize the worldwide interoperability
for microwave access license in Taiwan, APPLIED MATHEMATICAL MODELLING, 36(2012), issue 8,
pp. 3856-3869. 2012
http://dx.doi.org/10.1016/j.apm.2011.11.017
A18-c237 Dragisa STANUJKIC, Nedeljko MAGDALINOVIC, Sanja STOJANOVIC, Rodoljub JOVANOVIC,
Extension of Ratio System Part of MOORA Method for Solving Decision-Making Problems with Interval
Data, INFORMATICA, 23(2012), number 1, pp. 141-154. 2012
http://www.mii.lt/informatica/pdf/INFO853.pdf
A18-c236 Ta-Chung Chua, Ranganath Varma, Evaluating Suppliers via a Multiple Levels Multiple Criteria
Decision Making Method under Fuzzy Environment, COMPUTERS & INDUSTRIAL ENGINEERING,
62(2012), number 2, pp. 653-660. 2012
http://dx.doi.org/10.1016/j.cie.2011.11.036
A18-c235 Roel Bosma, Jan van den Berg, Uzay Kaymak, Henk Udo, Johan Verreth, A generic methodology for
developing fuzzy decision models, EXPERT SYSTEMS WITH APPLICATIONS, 39(2012), issue 1, pp.
1200-1210. 2012
http://dx.doi.org/10.1016/j.eswa.2011.07.126
A18-c234 Zhi Pei, Li Zheng, A novel approach to multi-attribute decision making based on intuitionistic fuzzy
sets, EXPERT SYSTEMS WITH APPLICATIONS, 39(2012), number 3, pp. 2560-2566. 2012
http://dx.doi.org/10.1016/j.eswa.2011.08.108
A18-c263 Guozhong Zheng, Neng Zhu, Zhe Tian, Ying Chen, Binhui Sun, Application of a trapezoidal fuzzy
AHP method for work safety evaluation and early warning rating of hot and humid environments, SAFETY
SCIENCE, 5(21012), number 2, pp. 228-239. 2012
http://dx.doi.org/10.1016/j.ssci.2011.08.042
A18-c262 B. Naderi, M. Aminnayeri, M. Piri, M.H. Hairi Yazdi, Multi-objective no-wait flowshop scheduling
problems: models and algorithms, INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, 50:
(10) 2592-2608. 2012
http://dx.doi.org/10.1080/00207543.2010.543937
2011
A18-c261 Nirmale SS, Kumbhar TR, Mudholkar RR, Fuzzy based decision system for moisture-free PVC
temperature International Journal of Applied Engineering Research, 6(2011), number 12, pp. 1543-1554.
2011
Scopus: 84867243866
A18-c260 Ta-Chung Chu, Rong-Ho Lin, Evaluating Suppliers via a Total Integral Value based Fuzzy MCDM
Approach, ASIA PACIFIC MANAGEMENT REVIEW 16(2011), number 4, pp. 521-534. 2011
http://apmr.management.ncku.edu.tw/comm/updown/DW1112304380.pdf
A18-c259 Mohammadreza Mohammadrezaei, Mahsa Fathi, Nima Attarzadeh, Proposing a New Approach to
Applying Pervasive Computing in Agriculture Environments, INTERNATIONAL JOURNAL OF COMPUTER SCIENCE AND NETWORK SECURITY, 11(2011), number 9, pp. 101-105. 2011
226
http://paper.ijcsns.org/07_book/201109/20110917.pdf
A18-c258 Jagat Sesh Challa, Arindam Paul, Yogesh Dada, Venkatesh Nerella, Praveen Ranjan Srivastava, Ajit
Pratap Singh, Integrated Software Quality Evaluation: A Fuzzy Multi-Criteria Approach, JOURNAL OF
INFORMATION PROCESSING SYSTEMS, 7(2011), number 3, pp. 473-518. 2011
http://dx.doi.org/10.3745/JIPS.2011.7.3.473
A18-c257 Tony Prato, Adaptively Managing Wildlife for Climate Change: A Fuzzy Logic Approach, ENVIRONMENTAL MANAGEMENT 48(2011), number 1, pp. 142-149. 2011
http://dx.doi.org/10.1007/s00267-011-9648-x
A18-c256 Jie Lu, Jun Ma, Guangquan Zhang, Yijun Zhu, Xianyi Zeng, Koehl L, Theme-Based Comprehensive Evaluation in New Product Development Using Fuzzy Hierarchical Criteria Group Decision-Making
Method, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 58(2011), number 6, pp. 22362246. 2011
http://dx.doi.org/10.1109/TIE.2010.2096171
Carlsson and Fuller [A18] reviewed the developments in fuzzy MCDM methods and identified
some important applications. (page 2237)
A18-c255 Edmundas Kazimieras Zavadskas, Zenonas Turskis, Multiple criteria decision making (MCDM)
methods in economics: an overview, 17(2011), number 2, pp. 397-427. 2011
http://dx.doi.org/10.3846/20294913.2011.593291
A18-c254 M. VETRIVEL SEZHIAN, C. MURALIDHARAN, T. NAMBIRAJAN, S. G. DESHMUKH, PERFORMANCE MEASUREMENT IN A PUBLIC SECTOR PASSENGER BUS TRANSPORT COMPANY
USING FUZZY TOPSIS, FUZZY AHP AND ANOVA - A CASE STUDY, INTERNATIONAL JOURNAL
OF ENGINEERING SCIENCE AND TECHNOLOGY, 3(2011), number 2, pp. 1046-1059. 2011
http://www.ijest.info/docs/IJEST11-03-02-251.pdf
Solving a MADM problem involves sorting and ranking. (Kavita Devi et al 2009). MADM
requires inter- and intra-attribute comparisons, and involve appropriate explicit tradeoffs (Carlsson
1996). (page 1047)
A18-c253 J Jlassi, A El Mhamedi, H Chabchoub, The improvement of the performance of the emergency
department: Application of simulation model and multiple criteria decision method, JOURNAL OF INDUSTRIAL ENGINEERING INTERNATIONAL, 7(2011), number 12, pp. 60-71. 2011
http://www.sid.ir/En/VEWSSID/J_pdf/117320111208.pdf
A18-c252 Jurate Skupiene, Score Calculation in Informatics Contests Using Multiple Criteria Decision Methods, INFORMATICS IN EDUCATION, 10(2011), number 1, pp. 89-103. 2011
Scopus: 79955430660
http://www.mii.lt/informatics_in_education/htm/INFE179.htm
A18-c251 Antonio Vanderley Herrero Sola, Caroline Maria de Miranda Mota, Joao Luiz Kovaleski, A model
for improving energy efficiency in industrial motor system using multicriteria analysis, ENERGY POLICY,
39(2011), number 6, pp. 3645-3654. 2011
http://dx.doi.org/10.1016/j.enpol.2011.03.070
A18-c250 Alireza Aliahmadi, Seyed Jafar Sadjadi, Meisam Jafari-Eskandari, Design a new intelligence expert
decision making using game theory and fuzzy AHP to risk management in design, construction, and operation of tunnel projects (case studies: Resalat tunnel), INTERNATIONAL JOURNAL OF ADVANCED
MANUFACTURING TECHNOLOGY, 53(2011), numbers 5-8, pp. 789-798. 2011
http://dx.doi.org/10.1007/s00170-010-2852-7
Most of the real-world decision problems occur in a complex environment where conflicting systems of logic, uncertain, and imprecise knowledge need to be considered. To face such complexity,
preference modeling needs the use of specific tools, techniques, and concepts to reveal the available information with the appropriate granularity [1, A18]. (page 789)
227
A18-c249 A. Hadi-Vencheh, M.N. Mokhtarian, A new fuzzy MCDM approach based on centroid of fuzzy
numbers, EXPERT SYSTEMS WITH APPLICATIONS, 38(2011), issue 5, pp. 5226-5230. 2011
http://dx.doi.org/10.1016/j.eswa.2010.10.036
A18-c248 J. Ignatius et al, A multi-objective sensitivity approach to training providers’ evaluation and quota
allocation planning, INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY AND DECISION MAKING, 10(2011), issue 1, pp. 147-174. 2011
http://dx.doi.org/10.1142/S0219622011004269
A18-c247 A. Choi, W. Woo, Multiple-Criteria Decision-Making Based On Probabilistic Estimation With Contextual Information For Physiological Signal Monitoring, INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY AND DECISION MAKING, 10(2011), number 1, pp. 109-120. 2011
http://dx.doi.org/10.1142/S0219622011004245
A18-c246 Chi-Cheng Huang and Pin-Yu Chu, Using the fuzzy analytic network process for selecting technology
R&D projects, INTERNATIONAL JOURNAL OF TECHNOLOGY MANAGEMENT, 53(2011), number
1, pp. 89-115. 2011
http://inderscience.metapress.com/link.asp?id=u58122rt2768qx54
A18-c245 Anjali Awasthi, S S Chauhan, S K Goyal, A multi-criteria decision making approach for location
planning for urban distribution centers under uncertainty, MATHEMATICAL AND COMPUTER MODELLING, 53(2011), pp. 98-109. 2011
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2010
A18-c244 G R Jahanshahloo, M Zohrehbandian, S Abbasian-Naghneh, E Hadavandi, A Ghanbari, Using dea for
evaluating the attribute weights and solving one MADM problem, AUSTRALIAN JOURNAL OF BASIC
AND APPLIED SCIENCES, 4(2010), number 10, pp. 5271-5276. 2010
http://www.insipub.com/ajbas/2010/5271-5276.pdf
A18-c243 Dahmardeh Nazar, Finding industrial clusters in sistan and baloochistan state and specify their development priority by fuzzy MADM, ASIAN JOURNAL OF DEVELOPMENT MATTERS, 4(2010), issue 2,
article number 34. 2010
http://www.indianjournals.com/ijor.aspx?
target=ijor:ajdm&volume=4&issue=2&article=034
A18-c242 Kejiang Zhang; Gopal Acharia, Uncertainty propagation in environmental decision making using
random sets, PROCEDIA ENVIRONMENTAL SCIENCES, 2(2010), 576-584. 2010
http://dx.doi.org/10.1016/j.proenv.2010.10.063
A18-c241 Maninder Jeet Kaur, Moin Uddin, Harsh K Verma, Analysis of Decision Making Operation in Cognitive radio using Fuzzy Logic System, INTERNATIONAL JOURNAL OF COMPUTER APPLICATIONS,
4(2010), number 10, pp. 35-39. 2010
http://dx.doi.org/10.5120/861-1210
A18-c240 Dorit S Hochbaum, Asaf Levin, How to allocate review tasks for robust ranking, ACTA INFORMATICA, 47(2010), number 5-6, pp. 325-345. 2010
http://dx.doi.org/10.1007/s00236-010-0120-9
A18-c239 Rajender Kumar, Brahmjit Singh, Comparison of vertical handover mechanisms using generic QoS
trigger for next generation network, INTERNATIONAL JOURNAL OF NEXT-GENERATION NETWORKS,
2(2010), number 3, pp. 80-97 [doi 10.5121/ijngn.2010.2308]. 2010
http://www.airccse.org/journal/ijngn/papers/0910ijngn08.pdf
A18-c238 V. Peneva, I. Popchev, Fuzzy multi-criteria decision making algorithms, COMPTES RENDUS DE
L’ACADEMIE BULGARE DES SCIENCES, 63(2010), Issue 7, pp. 979-992. 2010
A18-c237 Tony Prato, Sustaining Ecological Integrity with Respect to Climate Change: Adaptive Management
Approach, ENVIRONMENTAL MANAGEMENT 45(2010), number 6, pp. 1344-1351. 2010
http://dx.doi.org/10.1007/s00267-010-9493-3
228
The framework employs ex post and ex ante evaluations of ecological integrity. The ex post
evaluation uses fuzzy logic (Barrett and Pattanaik 1989; Carlsson and Fuller 1996; Andriantiatsaholiniaina and others 2004; Prato 2005, 2009) to test hypotheses about the vulnerability to losing
ecological integrity in an historical period and the ex ante evaluation determines the best CMA
for alleviating potential adverse impacts of climate change on ecosystem vulnerability to losing
ecological integrity in a future period. (page 1346)
A18-c236 Vikas Kumar; Marta Schuhmacher, Integrated fuzzy framework to incorporate uncertainty in risk
management, INTERNATIONAL JOURNAL OF ENVIRONMENT AND POLLUTION, 42(2010), numbers 1-2, pp. 270-288. 2010
http://dx.doi.org/10.1504/IJEP.2010.034244
A18-c235 Kalyan Mitra, Validating AHP, fuzzy alpha cut and fuzzy preference programming method using
clustering technique, OPSEARCH 47(2010), number 1, pp. 5-15. 2010
http://dx.doi.org/10.1007/s12597-010-0001-6
A18-c234 Andreas Merentitis, Dionysia Triantafyllopoulou, Resource Allocation with MAC Layer Node Cooperation in Cognitive Radio Networks, INTERNATIONAL JOURNAL OF DIGITAL MEDIA BROADCASTING, vol. 2010, pp. 1-11. 2010
http://dx.doi.org/10.1155/2010/458636
A18-c233 B. K. Mohanty and B. Aouni, Product selection in Internet business: a fuzzy approach, INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, 17(2010) 317-331. 2010
http://dx.doi.org/10.1111/j.1475-3995.2009.00712.x
A18-c232 Jih-Jeng Huang, Chin-Yi Chen, Hsiang-Hsi Liu, Gwo-Hshiung Tzeng, A multiobjective programming model for partner selection-perspectives of objective synergies and resource allocations, EXPERT
SYSTEMS WITH APPLICATIONS, 37(2010), Issue 5, pp. 3530-3536. 2010
http://dx.doi.org/10.1016/j.eswa.2009.09.044
A18-c231 Amir Sanayei, S. Farid Mousavi, A. Yazdankhah, Group decision making process for supplier selection with VIKOR under fuzzy environment, EXPERT SYSTEMS WITH APPLICATIONS, 37(2010), pp.
24-30. 2010
http://dx.doi.org/10.1016/j.eswa.2009.04.063
A18-c230 Kwangyeol Ryu, Enver Yücesan, A fuzzy newsvendor approach to supply chain coordination, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 200(2010), pp. 421-438. 2010
http://dx.doi.org/10.1016/j.ejor.2009.01.011
A18-c229 Ling-Zhong Lin, Fuzzy multi-linguistic preferences model of service innovations at wholesale service
delivery, QUALITY AND QUANTITY, 44(2010), pp. 217-237. 2010
http://dx.doi.org/10.1007/s11135-008-9192-9
Since 1970, multiple criteria decision making (MCDM) has been a promising and important field
of study with many practical application (Carlsson and Fuller 1996). TraditionalMCDM methods
have been extended to support the fuzzy decision making. Fuzzy MCDM methods have found
many practical applications in the real word (Carlsson and Fuller 1996; Chen 2001). (page 220)
A18-c228 Mohammad H. Sabour; Mohammad F. Foghani, Design of Semi-composite Pressure Vessel using
Fuzzy and FEM, APPLIED COMPOSITE MATERIALS, 17(2010), issue 2, pp. 175-182. 2010
http://dx.doi.org/10.1007/s10443-009-9114-6
A18-c227 Javier Munguia; Joaquim Lloveras; Sonia Llorens; Tahar Laoui, Development of an AI-based Rapid
Manufacturing Advice System, INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH , Volume
48, Issue 8 January 2010 , pages 2261-2278. 2010
http://dx.doi.org/10.1080/00207540802552675
A18-c226 ZHANG Tao; XU Yunyun; LI Zancheng; LIN Zhenrong, Fuzzy Interpolation Algorithm Using Vague
Set Based Score Function Methods, JOURNAL OF DETECTION & CONTROL, 32(2010), number 1, pp.
61-64 (in Chinese). 2010
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2009
A18-c225 Kornyshova, C Salinesi, R Deneckere, Which method to support multicriteria decision making systematically in is engineering? SYSTEMS RESEARCH FORUM, 3(2009), number 1, pp. 15-24. 2009
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A18-c224 G. Uthra, R. Sattanathan, Confidence Analysis for Fuzzy Multicriteria Decision Making Using
Trapezoidal Fuzzy Numbers, INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY AND
KNOWLEDGE MANAGEMENT, 2(2009), pp. 333-336. 2009
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A18-c223 Amir Sanayei, Seyed Farid Mousavi, and Catherine Asadi Shahmirzadi, A Group Based Fuzzy
MCDM for Selecting Knowledge Portal System, Proceedings of World Academy of Science, Engineering and Technology, 52(2009), pp. 455-462. 2009
http://www.waset.org/journals/waset/v52/v52-72.pdf
This approach helps decision-makers solve complex decision-making problems in a systematic,
consistent and productive way [A18] and has been widely applied to tackle DM problems with
multiple criteria and alternatives [27]. In short, fuzzy set theory offers a mathematically precise
way of modeling vague preferences for example when it comes to setting weights of performance
scores on criteria. Simply stated, fuzzy set theory makes it possible to mathematically describe a
statement like: ”criterion X should have a weight of around 0.8” [28]. (page 457)
A18-c22 Emre Cevikcan, Selcuk Cebi and Ihsan Kaya, Fuzzy VIKOR and Fuzzy Axiomatic Design Versus to
Fuzzy Topsis: An Application of Candidate Assessment, JOURNAL OF MULTIPLE-VALUED LOGIC
AND SOFT COMPUTING, 15(2009), pp. 181-208. 2009
A18-c221 Tony Prato, Fuzzy adaptive management of social and ecological carrying capacities for protected
areas, JOURNAL OF ENVIRONMENTAL MANAGEMENT, 90(2009), pp. 2551-2557. 2009
http://dx.doi.org/10.1016/j.jenvman.2009.01.015
A18-c220 Gholam Ali Montazer, Hamed Qahri Saremi, Maryam Ramezani, Design a new mixed expert decision aiding system using fuzzy ELECTRE III method for vendor selection, EXPERT SYSTEMS WITH
APPLICATIONS, 36(2009), pp. 10837-10847. 2009
http://dx.doi.org/10.1016/j.eswa.2009.01.019
A18-c219 Min Guo; Jian-Bo Yang; Kwai-Sang Chin; Hong-Wei Wang; Xin-Bao Liu, Evidential Reasoning
Approach for Multiattribute Decision Analysis Under Both Fuzzy and Interval Uncertainty, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 17(2009), pp. 683-697. 2009
http://dx.doi.org/10.1109/TFUZZ.2008.928599
A18-c218 Mousumi Dutta, Zakir Husain An application of Multicriteria Decision Making to built heritage. The
case of Calcutta, JOURNAL OF CULTURAL HERITAGE, 10(2009), pp. 237-243. 2009
http://dx.doi.org/10.1016/j.culher.2008.09.007
A18-c217 Tony Prato, Adaptive management of natural systems using fuzzy logic, ENVIRONMENTAL MODELLING & SOFTWARE, 24(2009), pp. 940-944. 2009
http://dx.doi.org/10.1016/j.envsoft.2009.01.007
A18-c216 Ta-Chung Chu, Yichen Lin, An extension to fuzzy MCDM, COMPUTERS AND MATHEMATICS
WITH APPLICATIONS, 57(2009), pp. 445-454. 2009
http://dx.doi.org/10.1016/j.camwa.2008.10.076
A18-c215 Tony Prat, Evaluating and managing wildlife impacts of climate change under uncertainty, ECOLOGICAL MODELLING, 220(2009), pp. 923-930. 2009
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A18-c214 Torbert, H.A., Krueger, E., Kurtener, D., Potter, K.N. Evaluation of Tillage Systems for Grain
Sorghum and Wheat Yields and Total N Uptake in The Texas Blackland Prairie, JOURNAL OF SUSTAINABLE AGRICULTURE, 33(2009), pp. 96-106. 2009
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A18-c213 P. Kumar, P. Bauer, Progressive design methodology for complex engineering systems based on
multiobjective genetic algorithms and linguistic decision making, SOFT COMPUTING, 13(2009), pp. 649679. 2009
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A18-c212 Ni-Bin Chang, Ying-Hsi Chang, Ho-Wen Chen, Fair fund distribution for a municipal incinerator
using GIS-based fuzzy analytic hierarchy process, JOURNAL OF ENVIRONMENTAL MANAGEMENT,
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A18-c211 W.K. Wong; X.H. Zeng; W.M.R. Au; P.Y. Mok; S.Y.S. Leung, A fashion mix-and-match expert
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A18-c210 Chung-Tsen Tsao, Applying a fuzzy multiple criteria decision-making approach to the M & A due
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A18-c209 Chen Qin Lan, Guodong Jiang, Fuzzy AHP method based on the service industry, and elements of
evaluation model and empirical study - A Case Study of Quanzhou, Fujian Tourism Industry, JOURNAL
OF TIANSHUI NORMAL UNIVERSITY, 29(2009), number 5, pp. (in Chinese). 2009
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A18-c208 Robert I. John, Shang-Ming Zhou, Jonathan M. Garibaldi and Francisco Chiclana, Automated Group
Decision Support Systems Under Uncertainty: Trends and Future Research, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE RESEARCH, 4(2008), pp. 357-371. 2008
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A18-c207 Chuang, S.-N., Chan, A.T.S. Dynamic QoS adaptation for mobile middleware IEEE TRANSACTIONS ON SOFTWARE ENGINEERING, 34(2008), pp. 738-752. 2008
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A18-c206 Mehrzad Samadi; Ali Afzali-Kusha, Dynamic power management with fuzzy decision support system, IEICE ELECTRONICS EXPRESS, 5(2008) , No. 19, pp. 789-795. 2008
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A18-c205 E. Lai, S. Lundie, N.J. Ashbolt, Review of multi-criteria decision aid for integrated sustainability
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A18-c204 T. Prato, Accounting for risk and uncertainty in determining preferred strategies for adapting to future
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A18-c203 Lu J, Zhang G, Ruan D Intelligent multi-criteria fuzzy group decision-making for situation assessments, SOFT COMPUTING, vol. 12, pp. 289-299. 2008
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Carlsson and Fullér (1996) widely reviewed the developments in fuzzy multi-criteria decision
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A18-c202 Chang N -B, Srilakshmi K R, Parvathinathan G, Comparison of models of simazine transport and
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A18-c201 Fuzhan Nasiri, Gordon Huang, A fuzzy decision aid model for environmental performance assessment in waste recycling, Environmental Modelling & Software 23 (2008) 677-689. 2008
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A18-c200 Zhu Yan, Fuzzy Assessment of Web resource quality, JOURNAL OF SOUTHWEST JIAOTONG
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A18-c199 Zhang Ling, Multi-attribute decision making based on association theory research, MANAGEMENT
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A18-c198 PENG Shao-ming, LI Qun, YANG Li-bin, Flexible Decision-Making Mode of Multiple Water Resources Use in the Yellow River Basin, RESOURCES SCIENCE, 30(2008), number 2, pp. 254-260 (in
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A18-c197 Wei Ping; Cheng-Xian Xu, Fuzzy Algorithm of Multi-objective Group Decision-Making, EQUIPMENT MANUFACTURING TECHNOLOGY, 8(2007), pp. 35-36 (in Chinese). 2007
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A18-c196 Liu Taomeng, Weighted Fuzzy Random Multiobjective Linear Programming, Journal of Jingmen
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A18-c194 Lai, E., Lundie, S., Ashbolt, N.J., A new approach to aid urban water management decision making
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A18-c193 Fuzhan Nasiria, G.H. Huang, Ecological viability assessment: A fuzzy multiple-attribute analysis
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A18-c192 Wang, T.-C., Chang, T.-H. Application of TOPSIS in evaluating initial training aircraft under a fuzzy
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A18-c186 T. Prato, Assessing ecosystem sustainability and management using fuzzy logic, ECOLOGICAL
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A18-c185 I.D. Rudinskiy, Fuzzy knowledge evaluation model as a methodological basis for automation of
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Since Zadeh and Bellman and a few years later Zimmermann developed the theory of decision
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A18-c112 Hossein Farid Ghassem Nia, Huosheng Hu, Vision-based Precise Cash Counting in ATM Machines,
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A18-c109 Ghosh D, Chakraborty D, Fuzzy ideal cone: A method to obtain complete fuzzy non-dominated set
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A18-c108 Hana Tomaskova, Martin Gavalec, Preference Matrices In Tropical Algebra, Proceedings of the
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A18-c106 Wang H, Huo D, Server farm site selection using green computing criteria, Proceedings of the 6th
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A18-c100 Yun-zhi Liu and Si-zong Guo, Fuzzy Multi-objective Programming Problem with Fuzzy Structured
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A18-c99 Victoria López, Matilde Santos, Toribio Rodrı́guez, An Approach to the Analysis of Performance, Reliability and Risk in Computer Systems, Sixth International Conference on Intelligent Systems and Knowledge Engineering, December 15-17, 2011, Shanghai, China, Advances in Intelligent and Soft Computing,
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A18-c98 Badawy R, Heßler A, Hirsch B, Albayrak S, Integrating multi-agent and quantum-inspired evolution
for supply and demand matching in the future power energy networks, IASTED International Conference
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A18-c97 Villarroel F, Espinoza J, Rojas C, Molina C, Rodrguez J, Application of fuzzy decision making to
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A18-c96 M.M. Zalloi; M.A. Sadrnia; M.M. Fateh, A novel flow meter selection method based on fuzzy multiple
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A18-c95 Ta-Chung Chu, Evaluating Consulting Firms Using a Centroid Ranking Approach based Fuzzy MCDM
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2010
A18-c94 Adam Patrick Nyaruhuma, Markus Gerke, George Vosselman, Evidence of walls in oblique images for
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A18-c92 Sohrab Khanmohammadi, Javad Jassbi, Electrical Power Scheduling in Emergency Conditions using a new Fuzzy Decision Making Procedure, 2010 IEEE International Conference on Systems Man and
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Fuzzy logic is based on fuzzy set theory in which every object has a grade of membership in various sets. Inputs are mapped to membership functions, or sets (fuzzification process). Knowledge
of a restricted domain is captured in the form of linguistic rules. Relationships between two goals
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A18-c87 M.A. Abido, Multiobjective evolutionary algorithms for electric power dispatch problem, in: C.L.
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As we can see, we have to deal with both quantitative and qualitative criteria during outsourcing supplier evaluation process, an effective decision making tool must be utilized to fulfill our
needs. Although several fuzzy MCDM methods such as multi-objective fuzzy decision making
(MOFDM), hierarchical weight decision making (HWDM), PROMETHEE, etc. could be utilized
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in Ph.D. dissertations
• Siddharth Agarwal, Computational intelligence based complex adaptive system-of-systems architecture evolution strategy, Missouri University of Science and Technology. 2015
http://scholarsmine.mst.edu/doctoral_dissertations/2401
The model used is Multi criteria decision making (MCDM) Dodgson, Spackman, Pearman, &
Phillips, 2009) with 2-tuple fuzzy linguistics (Carlsson & Fullér, 1996). (page 68)
• Tran Xuan Sang, MULTI-CRITERIA DECISION MAKING AND TASK ALLOCATION IN MULTI-AGENT
BASED RESCUE SIMULATION, Department of Science and Advanced Technology Graduate School of
Science and Engineering, Saga University, JAPAN, 2013
http://portal.dl.saga-u.ac.jp/bitstream/
123456789/120760/1/sang_201303.pdf
With different theoretical basis, there are four major branches of methods in MCDM: (i) Bernard
Roy introduced the outranking approach and it help implementing in the Electre and Promethee
methods; (ii) Keeney and Raiffa introduced the value and utility theory approaches and it help
implementing in a number of methods; a special method in this branch is the Analytic Hierarchy
Process (AHP) developed by Thomas L. Saaty; (iii) P.L.Yu, Stanley Zionts, Milan Zeleny, Ralph
Steuer introduced the interactive multiple objective programming approach; (iv) The last branch
is based on group decision and negotiation theory. It allows making decision with group dynamics
and with differences in knowledge, value systems and objectives among group members (Carlsson
et al., 1996). (pages 7-8)
• Yin Kia Chiam, Representation and Selection of Quality Attribute Techniques for Software Development
Process, University of New South Wales, Australia, 2011
http://unsworks.unsw.edu.au/fapi/datastream/unsworks:10099/SOURCE02
• Patrick Meyer, Progressive Methods in Multiple Criteria Decision Analysis, Faculte de Droit, d’Economie et
de Finance, Universite du Luxembourg, 2007.
http://citeseerx.ist.psu.edu/viewdoc/download?
doi=10.1.1.124.9749&rep=rep1&type=pdf
• Nicholas Keith Borer, Decision Making Strategies for Probabilistic Aerospace Systems Design, School of
Aerospace Engineering, Georgia Institute of Technology. 2006
https://smartech.gatech.edu/bitstream/handle/1853/10469/
borer_nicholas_k_200605_phd.pdf?sequence=1
249
The final contributor to the static relative importance follows from evaluation of the interdependence of the metrics. This procedure is possible only if polynomial surrogate models are
created for each of the decision metrics, and these models are all of the exact same functional
form. The overall procedure is a highly modified version inspired by Carlsson’s interdependent
decision making models [Carlsson and Fullér, 1996]. This procedure follows from determination
of the vector angles of the response coefficients. The sums of the cosines of these vector angles
provide a measure of interdependence for each metric. The method for evaluating the interdependent corrections is given in Algorithm 2. (page 112)
• Erkki Patokorpi, ROLE OF ABDUCTIVE REASONING IN DIGITAL INTERACTION, Faculty of Technology at Åbo Akademi University, December 2006.
• Elcin Kentel, Uncertainty Modeling Health Risk Assessment and Groundwater Resources Management, Georgia Institute of Technology, August 2006
http://hdl.handle.net/1853/11584
• Mao-Hua Yang, Nash-Stackelberg equilibrium solutions for linear multidivisional multilevel programming
problems, STATE UNIVERSITY OF NEW YORK AT BUFFALO. 2005
http://www.acsu.buffalo.edu/˜bialas/public/pub/
Papers/YangMHPhD05.pdf
• Fabian Bastin, Trust-Region Algorithms for Nonlinear Stochastic Programming and Mixed Logit Models,
FACULTES UNIVERSITAIRES NOTRE-DAME DE LA PAIX NAMUR, FACULTE DES SCIENCES.
2004
http://hdl.handle.net/2078.2/4153
• Sudaryanto, A fuzzy multi-attribute decision making approach for the identification of the key sectors of an
economy: The case of Indonesia, RWTH Aachen Germany. 2003
http://darwin.bth.rwth-aachen.de/opus3/volltexte/2003/591/
The main feature of this approach is that the imprecision inherent in the qualitative information
can be formalized by applying fuzzy sets theory. The fuzzy-MCDM methods have basically been
developed along the same lines as conventional MCDM methods, but are designed with the help of
fuzzy set theory to deal specifically with MCDM problems containing fuzzy data [Zimmmermann,
1987, 1996], [Chen and Hwang, 1992], [Carlsson and Fuller, 1996, p. 139]. The introduction of
fuzzy set theory to the field of decision making provides a consistent representation of qualitatively
or linguistically formulated knowledge in such a way that still allows the use of precise operators
and algorithms. (pages 168-169)
• A. Valls Mateu, CLUSDM: a multiple criteria decision making method for heterogeneous data sets, Polytechnic University of Catalonia. 2002
http://www.tesisenred.net/TDX-0206103-205841
[A19] Christer Carlsson and Robert Fullér, Multiple Criteria Decision Making: The Case for Interdependence,
COMPUTERS & OPERATIONS RESEARCH, 22(1995) 251-260. [Zbl.827.90081].
doi 10.1016/0305-0548(94)E0023-Z
in journals
2016
A19-c66 XU Lan, LI Jiaming, ZHAO Yamin, Optimization of Project Portfolio Selection Considering Interactions Among Multiple Projects, Management Science and Engineering, 10: (1) pp. 1-7. 2016
http://dx.doi.org/10.3968/8221
However, these studies have neither considered projects’ interactions, nor considered investors’
preference for projects’ selection criteria. Interaction between projects was first proposed by Baker
and Freland, and when two or more projects are selected for investment, it will produce positive or
250
negative interactions between projects in the project portfolio (Baker & Freeland, 1975). Carlsson
and Fuller (1995) pointed out that negligence of projects’ interactions would result in an undesirable outcome. Therefore, it is necessary to analyze projects’ interactions in portfolio selection.
(page 1)
Carlsson pointed out that the impact of individual projects in different attributes to decision results
is different from the impact of interactions among projects in different attributes to decision results,
and the negligence of projects’ interactions will result in an undesirable outcome (Carlsson &
Fuller, 1995). Therefore, considering interactions of different projects’ attributes is very necessary.
(page 4)
2015
A19-c65 YUE Lizhu, YAN Yan, LI Liangqiong, The Way of Determining the Index Weights Under the Condition of Related Indicators, ACTA ANALYSIS FUNCTIONALIS APPLICATA, 17: (4) pp. 400-406. (in
Chinese). 2015
http://dx.doi.org/10.3724/SP.J.1160.2015.00400
A19-c64 Neha Singh, Kirti Tyagi, Ranking of services for reliability estimation of SOA system using fuzzy multicriteria analysis with similarity-based approach, International Journal of System Assurance Engineering
and Management (to appear). 2015
http://dx.doi.org/10.1007/s13198-015-0339-5
2014
A19-c63 Franck Taillandiera, Irene Abi-Zeid, Patrick Taillandier, Gérard Sauced, Régis Bonetto, An interactive
decision support method for real estate management in a multi-criteria framework – REMIND, International
Journal of Strategic Property Management, 18(2014), number 3, pp. 265-278. 2014
http://dx.doi.org/10.3846/1648715X.2014.941432
A19-c62 Yang H, Ji P, Song D, Chen X, Evaluation and screening method for power grid planning schemes
under high penetration of variable generation, Dianli Xitong Zidonghua/Automation of Electric Power Systems, 38: (11) pp. 42-47 and 122. 2014
http://dx.doi.org/10.7500/AEPS20130604004
A19-c61 Antonio López Jaimes, Carlos A. Coello Coello, Hernan Aguirre, Kiyoshi Tanaka, Objective Space
Partitioning Using Conflict Information for Solving Many-Objective Problems, Information Sciences, 268(2014),
pp. 305-327. 2014
http://dx.doi.org/10.1016/j.ins.2014.02.002
In the current literature it is possible to find several definitions of conflict among objectives (see
e.g., [20, 1, 34, 4]). However, we used the definition proposed by Carlsson and Fullér [A19] since
it is intuitive and, as we explain in Section 4, it can be estimated using a low time complexity
algorithm. Let SX be a subset of X, then, according to Carlsson and Fullér, two objectives can be
related in the following ways (assuming minimization): (page 307)
In this paper we suggest using the correlation (see Def. 10) among the solutions in P Fapprox to
estimate the conflict among objectives in the sense defined by Carlsson and Fullér (Section 2.1). In
this approach, each solution in P Fapprox is an observation. A negative correlation between a pair
of objectives means that one objective increases while the other decreases and vice versa. Thus,
a negative correlation estimates the conflict between a pair of objectives. On the other hand, if
the correlation is positive, then both objectives increase or decrease at the same time. That is, the
objectives support each other. Furthermore, since the correlation coefficient values are in the range
[−1, 1], it is possible to define a measure of the degree of conflict between objectives. Therefore,
in our approach we interpret that the more negative the correlation between two objectives, the
more the conflict between them. (page 310)
251
A19-c60 Ahmad Jafarnejad Chaghooshi, Hossein Janatifar, Maedeh Dehghan, An Application of AHP and
Similarity-Based Approach to Personnel Selection, International Journal of Business Management and Economics, 1: (1) pp. 24-32. 2014
http://academicjournalscenter.org/index.php/IJBME/article/view/18
There are various ways to represent the conflict between two alternatives in multicriteria analysis
problems (Carlsson et al, 1995, Chen et al, 1992, Diakoulaki et al, 1995, Zeleny, 1998). (page 27)
A19-c59 Reza Avazpour, Elham Ebrahimi, Mohammad Reza Fathi, Prioritizing Agility Enablers Based on
Agility Attributes Using Fuzzy Prioritization Method and Similarity-Based Approach, International Journal
of Economy, Management and Social Sciences, 3: (1) pp. 143-153. 2014
A19-c58 Majid Moradi and Elham Ebrahimi, Applying Fuzzy AHP and Similarity-Based Approach for Economic Evaluating Companies Based on Corporate Governance Measures, Global Journal of Management
Studies and Researches, 1(2014), pp. 10-20. 2014
http://academicjournalscenter.org/index.php/GJMSR/article/viewFile/9/pdf_1
2013
A19-c57 Safari H, Khanmohammadi E, Hafezamini A, Ahangari SS, A new technique for multi criteria decision
making based on modified similarity method, Middle East Journal of Scientific Research, 14(2013), number
5, pp. 712-719. 2013
http://dx.doi.org/10.5829/idosi.mejsr.2013.14.5.335
A19-c56 Dong-Ping Fan, Yin-Yin Kuang, A Study on Management Methodology for the Complexity of Social
System - the Combination of MCDM and SSM, International Journal of Operations Research 10(2013),
number 2, pp. 49-55. 2013
http://www.orstw.org.tw/ijor/vol10no2/ijor_vol10_no2_p49_p55.pdf
Today, it has become a very important and active field in decision sciences, systems engineering,
management science and operations research, attracting a growing number of scholars to this
research. Interested readers are referred to Korhonen et al., (1992) and Stewart (1992) for the
surveys of MCDM. MCDM evolved from single criteria to multiple criteria, then made continuous
progress in decision making under uncertainty, giving rise to Stochastic Multiple Criteria Decision
Making (Calballero et al., 2004; Hahn, 2006; Nowak, 2007; Fan, Liu and Feng, 2010), Fuzzy
Multiple Criteria Decision Making (Carlsson, 1982; Carlsson and Fuller, 1995; Ostermark, 1997;
Bailey et al., 2003; Chang et al., 2008), seeking to deal with more management complexity of
human activity systems. (page 49)
A19-c55 Vandana Bagla, Anjana Gupta, Site Selection Using Optimization Techniques, International Journal
of Scientific & Engineering Research, 4(2013), number 4, pp. 1687-1694. 2013
A19-c54 Bin Bin Pang, Zi Li Liao, Yu Lin Yan, Zhi Feng Yan, Evaluation Research on Hybrid Electric Drive
System of Armored Vehicles Based on Multiple Attribute Decision Making, APPLIED MECHANICS AND
MATERIALS 310(2013), pp. 334-338. 2013
http://www.scientific.net/AMM.310.334
2012
A19-c53 Lertprapai S, Tiensuwan M, On a comparison of the variance estimates of exponential distribution
by multiple criteria decision making method, MODEL ASSISTED STATISTICS AND APPLICATIONS,
7(2012), number 3, pp. 251-260. 2012
http://dx.doi.org/10.3233/MAS-2012-0230
A19-c52 Yu L, Wang S, Wen F, Lai KK, Genetic algorithm-based multi-criteria project portfolio selection,
ANNALS OF OPERATIONS RESEARCH, 197(2012), number, pp. 71-86. 2012
http://dx.doi.org/10.1007/s10479-010-0819-6
252
In accordance with the above analyses, it can be found that the existing approaches for project
portfolio selection did not handle project interactive effects in terms of different selection criteria,
nor did they consider preference of decision-makers in terms of the importance of selection criteria. Actually, in project portfolio selection problem, if a project is selected in conjunction with
other projects, it may have positive or negative interactive effects in terms of a specific selection
criterion. If one does not consider project interactive effects based on different selection criteria,
the decision process may yield an undesirable outcome (Carlsson and Fuller 1995). Usually, Interaction is a kind of action that occurs as two or more objects have an effect upon one another
and it can be measured by some statistical methods such as Analysis of Variance (ANOVA) (Cox
1984). (page 73)
A19-c51 Doraid Dalalah, Mohammad Al-Tahat, Khaled Bataineh, Mutually dependent multi-criteria decision
making, FUZZY INFORMATION AND ENGINEERING, 4(2012), number 2, pp. 195-216. 2012
http://dx.doi.org/10.1007/s12543-012-0111-3
A19-c50 Tang H, Multiple-attribute decision making based on attribute preference, JOURNAL OF SOFTWARE
7(2012), number 3, pp. 644-650. 2012
http://dx.doi.org/10.4304/jsw.7.3.644-650
2011
A19-c49 Bart D. Frischknecht, Diane L. Peters, Panos Y. Papalambros, Pareto set analysis: local measures of
objective coupling in multiobjective design optimization, STRUCTURAL AND MULTIDISCIPLINARY
OPTIMIZATION 43(2011), number 5, pp. 617-630. 2011
http://dx.doi.org/10.1007/s00158-010-0599-2
2010
A19-c48 Peter Lindroth, Michael Patriksson, Ann-Brith Stromberg, Approximating the Pareto optimal set
using a reduced set of objective functions, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH,
207(2010), number 3, pp. 1519-1534. 2010
http://dx.doi.org/10.1016/j.ejor.2010.07.004
Additional definitions of conflict can be found in [4]. Measures of interdependency are defined
in [A19]; equal or opposite sorting over the decision space is required for two objectives to be
interdependent. (page 1520)
A19-c47 L. Warren, Strategy Selection with Uncertain Payoffs, MILITARY OPERATIONS RESEARCH, 15(2010),
issue 2, pp. 39-50. 2010
http://www.ingentaconnect.com/content/mors/mor/2010/00000015/00000002/art00004
A19-c46 Jih-Jeng Huang, Chin-Yi Chen, Hsiang-Hsi Liu, Gwo-Hshiung Tzeng, A multiobjective programming
model for partner selection-perspectives of objective synergies and resource allocations, EXPERT SYSTEMS WITH APPLICATIONS, 37(2010), Issue 5, pp. 3530-3536. 2010
http://dx.doi.org/10.1016/j.eswa.2009.09.044
2008
A19-c45 Alexander Engau, Margaret M. Wiecek, Interactive Coordination of Objective Decompositions in
Multiobjective Programming, MANAGEMENT SCIENCE, Vol. 54, No. 7, July 2008, pp. 1350-1363.
2008
http://dx.doi.org/10.1287/mnsc.1070.0848
A19-c44 Zhang Ling, Multi-attribute decision making based on association theory research, MANAGEMENT
REVIEW, 20(2008), number 5, pp. 51-57 (in Chinese). 2008
http://www.cqvip.com/qk/96815a/2008005/27274741.html
2007
253
A19-c43 Chang JR, Cheng CH, Chen LS, A fuzzy-based military officer performance appraisal system, APPLIED SOFT COMPUTING 7 (3): 936-945 JUN 2007
http://dx.doi.org/10.1016/j.asoc.2006.03.003
Carlsson and Fullér [A19, A20] introduced the concept of interdependence in multiple criteria
decision making (MCDM), and some researchers showed that fuzzy set theory [28] could be successfully applied to resolve multiple criteria problems [10,23,26,27]. In general, the appraisal
from among two or more people is a multiple criteria decision making problem. Under many situations, the values for the qualitative criteria are often imprecisely defined for the decision makers.
(page 937)
2006
A19-c42 Jain HK, Ramamurthy K, Sundaram S, Effectiveness of visual interactive modeling in the context of
multiple-criteria group decisions, IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS
PART A-SYSTEMS AND HUMANS 36 (2): 298-318 MAR 2006
http://dx.doi.org/10.1109/TSMCA.2005.851296
Decisions in a complex business environment usually involve multiple interdependent criteria that
are often conflicting in nature [A19]. (page 298)
A19-c41 Gal T, Hanne T, Nonessential objectives within network approaches for MCDM, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 168 (2): 584-592 JAN 16 2006
http://dx.doi.org/10.1016/j.ejor.2004.04.045
Although the problem of obtaining well-defined criteria for a multiple criteria decision making
(MCDM) problem is well-known (See, e.g., Bouyssou, 1992; Keeney and Raiffa, 1976, pp. 5053; Keeney, 1992, pp. 82-87, 120; Roy, 1977, Roy and Vincke, 1984; for more general results
cf. Gal (1995) and Karwan et al. (1983).), it is often neglected in MCDM theory, methods, and
applications (Carlsson and Fullér, 1995; see also Carlsson and Fullér, 1994). (page 584)
2004
A19-c40 Pandian Vasant, R. Nagarajan and Sazali Yaacob, Decision making in industrial production planning
using fuzzy linear programming, IMA Journal of Management Mathematics, 2004 15(1):53-65. 2004
doi:10.1093/imaman/15.1.53
A19-c39 Angilella S, Greco S, Lamantia F, et al. Assessing non-additive utility for multicriteria decision aid,
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 158 (3): 734-744 NOV 1 2004.
http://dx.doi.org/10.1016/S0377-2217(03)00388-6
In the literature it is widely recognized that in many decisional problems criteria are interdependent
(see e.g. [1,9]). For example, Carlsson and Fullér in [A19] define a constant to express the degree
of interdependence among criteria, representing their potential conflict or support. (page 735)
2002
A19-c38 Matthias Ehrgott and Stefan Nickel, On the number of Criteria Needed to Decide Pareto Optimality,
MATH METH OPER RES, 55(2002) 329–345. 2002
http://dx.doi.org/10.1007/s001860200207
A more general concept of interdependent criteria has been discussed in [A19], see also [A20].
Our approach is related to this topic in the sense that we determine the number of objectives which
are necessary to prove Pareto optimality for a given point. However, the theory presented in this
paper is more general: the results also hold in the absence of nonessential criteria, as will be
. . . (page 330)
A19-c37 Wu CH, SODPM: a sequence-oriented decision process model for unstructured group decision problems, BEHAVIOUR AND INFORMATION TECHNOLOGY, 21 (1): 59-69. JAN-FEB 2002.
http://dx.doi.org/10.1080/01449290210121842
254
A19-c36 Xiong G, Litokorpi A, Nyberg TR, et al. A kind of over-all optimization technology used in CIPS,
PULP PAP-CANADA, 103 (2): 31-35. FEB 2002.
1999
A19-c35 C. Kahraman, Z. Ulukan, E. Tolga, Selection among advanced manufacturing technologies using fuzzy
data envelopment analysis, Tatra Mountains Mathematical Publications, vol. 16, 311-323. 1999
http://tatra.mat.savba.sk/Full/16/14kahram.ps
A19-c34 Jayaram J.S.R.; Ibrahim Y., Multiple response robust design and yield maximization, International
Journal of Quality & Reliability Management, Volume 16, Number 9, 1999 , pp. 826-837. 1999
http://dx.doi.org/10.1108/02656719910274308
A19-c33 Gal T, Hanne T, Consequences of dropping nonessential objectives for the application of MCDM
methods, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH , 119 (2): 373-378. DEC 1 1999.
http://dx.doi.org/10.1016/S0377-2217(99)00139-3
The problem of obtaining well-designed criteria for a multiple criteria decision making problem
is well known (see e.g. Bouyssou, 1992; Keeney and Raiffa, 1976, pp. 50-53; Keeney, 1992, pp.
82-87, 120; Roy, 1977; Roy and Vincke, 1984). However, the problem of interdependence among
the criteria is seldom treated in the literature (Carlsson and Fullér, 1995; see also Carlsson and
Fullér, 1994). (page 373)
1998
A19-c32 Bistline WG, Banerjee S, Banerjee A, RTSS: An interactive decision support system for solving real
time scheduling problems considering customer and job priorities with schedule interruptions, COMPUT
OPER RES, 25 (11): 981-995 NOV. 1998.
http://dx.doi.org/10.1016/S0305-0548(97)00092-0
1997
A19-c31 R.Östermark, Temporal interdependence in fuzzy MCDM problems, FUZZY SETS AND SYSTEMS,
88(1997) 69-79. 1997
http://dx.doi.org/10.1016/S0165-0114(96)00046-2
The concept of interdependence in multiple criteria decision making (MCDM) was introduced by
Carlsson and Fullér [A19,A20]. The authors showed that fuzzy set theory can be successfully
applied to resolve multiple criteria problems with interdependent objectives [13]. While the authors focused on static MCDM problems, most decision models become both more realistic and
complicated when time is explicitely recognized [10]. In the present paper we consider the interdependence concept in a dynamic setting. We show that the approach can be naturally extended
to temporal cases. We then apply the temporal concept to describe goal conflicts in a multiperiod
firm model in which the concept of static interdependence would fail. Finally, the static membership function by Carlsson and Fullér is generalized to a dynamic membership function for both
multiobjective programming (MOP) and fuzzy multiobjective programming (FMOP) problems.
(page 69)
A19-c30 F. Herrera, E. Herrera-Viedma, J.L. Verdegay. Linguistic Measures Based on Fuzzy Coincidence
for Reaching Consensus in Group Decision Making, INTERNATIONAL JOURNAL OF APPROXIMATE
REASONING, vol. 16, pp. 309-334. 1997
http://dx.doi.org/10.1016/S0888-613X(96)00121-1
in proceedings and edited volumes
2015
255
A19-c27 Antonio Lpez Jaimes, Carlos A Coello Coello, Many-Objective Problems: Challenges and Methods,
In: Springer Handbook of Computational Intelligence, Springer, (ISBN 978-3-662-43504-5), pp. 10331046.
http://dx.doi.org/10.1007/978-3-662-43505-2_51
A19-c26 Sweta Kumari, Shashank Pushkar, A Genetic Algorithm Approach for Multi-criteria Project Selection
for Analogy-Based Software Cost Estimation, In: Computational Intelligence in Data Mining - Volume 3:
Proceedings of the International Conference on CIDM, 20-21 December 2014, Smart Innovation, Systems
and Technologies, vol. 33/2015) Springer Verlag, [ISBN 978-81-322-2201-9], pp. 13-24. 2015
http://dx.doi.org/10.1007/978-81-322-2202-6_2
2014
A19-c25 S Le, H Dong, FK Hussain, OK Hussain, J Ma, Y Zhang, Multicriteria Decision Making with Fuzziness and Criteria Interdependence in Cloud Service Selection, Proceedings of the IEEE International Conference on Fuzzy Systems. IEEE, [ISBN 978-1-4799-2072-3], pp. 1929-1936. 2014
2012
A19-c24 Wang H, Huo D, Server farm site selection using green computing criteria, Proceedings of the 6th
International Conference on New Trends in Information Science, Service Science and Data Mining (NISS,
ICMIA and NASNIT), ISSDM 2012, October 23-25, 2012, Taipei, Taiwan, [ISBN: 978-899436419-3], pp.
63-67. 2012
Scopus: 84880996921
2011
A19-c23 Jih-Jeng Huang, Chin-Yi Chen, Interdependent Multiple Objective Programming - A Monte Carlo
Method, 2011 IEEE International Conference on Fuzzy Systems, June 27-30, 2011, Taipei, Taiwan, [ISBN:
978-1-4244-7316-8], pp. 1497-1503. 2011
Abstract - Although multiple objective programming (MOP) skills have been extensively studied
in various issues, the problem of MOP with interdependence has received little attention. In this
paper, we overcome the problem of Carlsson and Fullér’s method and propose a novel index
to measure the interdependence grade between objectives by using Monte Carlo simulation and
regression analysis. Then, an interdependent multiple objective programming (IMOP) model is
proposed. In addition, we give three numerical examples to demonstrate the proposed method.
From the numerical results, we can conclude that the proposed method can rationally deal with
the problem of MOP with interdependence. (page 1497)
Although Carlsson and Fullér have proposed several papers to deal with the IMOP problems, their
method can only deal with the simple IMOP problems and cannot measure the grade of interdependence between the objectives precisely. In this paper, we propose another index by using
Monte Carlo simulation and regression analysis to overcome the above problems simultaneously.
From the results of numerical examples, it can be seen that the interdependent grade of the proposed method and Carlsson and Fullér’s method have the similar results. Therefore, it enhances
the justification of the proposed method. On the other hand, it also shows that the proposed
method should be more flexible and useful than Carlsson and Fullér’s method because the proposed method can be used in the high dimensional decision space, linear and nonlinear problems,
and asymmetric interdependent grade situations. In addition, all kinds of interdependent grade
between objectives can be solved using the standard operating procedures. (page 1502)
A19-c22 Antonio López Jaimes, Carlos A Coello Coello, Hernán Aguirre, Kiyoshi Tanaka, Adaptive Objective
Space Partitioning Using Conflict Information for Many-Objective Optimization, 6th International Conference on Evolutionary Multi-Criterion Optimization, April 5-8, 2011, Preto, Brazil, Lecture Notes in
Computer Science, vol. 6576/2011, Springer, [ISBN: 978-3-642-19892-2], pp. 151-165. 2011
Scopus: 79953807528
256
http://dx.doi.org/10.1007/978-3-642-19893-9_11
By grouping objectives in terms of the conflict among them, we are trying to separate the MOP into
subproblems in such a way that each subspace contains information to preserve most of the structure of the original problem. The correlation among solutions in PFapprox is defined to estimate
the conflict among objectives in the sense defined by Carlson and Fullér [A19]. A negative correlation between a pair of objectives means that one objective increases while the other decreases
and vice versa. Thus, a negative correlation estimates the conflict between a pair of objectives. On
the other hand, if the correlation is positive, then both objectives increase or decrease at the same
time. That is, the objectives support each other. (page 154)
A19-c21 Houxing Tang, Guoping Ji, Multiple-Attribute Decision Making with Complete-Imperfect Substitution
between Attributes, Fourth International Conference on Intelligent Computation Technology and Automation, March 28-29, 2011, Shenzhen, China, [ISBN: 978-1-61284-289-9], pp. 1078-1081. 2011
http://dx.doi.org/10.1109/ICICTA.2011.271
The other way is the multiple-attribute decision making in the presence of relationship (RMADM).
This method considers the correlation between attributes and tries to measure the importance of
attributes and attributes sets properly. Christer and Fuller (1995) gave an operator and transformed
the RMADM problem into a single-attribute decision making. (page 1079)
2010
A19-c20 Will Fleury, Complex selection processes: Dealing with dependencies, 2010 IEEE International Conference on Fuzzy Systems (FUZZ), 18-23 July 2010, Barcelona, Spain, [ISBN 978-1-4244-6919-2] pp. 1-8.
2010
http://dx.doi.org/10.1109/FUZZY.2010.5584198
One of the most surprising features which is lacking in the majority of these approaches is the
ability to account for dependencies between the objectives when structuring the preferences. The
majority of science, engineering and financial problems deal with objectives which are dependent
upon each other [A19]. The inability of the majority of these methods to capture such dependencies makes them inapplicable to any problem where such dependencies exist. Despite this, in
both practice and literature the overwhelming majority of applications of these methods treat the
objectives (and hence the attributes) as being independent of each other. The reason for this may
due to the initial habitual domain of MCDM which assumes there is no interdependence among
criteria, as interdependence was initially considered too complex a problem [A19]. (page 1)
2009
A19-c19 Ling Zhang, Dequn Zhou, A Study on R-OWGA Operators, 2009 IEEE International Conference on
Grey Systems and Intelligent Services, November 10-12, 2009, Nanjing, China, pp. 1042-1045. 2009
http://dx.doi.org/10.1109/GSIS.2009.5408013
A19-c18 Bart D. Frischknecht, Diane L. Peters, Panos Y. Papalambros, Pareto Set Analysis: Local Measures
of Objective Coupling in Multi-objective Design Optimization, In: 8th World Congress on Structural and
Multidisciplinary Optimization. Lisbon, Portugal, pp. 1-10. 2009
http://ode.engin.umich.edu/publications/PapalambrosPapers/2009/264.pdf
Several researchers have applied the concept of objective function gradient differences in order to
compare solutions [6, A19, 8]. Lootsma examined how the Pareto frontier relates to sensitivity
in the objective functions [9]. Additionally, analogies to postoptimal analysis in single objective
problems have been proposed, particularly for vector objective linear programming [10, 11]. (page
2)
2008
257
A19-c17 Cengiz Kahraman, Ihsan Kaya, Fuzzy Multiple Objective Linear Programming, in: Cengiz Kahraman
ed., Fuzzy Multi-Criteria Decision Making. Springer Optimization and Its Applications, vol. 16/2008,
[ISBN 978-0-387-76812-0], pp. 325-337. 2008
http://dx.doi.org/10.1007/978-0-387-76813-7_13
2007
A19-c16 Ling Zhang, Dequn Zhou, Yaping Wang, Peifeng Zhu, An Axiomatic Approach of the Ordered Sugeno
Integrals as a Tool to Aggregate Interacting Attributes In: IEEE International Conference on Grey Systems
and Intelligent Services, November 18-20, 2007, (China) Nanjing, pp. 231-234. 2007
http://dx.doi.org/10.1109/GSIS.2007.4443271
A19-c15 Irina Georgescu, Concluding remarks, in: Fuzzy Choice Functions, Studies in Fuzziness and Soft
Computing series, vol. 214/2007, Springer, pp. 265-270. 2007
http://dx.doi.org/10.1007/978-3-540-68998-0_11
A19-c14 Hepu Deng, A Similarity-Based Approach to Ranking Multicriteria Alternatives, in: D.-S. Huang, L.
Heutte, and M. Loog (Eds.): ICIC 2007, Lecture Notes in Computer Science, vol. 4682, Springer, [ISBN
978-3-540-74201-2], pp. 253-262. 2007
http://www.springerlink.com/content/t5lkl1755n014106/
As a result, numerous applications of such an approach have been reported in the literature for
addressing various practical multicriteria analysis problems in the real world setting. The process
of actually calculating the performance index for each alternative across all criteria using the
TOPSIS approach, however, may need further consideration [A19, 3]. (pages 253-254)
2006
A19-c13 Z.K. Öztürk, A review of multi criteria decision making with dependency between criteria, 18th International Conference on Multiple Criteria Decision Making, June 19-23, 2006, Chania, Greece. 2006
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.1782
A19-c12 Borer, N.K., Mavris, D.N. Relative importance modeling in the presence of uncertainty and interdependent metrics, Collection of Technical Papers - 11th AIAA/ISSMO Multidisciplinary Analysis and
Optimization Conference, 6 - 8 Sep 2006, Renaissance Portsmouth Portsmouth, Virginia, USA, vol. 3, pp.
1954-1967. 2006
A19-c11 Ling Zhang; Dequn Zhou; Peifeng Zhu; Hongwei Li, Comparison analysis of MAUT expressed in
terms of Choquet integral and utility axioms, 1st International Symposium on Systems and Control in
Aerospace and Astronautics, ISSCAA 2006, 19-21 January 2006, Harbin, China, pp. 85-89. 2006
http://dx.doi.org/10.1109/ISSCAA.2006.1627708
2003
A19-c10 Xin-Wang Liu Qing-Li Da Liang-Hua Chen, A note on the interdependence of the objectives and their
entropy regularization solution, Proceedings of the Second International Conference on Machine Learning
and Cybernetics, Xi’an, 2-5 November 2003, [ISBN: 0-7803-7865-2], pp. 2677-2682. 2003
http://ieeexplore.ieee.org/iel5/8907/28160/01259991.pdf?
Considering that the concept of interdependence concept proposed by Carlsson and Fullér [A20,
A19, A18] we found that it can only be applied to one dimension decision space. In this paper,
we generalize the concept of objectives interdependence under the multidimensional conditions
based on the gradients of the objectives. The new interdependence concept can reflect both the
relationship and the degrees of the objectives’ support or conflict. Then the application functions
are constructed based on the interdependence grades of the objectives, and they are aggregated by
entropy regularization procedure to solve the multiobjective programming problems. A numerical
example shows the effect of the approach. (page 2677)
258
A19-c9 J.M. Cadenas, M.C. Garrido and F. Jimenez, Heuristics for Optimization: two approaches for problem.
resolution, in: J.L. Verdegay, ed. Fuzzy Sets Based Heuristics for Optimization, Studies in Fuzziness and
Soft Computing, Vol.126, Springer, 2003 pp. 97-112. 2003
A19-c8 Purshouse RC, Fleming PJ, Conflict, harmony, and independence: Relationships in evolutionary multicriterion optimisation, in: Fonseca, C.M.; Fleming, P.J.; Zitzler, E.; Deb, K.; Thiele, L. (Eds.) Evolutionary
Multi-Criterion Optimization Second International Conference, EMO 2003, Faro, Portugal, April 8-11,
2003, Proceedings Series: Lecture Notes in Computer Science , Vol. 2632 Springer, [ISBN: 978-3-54001869-8], pp. 16-30. 2003
http://dx.doi.org/10.1007/3-540-36970-8_2
This type of relationship has received some consideration in the classical OR community, usually
for ZR = Z ∗ , where one member of the criterion pair is known variously as redundant, supportive,
or nonessential [12] [A19] [14]. It remains an open question whether or not to include redundant
criteria in the optimisation process. (pages 23-24)
2002
A19-c7 Jesse D. Beeler, James E. Hunton, Contingent economic rents: Insidious threats to audit independence,
in Vicky Arnold (ed.) (Advances in Accounting Behavioral Research, Volume 5), Emerald Group Publishing Limited, [ISBN 0-7623-0953-9], pp. 21-50. 2002
http://dx.doi.org/10.1016/S1474-7979(02)05036-6
A19-c6 Xin-Wang Liu, Fuzzy inference based aggregation method for multiobjective decision making problems, 2002 International Conference on Machine Learning and Cybernetics, November 4-5, 2002, Beijing,
China, vol. 3, pp. 1296-1300. 2002
http://dx.doi.org/10.1109/ICMLC.2002.1167413
A19-c5 Tao Wang; Yan-Ping Wang, A new algorithm for nonlinear mathematical programming based on fuzzy
inference, 2002 International Conference on Machine Learning and Cybernetics, November 4-5, 2002,
Beijing, China, vol. 2, pp. 694-698. 2002
http://dx.doi.org/10.1109/ICMLC.2002.1174436
1999
A19-c4 Cengiz Kahraman, Ziya Ulukan Multi-Criteria Capital Budgeting Using FLIP In: Third International
Conference on Computational Intelligence and Multimedia Applications (ICCIMA’99), September 23-26,
1999, New Delhi, India, pp. 426-431. 1999
http://dx.doi.org/10.1109/ICCIMA.1999.798568
The optimization of an objective function with fuzzy number coefficients is formulated as the
user oriented extension of the optimization of an objective function with real coefficients by the
proposed ranking criteria. Carlsson and Fuller (1995) introduce measures of interdepence between
the objectives in order to provide for a better understanding of the decision problems and to find
effective and more correct solutions to multiple criteria decision making problems. (page 427)
A19-c3 Sz. Csikai and M. Kovács, A multiobjective linear programming algorithm based on the DempsterShafer theory of evidence, in: B.De Baets, J. Fodor and L. T. Kóczy eds., Proceedings of the Fourth Meeting
of the Euro Working Group on Fuzzy Sets and Second International Conference on Soft and Intelligent
Computing (Eurofuse-SIC’99), Budapest, Hungary, 25-28 May 1999, Technical University of Budapest,
[ISBN 963 7149 21X], pp. 399-403. 1999
One of the interesting problems is how we can handle the conflicts between the objective functions
(e.g. [A19]). (page 399)
A19-c2 Matthias Ehrgott and Stefan Nickel, On the number of Criteria Needed to Decide Pareto Optimality,
WIMA Report, Fachbereich Mathematik, Universität Kaiserslautern, No. 2, 1999.
259
A more general concept of interdependent criteria has been discussed in [A19], see also [A20].
Our approach is related to this topic in the sense that we determine the number of objectives which
are necessary to prove Pareto optimality for a given point.
in books
A19-c2 Gwo-Hshiung Tzeng, Jih-Jeng Huang, Fuzzy Multiple Objective Decision Making, Chapman and
Hall/CRC, 322 p. [ISBN 9781466554610]. 2013
A19-c1 S.N. Sivanandam and S. N. Deepa, Introduction to Genetic Algorithms, Springer, [ISBN 9783540731894],
2007.
in Ph.D. dissertations
• Vandana Bagla, Applications of vector optimization problems, Delhi Technological University, Delhi, India.
2013
http://hdl.handle.net/10603/12351
• Antonio López Jaimes, Techniques to Deal with Many-objective Optimization Problems Using Evolutionary
Algorithms, Computer Science Department, Center for Research and Advanced Studies of the National
Polytechnic Institute of Mexico. 2011
http://delta.cs.cinvestav.mx/˜ccoello/tesis/thesis-alopez.pdf.gz
• Henri Ruotsalainen, Interactive Multiobjective Optimization in Model-based Decision Making with Applications, Department of Physics, University of Kuopio, Finland, [ISBN 978-951-27-1407-0, ISBN 978-95127-1462-9] (PDF). 2010
http://epublications.uef.fi/pub/urn_isbn_978-951-27-1462-9/
urn_isbn_978-951-27-1462-9.pdf
• Nicholas Keith Borer, Decision Making Strategies for Probabilistic Aerospace Systems Design, School of
Aerospace Engineering, Georgia Institute of Technology. 2006
https://smartech.gatech.edu/bitstream/handle/1853/10469/
borer_nicholas_k_200605_phd.pdf?sequence=1
The scant literature on interdependence for decision making does indicate a procedure that can be
modified for the current systems design formulation. The work by Carlsson and Fullér uses the
idea of supporting and conflicting requirements while creating a composite objective. They define
the following for two objectives fi (x) and fj (x), x ∈ Rn [Carlsson and Fullér, 1996, 1995]: (page
110)
• Robin Charles Purshouse, On the Evolutionary Optimisation of Many Objectives, Department of Automatic
Control and Systems Engineering The University of Sheffield, September 2003
http://delta.cs.cinvestav.mx/˜ccoello/EMOO/purshouse_thesis.pdf.gz
In either form of total harmony, one of the objectives can be removed without a?ecting the partial
ordering imposed by the Pareto dominance relation on the set ZR of candidate solutions. This
type of relationship has received some consideration in the classical OR community, usually for
ZR = Z∗ , where one member of the ob jective pair is known variously as redundant, supportive,
or nonessential (Agrell 1997, Carlsson and Fullér 1995, Gal and Hanne 1999). It remains an open
question whether or not to include redundant ob jectives in the optimisation process. (page 97)
[A20] Christer Carlsson and Robert Fullér, Interdependence in fuzzy multiple objective programming, FUZZY
SETS AND SYSTEMS, 65(1994), 19-29. [MR: 95e:90124]. doi 10.1016/0165-0114(94)90244-5
in journals
260
A20-c32 W.Z Yang, Y. Li, Fuzzy multi-level hierarchy of interdependent criteria decision making and its application to nuclear emergency management, Advances in Information Sciences and Service Sciences, Volume
5, Issue 6, 31 March 2013, Pages 391-401. 2013
http://dx.doi.org/10.4156/AISS.vol5.issue6.47
Carlsson and Fuller first put forth the concept of interdependence among criteria, and handle the
dependency structure with fuzzy set theory by application function [A20]. Östemark showed that
this structure is static, and generalized it to a dynamic fuzzy multi objective problem (FMOP) [4].
Carlsson and Fuller developed a new method with if-then rules [C45]. (page 391)
A20-c31 Doraid Dalalah, Mohammad Al-Tahat, Khaled Bataineh, Mutually dependent multi-criteria decision
making, FUZZY INFORMATION AND ENGINEERING, 4(2012), number 2, pp. 195-216. 2012
http://dx.doi.org/10.1007/s12543-012-0111-3
A20-c31 Chi-Cheng Huang and Pin-Yu Chu, Using the fuzzy analytic network process for selecting technology
R&D projects, INTERNATIONAL JOURNAL OF TECHNOLOGY MANAGEMENT, 53(2011), number
1, pp. 89-115. 2011
http://inderscience.metapress.com/link.asp?id=u58122rt2768qx54
A20-c30 Jih-Jeng Huang, Chin-Yi Chen, Hsiang-Hsi Liu, Gwo-Hshiung Tzeng, A multiobjective programming
model for partner selection-perspectives of objective synergies and resource allocations, EXPERT SYSTEMS WITH APPLICATIONS, 37(2010), Issue 5, pp. 3530-3536. 2010
http://dx.doi.org/j.eswa.2009.09.044
Carlsson and Fullér (1994, 1996) first proposed two methods to reshape the membership function
for considering the problem of multiobjective programming with interdependence. Thereafter,
several issues have been proposed to consider further situations such as uncertainty environment
(Carlsson & Fullér, 1996) and temporal interdependence (Östermark, 1997). However, several
short-comings of their methods should be modified for considering the problem of partner selection in this paper. The first method (Carlsson & Fullér, 1995), proposed by Carlsson and Fullér,
does not precisely measure the supportive or the conflicting degree between the objectives and can
only deal with the one-dimensional decision space. In contrast, the second method (Carlsson &
Fullér, 2002) can only be employed in the linear case. It can be seen that, the precise objective
synergies is important for firms to choose partners and the objectives in firms or alliances are usually complex and nonlinear functions. Therefore, a more accurate and flexible index should be
given in order to choose the best partners in alliances. (page 3532)
A20-c29 Fuzhan Nasiri; Anastassia Manuilova; Guo H. Huang, Environmental Policy Analysis in Freight Transportation Planning: An Optimality Assessment Approach, INTERNATIONAL JOURNAL OF SUSTAINABLE TRANSPORTATION, 3(2009), pp. 88-109. 2009
http://dx.doi.org/10.1080/15568310701779519
A20-c28 XH Yu, ZS Xu, Hierarchical Aggregation Methods Based on Weighted Combination Operators,
INFORMATION-AN INTERNATIONAL INTERDISCIPLINARY JOURNAL, 12(2009), issue 1, pp. 5164. 2009
A20-c27 Fuzhan Nasiri, Gordon Huang, A fuzzy decision aid model for environmental performance assessment
in waste recycling, Environmental Modelling & Software 23 (2008) 677-689. 2008
http://dx.doi.org/10.1016/j.envsoft.2007.04.009
A20-c26 Zhang Ling, Multi-attribute decision making based on association theory research, MANAGEMENT
REVIEW, 20(2008), number 5, pp. 51-57 (in Chinese). 2008
http://www.cqvip.com/qk/96815a/2008005/27274741.html
A20-c25 Chang JR, Cheng CH, Chen LS, A fuzzy-based military officer performance appraisal system, APPLIED SOFT COMPUTING 7 (3): 936-945 JUN 2007
http://dx.doi.org/10.1016/j.asoc.2006.03.003
Carlsson and Fullér [A19, A20] introduced the concept of interdependence in multiple criteria
decision making (MCDM), and some researchers showed that fuzzy set theory [28] could be successfully applied to resolve multiple criteria problems [10,23,26,27]. In general, the appraisal
261
from among two or more people is a multiple criteria decision making problem. Under many situations, the values for the qualitative criteria are often imprecisely defined for the decision makers.
(page 937)
A20-c24 Nasiri F, Maqsood I, Huang G, et al., Water quality index: A fuzzy river-pollution decision support
expert system, JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT - ASCE, 133
(2): 95-105 MAR-APR 2007
http://dx.doi.org/10.1061/(ASCE)0733-9496(2007)133:2(95)
A20-c23 Gal T, Hanne T Nonessential objectives within network approaches for MCDM EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 168 (2): 584-592 JAN 16 2006
http://dx.doi.org/10.1016/j.ejor.2004.04.045
A20-22 Myung HC, Bien ZZ, Design of the fuzzy multiobjective controller based on the eligibility method,
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 18 (5): 509-528 MAY 2003
http://dx.doi.org/10.1002/int.10101
Define the relation between two objectives as follows [A20]:
1. fi supports fj if fi (u(t1 ), x(t1 )) ≥ fi (u(t2 ), x(t2 )) entails fj (u(t1 ), x(t1 )) ≥ fj (u(t2 ), x(t2 )),
for u ∈ U and t1 ≤ t2 ,
2. fi conflicts fj if fi (u(t1 ), x(t1 )) ≥ fi (u(t2 ), x(t2 )) entails fj (u(t1 ), x(t1 )) < fj (u(t2 ), x(t2 )),
for u ∈ U and t1 ≤ t2 ,
3. fi and fj are independent, otherwise
(page 518)
A20-c21 Lei, X., Shi, Z. Overview of multi-objective optimization methods, JOURNAL OF SYSTEMS ENGINEERING AND ELECTRONICS, 15 (2), pp. 142-146. 2004
A20-c20 Matthias Ehrgott and Stefan Nickel, On the number of Criteria Needed to Decide Pareto Optimality,
MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 55(2002) 329-345. 2002
http://dx.doi.org/10.1007/s001860200207
A more general concept of interdependent criteria has been discussed in [A19], see also [A20].
Our approach is related to this topic in the sense that we determine the number of objectives which
are necessary to prove Pareto optimality for a given point. However, the theory presented in this
paper is more general: the results also hold in the absence of nonessential criteria, as will be
. . . (page 330)
A20-c19 Gal T, Hanne T, Consequences of dropping nonessential objectives for the application of MCDM
methods, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 119(2): 373-378 DEC 1 1999
http://dx.doi.org/10.1016/S0377-2217(99)00139-3
The problem of obtaining well-designed criteria for a multiple criteria decision making problem
is well known (see e.g. Bouyssou, 1992; Keeney and Raiffa, 1976, pp. 50-53; Keeney, 1992, pp.
82-87, 120; Roy, 1977; Roy and Vincke, 1984). However, the problem of interdependence among
the criteria is seldom treated in the literature (Carlsson and Fullér, 1995; see also Carlsson and
Fullér, 1994). (page 373)
A20-c18 Jonathan Lee, Jong-Yih Kuo, New approach to requirements trade-off analysis for complex systems
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, 10 (4), pp. 551-562 JUL-AUG
1998
http://dx.doi.org/10.1109/69.706056
Carlsson and Fullér [A20] propose an approach to fuzzy multiple objective programming (FMOP)
with interdependency relationships among objectives, which is an extension of Carlsson’s MOP
[4] to fuzzy logic. Three kinds of relationships have been identified: supportive, conflicting, and
independent. The basic idea is to utilize these relationships to modify the membership function of
the so called ”good solution.” Felix [15] and Felix et al. [17] propose an approach, called DMRG
(Decision Making Based on Relationship between Goals), to defining a spectrum of relationships
262
based on fuzzy inclusion and fuzzy noninclusion: independent, assist, cooperate, analogous, hinder, compete, trade-off, and unspecified dependent, and to determining the final set of decision
alternatives according to the relationships. These approaches are similar to ours in two aspects:
the problems of modeling the relationships, and the issues of aggregation.(page 558)
A20-c17 Jonathan Lee, Jong-Yih Kuo, Fuzzy decision making through trade-off analysis between criteria, INFORMATION SCIENCES, 107(1998) 107-126. 1998
http://dx.doi.org/10.1016/S0020-0255(97)10020-2
In addition, Carlsson and Fullér [A20] advocated that much closer to MCDM in the real world than
the traditional MCDM are the cases with interdependent criteria. However, current relationship
analysis approaches (e.g. fuzzy multiple objective programs (FMOP) [A20] and decision making
based on relationship between goals (DMRG) [2,4,5]) usually result in identifying relationships
that are contradictory to each other. (page 108)
Recently, Carlsson and Fullér [A20] proposed an approach to FMOP with interdependency relationships among objectives, which is an extension of Carlsson’s MOP [20] to fuzzy logic. The
basic idea is to utilize these relationships to modify the membership function of the so-called
’good solution’, denoted as Hi . (page 121)
A20-c16 J. Tang and D. Wang, An interactive approach based on a genetic algorithm for a type of quadratic programming problems with fuzzy objectives and resources, COMPUTERS & OPERATIONS RESEARCH,
24(1997) 413-422. 1997
http://dx.doi.org/10.1016/S0305-0548(96)00059-7
The current research on fuzzy mathematical programming was largely limited in the range of
linear programming [10-12] and multiobjective programming [13, A20, 15], but fuzzy nonlinear
programming [16] including fuzzy quadratic programming is rarely involved. (page 414)
A20-c15 R. Östermark, Temporal interdependence in fuzzy MCDM problems, FUZZY SETS AND SYSTEMS,
88(1997) 69-79. 1997
http://dx.doi.org/10.1016/S0165-0114(96)00046-2
The case with unknown parameter values, e.g., future sales prices, interest rates etc. is not considered in the present study. Compared to the static concept of Carlsson and Fullér [A20], we have
set of k objective function trajectories defined over the planning horizon, not merely k (static)
objective function values. (page 71)
In this study we have considered temporal interdependence in multiple criteria decision making.
Our analysis extends the (static) concept introduced by Carlsson and Fullér [A20] in a way that
allows coping with goal conflicts typically arising in managerial decisioin making. The concept
of temporal interdependence was used to describe mutually supportive and mutually conflicting
criteria in a multiperiod firm model. Next, the static membership function proposed by Carlsson
and Fullér [A20] was generalized to the dynamic case both for DMOP and DFMOP problems. We
showed that incorporating the discount rate of the firm, i.e., the risk-adjusted weighted average
cost of capital in the dynamic objective functions is essential in corporate planning. The cost
of capital affects the shape of the membership functions and, therefore, the mutual support vs.
conflict in the objective set. In the derivations we have utilized the simplifying assumption that
all objectives are equally important. This allows usage of the number of criteria as a measure of
support/conflict in the objective set, precisely as in Carlsson and Fullér [A20]. (page 78)
in proceedings and edited volumes
A20-c15 Liu MeiFen, Wu Berlin, All Work and No Play Makes Jack a Dull Leader? Impact Evaluation with
Leisure Activities and Management Performance for the School Leaders, in: Watada Junzo, Xu Bing, Wu
Berlin eds., Innovative Management in Information and Production. Springer New York, [ISBN 978-14614-4856-3], pp. 93-103. 2014
http://dx.doi.org/10.1007/978-1-4614-4857-0_10
263
A20-c14 Jih-Jeng Huang, Chin-Yi Chen, Interdependent Multiple Objective Programming - A Monte Carlo
Method, 2011 IEEE International Conference on Fuzzy Systems, June 27-30, 2011, Taipei, Taiwan, [ISBN:
978-1-4244-7316-8], pp. 1497-1503. 2011
Carlsson and Fullér [A19, A20, B1,] first proposed two methods to consider the problem of MOP
with interdependence by estimating the interdependent grade between objectives. Thereafter, several issues have been proposed to consider further situations, such as uncertainty environment
[A20, B1] and temporal interdependence [15]. However, several shortcomings of their methods
should be modified so that we can employ interdependent multiple objective programming (IMOP)
in practice. Firstly, their first method [A19] does not precisely measure the supportive or conflicting grade between objectives and can only deal with the one-dimensional decision problem. In
contrast, their second method [A20] can only be suitable for symmetric linear interdependent multiple objective programming (SLIMOP). However, it can be seen that since real-life problems are
usually complex and intricate, a general method should be given to handle all kinds of IMOP
problems. (page 1497)
A20-c13 Weiyi Qian, An inexact approach based on Genetic Algorithm for fuzzy programming problems, Sixth
International Conference on Natural Computation (ICNC), 10-12 August 2010, Yantai, China, [ISBN 9781-4244-5958-2], pp. 2281-2285. 2010
http://dx.doi.org/10.1109/ICNC.2010.5584212
A20-c12 Z.K. Öztürk, A review of multi criteria decision making with dependency between criteria, 18th International Conference on Multiple Criteria Decision Making, June 19-23, 2006, Chania, Greece. 2006
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.1782
A20-c11 Zhang, L., Zhou, D., Zhu, P., Li, H. Comparison analysis of MAUT expressed in terms of choquet
integral and utility axioms 1st International Symposium on Systems and Control in Aerospace and Astronautics, 2006, art. no. 1627708, Jan. 19-21, 2006, Harbin, China, pp. 85-89. 2006
http://dx.doi.org/10.1109/ISSCAA.2006.1627708
Carlsson and Fullér demonstrated that the use of interdependences among objectives of MCDM
provides for more correct solutions and faster convergence [A18, A19, A20]. (page 85)
A20-c10 Jong-Yih Kuo and Jonathan Lee, Evolution of Intelligent Agent in Auction Market, in: FUZZY IEEE
2004 CD-ROM Conference Proceedings Budapest, July 26-29, 2004, IEEE Catalog Number: 04CH37542C,
[ISBN 0-7803-8354-0], pp. 331-336 (file name: 0052-1350.pdf). 2004
http://ieeexplore.ieee.org/iel5/9458/30040/01375744.pdf?
Most of the existing approaches in multiple criteria making lack the aspect of an explicit modeling
of relationships between goals. As was pointed out by Felix [8], a few of the existing MCDM
approaches refer to the aspect of an explicit modeling of relationships between goals. Carlsson and
Fullér [A20] advocated that much closer to MCDM in the real world than the traditional MCDM
are the case with interdependent criteria. However, current relationship analysis approaches (e.g.
[A20], [9]) usually result in identifying relationships that are contradictory to each other. Our
previous work on Criteria Trade-off Analysis has been on the formulation of soft criteria based on
Zadeh’s canonical form in test-score semantics and an extension of the notion of soft condition
[14]. The trade-off among soft goals is analyzed by identifying the relationships between goals.
A compromise overall satisfaction degree can be obtained through the aggregation of individual
goal based on the goals hierarchy. (page 334)
A20-c9 Xin-Wang Liu Qing-Li Da Liang-Hua Chen, A note on the interdependence of the objectives and their
entropy regularization solution, Proceedings of the Second International Conference on Machine Learning
and Cybernetics, Xi’an, 2-5 November 2003, [ISBN: 0-7803-7865-2], pp. 2677- 2682. 2003
A20-c8 Jonathan Lee, Jong-Yih Kuo et al., Trade-off Requirement Engineering, in: Jonathan Lee ed., Software
Engineering with Computational Intelligence Series: Studies in Fuzziness and Soft Computing , Vol. 121
Springer, [ISBN: 978-3-540-00472-1] 2003 pp. 51 -71. 2003
264
A20-c7 Myung, H.-C., Bien, Z.Z. Interdependent multiobjective control using Biased Neural Network (Biased
NN) Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS, 3, pp.
1378-1383. 2001
http://ieeexplore.ieee.org/iel5/7506/20427/00943750.pdf?arnumber=943750
A20-c6 Matthias Ehrgott and Stefan Nickel, On the number of Criteria Needed to Decide Pareto Optimality,
WIMA Report, Fachbereich Mathematik, Universität Kaiserslautern, No. 2, 1999.
A more general concept of interdependent criteria has been discussed in [A19], see also [A20].
Our approach is related to this topic in the sense that we determine the number of objectives which
are necessary to prove Pareto optimality for a given point. However, the theory presented in this
paper is more general: the results also hold in the absence of nonessential criteria, as will be . . .
A20-c5 Didier Dubois and Henri Prade, Fuzzy criteria and fuzzy rules in subjective evaluations - a general
discussion. In Proc. 5th European Congress on Intelligent Technologies and soft Computing (EUFIT 97),
September 8-12, 1997, Aachen, Germany, 975-978. 1997
ftp://ftp.irit.fr/pub/IRIT/RPDMP/FCFRSE.ps.gz
Such an approach raises several questions about
• the choice of proper scales (what kind? qualitative or numerical scale?), their commensurability, and the meaningfulness of the aggregation operations w.r.t. the scale;
• the practical elicitation of the membership functions, and of the appropriate operations (compensatory, or purely logical conjunctions, for instance); see (Dubois and Prade, 1988) on this
latter point, where the elicitation of aggregation operations is based on the knowledge of the
decision’s maker’s behavior in well-contrasted situations;
• the modelling of the importance (by means of weights or thresholds) of the criteria, and more
generally of the interaction between criteria (Carlsson and Fullér, 1994; Grabisch, 1997).
(page 976)
A20-c4 Lee J, Jong-Yih Kuo, W. T. Huang, Fuzzy decision making through relationships analysis between
criteria In: Fuzzy Systems Symposium, 1996. ’Soft Computing in Intelligent Systems and Information
Processing’, 11-14 December 1996, Kenting, Taiwan, pp. 296-301. 1996
http://dx.doi.org/10.1109/AFSS.1996.583617
Current relationships analysis approaches such as FMOP (fuzzy multiple objective programs)
[A20] and DMRG (decision making based on relationships between goals), however, usually result in identifying relationships between criteria that are contradictory to each other. Furthermore,
the aggregation operators selected in their aggregation procedures either derive more than one
alternative or fail to come up with any. (page 296)
in books
A20-c3 Gwo-Hshiung Tzeng, Jih-Jeng Huang, Fuzzy Multiple Objective Decision Making, Chapman and
Hall/CRC, 322 p. [ISBN 9781466554610]. 2013
A20-c2 S.N. Sivanandam and S. N. Deepa, Introduction to Genetic Algorithms, Springer, [ISBN 9783540731894],
2007.
A20-c1 G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, [ISBN
0-13-101171-5], 1995.
in Ph.D. dissertations
• Antonio López Jaimes, Techniques to Deal with Many-objective Optimization Problems Using Evolutionary
Algorithms, Computer Science Department, Center for Research and Advanced Studies of the National
Polytechnic Institute of Mexico. 2011
http://delta.cs.cinvestav.mx/˜ccoello/tesis/thesis-alopez.pdf.gz
265
In the current literature it is possible to find several definitions of conflict among objectives (see
e.g., [53, 1, 94, 12]). However, we used the definition proposed by Carlsson and Fullér [A20, A19]
since it is intuitive and, as we will explain later, it can be estimated using a low time complexity
algorithm. Let be SX a subset of X, then, according to Carlsson and Fullér, two objectives can be
related in the following ways (assuming minimization): (page 70)
• Lisy Cherian, Optimization in Fuzzy Environment. Union Christian College, Mahatma Gandhi University,
India. 2008
http://shodhganga.inflibnet.ac.in/handle/10603/22561
• Sudaryanto, A fuzzy multi-attribute decision making approach for the identification of the key sectors of an
economy: The case of Indonesia, RWTH Aachen Germany. 2003
http://darwin.bth.rwth-aachen.de/opus3/volltexte/2003/591/
[A21] Robert Fullér and Hans-Jürgen Zimmermann, Fuzzy reasoning for solving fuzzy mathematical programming problems, FUZZY SETS AND SYSTEMS, 60(1993) 121-133. [MR: 94k:90148] [Zbl.795.90086].
doi 10.1016/0165-0114(93)90341-E
in journals
2015
A21-c54 Gabriel Jaime Correa-Henao, Gloria Elena Pea-Zapata, Multi-objective Optimization Proposal with
Fuzzy Coefficients in both Constraints and Objective Functions, Cuaderno Activa, 7(2015), pp. 13-25.
2015
http://ojs.tdea.edu.co/index.php/cuadernoactiva/article/download/259/272
Once the constraints have been transformed into Eq. (5), it constitutes a system of crisp linear
inequalities, which can now be solved by any classical Linear Programming (LP) method (Tanaka
et al., 2000). It must be noted that the transformation in (5) can only be applied to the constraints.
The objective function needs to be defuzzified with an alternative methodology (Fullér & Zimmermann, 1993; Zimmermann, 1987), which will be described in the following paragraphs. (page
17)
2014
A21-c53 Khosrow Hosseinzad, Assembly Line Balancing Problem With Fuzzy Variable, International Journal
of Basic Sciences and Applied Research, 3(2014), pp. 159-166. 2014
http://isicenter.org/fulltext2/paper-231.pdf
A21-c52 Figueroa-Garcia JC, Hernández G, A method for solving linear programming models with interval
type-2 fuzzy constraints, Pesquisa Operacional, 34: (1) pp. 73-89. 2014
http://dx.doi.org/10.1590/S0101-74382014005000002
A21-c51 Fang-Yie Leu, Jung-chun Liu, Ya-Ting Hsu, Yi-Li Huang, The simulation of an emotional robot
implemented with fuzzy logic, Soft Computing (to appear). 2014
http://dx.doi.org/10.1007/s00500-013-1217-1
2012
A21-c50 Sylvia Encheva, Reasoning With Non-Binary Logics, World Academy of Science, Engineering and
Technology, 67(2012), pp. 143-146. 2012
https://waset.org/journals/waset/v67/v67-25.pdf
A21-c49 Doraid Dalalah, Mohammad Al-Tahat, Khaled Bataineh, Mutually dependent multi-criteria decision
making, FUZZY INFORMATION AND ENGINEERING, 4(2012), issue 2, pp 195-216. 2012
http://dx.doi.org/10.1007/s12543-012-0111-3
266
A21-c48 Figueroa-Garcia JC, Kalenatic D, Lopez-Bello CA, Multi-period Mixed Production Planning with
uncertain demands: Fuzzy and interval fuzzy sets approach, FUZZY SETS AND SYSTEMS, 206(2012),
pp. 21-38. 2012
http://dx.doi.org/10.1016/j.fss.2012.03.005
In the last 30 years, many developments in the fields of information, uncertainty and decision
making based on fuzzy theory have appeared together with the improvement of computing capabilities. Different decision making approaches have used fuzzy theory to solve complex problems,
especially the fuzzy optimization field treated by Klir and Yuan [1], Lai and Hwang [2], Kacprzyk
and Orlovski [3], Zimmermann [4], and Zimmermann and Fullér [5]. (page 22)
Imprecision and uncertainty are related to problems within the measurement of a specific variable.
According to Mendel [3032] and Zadeh [33,34], imprecision and uncertainty can be represented
through either classical or interval fuzzy sets, each one at different levels. Thus, an MPP model
with flexible demands can be addressed with fuzzy sets, where the main objective is to satisfy all
flexible constraints at an optimal degree through an α-cut. This satisfaction degree is an auxiliary
variable that is projected over all fuzzy constraints and the set of optimal solutions to return a
global solution of the problem, as defined by Zimmermann [4] and Zimmermann and Fullér [5].
(page 25)
A21-c47 Jafar Fathali, Ali Jamalian, Locating Multiple Facilities in Convex Sets with Fuzzy Data and Block
Norms, APPLIED MATHEMATICS 3(2012), pp. 1950-1958. 2012
http://dx.doi.org/10.4236/am.2012.312267
A formulation of fuzzy linear programming with fuzzy constraints and a solution method were
given by Tanaka and Asai [18]. Maleki et al. [19] introduced a linear programming problem
with fuzzy variables and proposed a method for solving it. Fang and Hu [20] consider linear
programming with fuzzy constraint coefficients (see also [A21]). (page 1954)
A21-c46 Farhad Hassanzadeh, Mikael Collan, Mohammad Modarres, A practical R&D selection model using fuzzy pay-off method, INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 58(2012), number 1-4, pp. 227-236. 2012
http://dx.doi.org/10.1007/s00170-011-3364-9
2011
A21-c45 Sanjay Jain, Adarsh Mangal, P R Parihar, Solution of fuzzy linear fractional programming problem,
OPSEARCH, 48(2011), number 2, pp. 129-135. 2011
http://dx.doi.org/10.1007/s12597-011-0043-4
A21-c44 R Ezzati, R Enayati, An Algorithm to Solve Fully Fuzzy Biobjective Linear Programming Based on
the Compromise Programming with Respect to the Ideal Points, AUSTRALIAN JOURNAL OF BASIC
AND APPLIED SCIENCES, 5(2011), number 6, pp. 1098-1108. 2011
http://www.insipub.com/ajbas/2011/june-2011/1098-1108.pdf
Fullér, (1993) studied the fuzzy linear programming (FLP) problems with fuzzy coefficients and
fuzzy inequality relations as multiple fuzzy reasoning schemes (MFR), where the antecedents of
the scheme correspond to the constraints of the FLP problem and the fact of the scheme is the
objective of the FLP problem. (page 1098)
2009
A21-c43 T. Bhaskar; R. Sundararajan; PG Krishnan, A fuzzy mathematical programming approach for crosssell optimization in retail banking, JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY, 60(2009),
pp. 717-727. 2009
http://dx.doi.org/10.1057/palgrave.jors.2602609
267
The use of fuzzy numbers leads us to represent the problem as one of fuzzy mathematical programming. There have been works related to the properties and solution methodologies for solving fuzzy linear programming. Zimmermann (1976, 1978) proposed a method for linear programming problems. Similar methods were proposed in Rommelfanger (1996), Gasimov and Yenilmez
(2002) and Fullér and Zimmermann (1993). We formulate the problem as a fuzzy integer linear
program. The fuzzy problem is then transformed to a multi-objective problem with crisp numbers.
The multiple objectives deal with the most likely of the fuzzy numbers as well as their spread in
either direction. This multi-objective problem is then solved using a method proposed by YoungJou and Ching-Lai (1994) that attempts to maximize the worst case satisfaction level of all the
objectives. (page 718)
A21-c42 Sylvia Encheva, Sharil Tumin, Problem Identification Based on Fuzzy Functions, WSEAS TRANSACTIONS ON ADVANCES IN ENGINEERING EDUCATION, Issue 4, Volume 6, April 2009, pp. 111120. 2009
http://www.wseas.us/e-library/transactions/education/2009/29-490.pdf
2008
A21-c41 Sanjay Jain and Kailash Lachhwani, Sum of Linear and Fractional Multiobjective Programming Problem under Fuzzy Rules Constraints, Australian Journal of Basic and Applied Sciences, 2(2008), number 4,
pp. 1204-1208. 2008
http://www.insinet.net/ajbas/2008/1204-1208.pdf
A21-c40 Abas Ali Noora, P Karami, Ranking Functions and its Application to Fuzzy DEA, INTERNATIONAL
MATHEMATICAL FORUM, 3(2008), pp.1469-1480. 2008
http://www.m-hikari.com/forth/nooraIMF29-32-2008.pdf
A21-c39 G. R. Jahanshahloo, F. Hosseinzadeh Lot, M. Alimardani Jondabeh, Sh. Banihashemi, L. Lakzaie,
Cost Efficiency Measurement with Certain Price on Fuzzy Data and Application in Insurance Organization,
APPLIED MATHEMATICAL SCIENCES, 2(2008), pp. 1-18. 2008
http://www.m-hikari.com/ams/ams-password-2008/ams-password1-4-2008/lotfiAMS1-4-2008-1.pdf
A21-c38 W. Dwayne Collins; Chenyi Hu, Studying interval valued matrix games with fuzzy logic, SOFT COMPUTING, vol. 12, pp. 147-155. 2008
http://dx.doi.org/10.1007/s00500-007-0207-6
2006
A21-c37 Mahdavi-Amiri N, Nasseri SH, Duality in fuzzy number linear programming by use of a certain linear
ranking function, APPLIED MATHEMATICS AND COMPUTATION, 180 (1): 206-216 SEP 1 2006
http://dx.doi.org/10.1016/j.amc.2005.11.161
Fang and Hu [5] consider linear programming with fuzzy constraint coefficients (see also [A21]).
(page 206)
A21-c36 Campos FA, Villar J, Jimenez M, Robust solutions using fuzzy chance constraints, ENGINEERING
OPTIMIZATION, 38 (6): 627-645 SEP 2006
http://dx.doi.org/10.1080/03052150600603165
2005
A21-35 D.R. Pavel, Optimisation with Fuzzy Linguistic Rules, Annals of ”Dunarea de Jos” University of
Galati. Fascicle II, Mathematics, Physics, Theoretical Mechanics. Vol. XXVIII, no. XXIII, pp. 77-80.
2005
http://www.phys.ugal.ro/Annals_Fascicle_2/year2005/Annals2005Abstract.pdf
A21-c34 Majura F. Selekwa and Emmanuel G. Collins, Jr., Numerical solutions for systems of qualitative
nonlinear algebraic equations by fuzzy logic, FUZZY SETS AND SYSTEMS, 150(2005) pp. 599-609.
2005
http://dx.doi.org/10.1016/j.fss.2004.06.008
268
Computational methods that use fuzzy logic have attracted attention in recent years; most of them
have addressed optimization problems. The methods of [1,2] were for solving a crisp linear programming problem by searching and reasoning. Extension of these methods to fuzzy mathematical
programs in which the linear program has fuzzy coefficients was accomplished in [3,4,A21]. (page
600)
2003
A21-c33 Ray KS, Dinda TK, Pattern classification using fuzzy relational calculus, IEEE TRANSACTIONS ON
SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS, 33 (1): 1-16 FEB 2003
http://dx.doi.org/10.1109/TSMCB.2002.804361
1999
A21-c32 Dinda TK, Ray KS, Chakraborty MK, Fuzzy relational calculus approach to multidimensional pattern
classification, PATTERN RECOGN, 32 (6): 973-995 JUN 1999
http://dx.doi.org/10.1016/S0031-3203(98)00133-2
1998
A21-c31 M.-S. Yang and M.-C. Liu, On possibility analysis of fuzzy data, FUZZY SETS AND SYSTEMS,
94(1998) 171-183. 1998
http://dx.doi.org/10.1016/S0165-0114(96)00259-X
The use of fuzzy set provides imprecise class membership information and is widely applied in
diverse areas such as control, cluster analysis, decision making, engineering systems, etc. See, for
example [2,3, A21, . . . ]. (page 171)
1997
A21-c30 Weldon A.Lodwick and K. David Jamison, Interval methods and fuzzy optimization, INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 5
pp. 239-249. 1997
http://dx.doi.org/10.1142/S0218488597000221
1995
A21-c29 B. Müller, Short-term planning of the production program in dairies by considering the subjective vagueness of data in mathematical models on the basis of fuzzy sets, Kieler Milchwirtschaftliche
Forschungsberichte : Veroeffentlichungen der Bundesanstalt fuer Milchforschung, 47(4), pp. 307-337.
1995
in proceedings and edited volumes
A21-24 Juan Carlos Figueroa-Garcia, Dusko Kalenatic, Cesar Amilcar Lopez-Bello Multiple Experts Knowledge in Fuzzy Optimization of Logistic Networks, In: Intelligent Techniques in Engineering Management,
Intelligent Systems Reference Library, vol. 87/2015, Springer, (ISBN 978-3-319-17905-6) pp. 623-643.
2015
http://dx.doi.org/10.1007/978-3-319-17906-3_24
A21-23 Juan C. Figueroa-Garcı́a, German Hernandez, A multiple means transportation model with type-2 fuzzy
uncertainty, In: Supply Chain Management Under Fuzziness, Studies in Fuzziness and Soft Computing, vol.
313/2004, Springer Verlag, [ISBN 978-364253938-1], pp. 449-468. 2014
http://dx.doi.org/10.1007/978-3-642-53939-8-19
A21-22 Juan C. Figueroa-Garcı́a, German Hernandez, Linear Programming with Interval Type-2 Fuzzy Constraints, in: Constraint Programming and Decision Making, Studies in Computational Intelligence, 539(2014),
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269
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A21-21 Figueroa Garcia JC, Hernandez G, A note on ’Solving Fuzzy Linear Programming Problems with Interval Type-2 RHS’ In: Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting,
IFSA/NAFIPS 2013. Edmonton, AB: IEEE Computer Society Press, 2013, pp. 591-594. 2013
http://dx.doi.org/10.1109/IFSA-NAFIPS.2013.6608467
The most used method to solve LP problems with fuzzy constraints was proposed by Zimmermann
[5] and [A21] who defined a fuzzy set of solutions z̆(x∗ ) to find a joint α-cut to z̆(x∗ ) and b̆, which
is summarized next: (page 591)
A21-20 Figueroa-Garca JC, Hernandez G, Behavior of the soft constraints method applied to interval type-2
fuzzy linear programming problems, 9th International Conference on Intelligent Computing, ICIC 2013,
Lecture Notes in Artificial Intelligence, vol. 7996/2013, 28-31 July 2013, Nanning, China, Springer Verlag,
[ ISBN: 978-364239481-2], pp. 101-109. 2013
http://dx.doi.org/10.1007/978-3-642-39482-9_12
A21-19 Garcia JCF, A general model for linear programming with interval type-2 fuzzy technological coefficients, Proceedings of the 2012 Annual Meeting of the North American Fuzzy Information Processing
Society, NAFIPS 2012; Berkeley, CA; United States; 6 August 2012 through 8 August 2012; IEEE, [ISBN:
978-146732337-6]. Article number: 6291064. 2012
http://dx.doi.org/10.1109/NAFIPS.2012.6291064
A21-18 Figueroa-Garcia JC, Hernandez G, A transportation model with interval type-2 fuzzy demands and
supplies, Intelligent Computing Technology. 8th International Conference on Intelligent Computing Technology, ICIC 2012; Huangshan; China; 25 July 2012 through 29 July 2012, Lecture Notes in Computer
Science, vol. 7389, Springer, [ISBN: 978-3-642-31587-9], pp. 610-617. 2012
http://dx.doi.org/10.1007/978-3-642-31588-6_78
A21-17 Garcia JCF, Mixed Production planning under fuzzy uncertainty: A cumulative membership function
approach, 2012 Workshop on Engineering Applications, WEA 2012. Article number: 6220081. 2012
http://dx.doi.org/10.1109/WEA.2012.6220081
A21-16 Figueroa-Garcia JC, Hernandez G, Computing optimal solutions of a linear programming problem with
interval type-2 fuzzy constraints, In: Hybrid Artificial Intelligent Systems, 7th International Conference,
HAIS 2012, Salamanca, Spain, March 28-30th, 2012. Proceedings, Part I, Lecture Notes in Artificial
Intelligence, vol. 7208, Springer, [ISBN: 978-364228941-5], pp. 567-576. 2012
http://dx.doi.org/10.1007/978-3-642-28942-2_51
A21-16 Sylvia Encheva, Individual Paths in Self-evaluation Processes, Computational Intelligence and Intelligent Systems, Communications in Computer and Information Science, Springer, [ISBN 978-3-642-342899], pp. 425-431. 2012
http://dx.doi.org/10.1007/978-3-642-34289-9_47
A21-c15 S. Encheva, Some Fuzzy Logic Based Predictions, 10th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases., February 20-22, 2011, Cambridge, England,
pp. 176-180. 2011
http://www.wseas.us/e-library/conferences/2011/Cambridge/AIKED/AIKED-30.pdf
A21-c14 Sylvia Encheva and Sharil Tumin, Fuzzy Knowledge Processing for Unveiling Correlations between Preliminary Knowledge and the Outcome of Learning New Knowledge, in: Magued Iskander,
Vikram Kapila and Mohammad A. Karim eds., Technological Developments in Education and Automation, Springer, [ISBN 978-90-481-3655-1], pp. 179-182. 2010
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A21-c13 Juan Carlos Figueroa Garcia, Cesar Amilcar Lopez Bello, Pseudo-optimal solutions of FLP problems
by using the Cumulative Membership Function, 28th North American Fuzzy Information Processing Society Annual Conference (NAFIPS2009). Cincinnati, USA, June 13-17, 2009, [ISBN 978-1-4244-4575-2],
pp. 1-6. 2009
http://dx.doi.org/10.1109/NAFIPS.2009.5156464
Now, this paper attempts to solve FLP problems with nonlinear membership functions, either
with finite or infinite support. A pre-defuzzification level is used to find intervals of solution of the
nonlinear membership functions and then it is solved by using the classical model of Zimmermann
(See [1] and [A21]) which involves Type-1 Fuzzy Sets on their parameters (page 1)
A21-c12 J C F Garcia, Solving fuzzy linear programming problems with Interval Type-2 RHS, IEEE International Conference on Systems, Man and Cybernetics, San Antonio, USA, [ISBN 978-1-4244-2793-2],
October 11-14, 2009, pp. 262-267. 2009
http://dx.doi.org/10.1109/ICSMC.2009.5345943
Zimmermann in [4] and [A21] presented the most used method to solve this problem. (page 263)
A21-c11 Sylvia Encheva, Frequent Sets Mining for Problem Identification, Proceedings of the 5th WSEAS/IASME
International Conference on Educational Technologies, July 01-03, 2009, Trenerife, Spain, Recent Advances in Computer Engineering Series, [ISBN 978-960-474-092-5], pp. 33-37. 2009
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A21-c10 Sylvia Encheva, Concepts in fuzzy logics, in: Proceedings of the 10th WSEAS international Conference on Automation & information, Prague, Czech Republic, March 23 - 25, 2009, N. E. Mastorakis, A.
Croitoru, V. E. Balas, E. Son, and V. Mladenov, Eds. Recent Advances In Electrical Engineering. World
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A21-c9 Sylvia Encheva, Sharil Tumin, Progress Evaluation Based on Fuzzy Relationships, in: New Directions
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vol. 226/2009, Springer, [ISBN 978-3-642-02936-3], pp. 201-210. 2009
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A21-c8 J.C. Figueroa Garcia, Linear programming with Interval Type-2 Fuzzy Right Hand Side parameters,
Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS 2008), 19-22 May
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A21-c7 Garcia, J.C.F.; Bello, C.A.L., Linear Programming with fuzzy joint parameters: A Cumulative Membership Function approach, Annual Meeting of the North American Fuzzy Information Processing Society
(NAFIPS 2008), 19-22 May 2008, pp.1-6. 2008
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A21-c6 T. Bhaskar, R. Sundararajan, and P.G. Krishnan, A fuzzy mathematical programming approach for
cross-sell optimization in retail banking, Proc. Artificial Intelligence and Applications, February 12 14,
2007, Innsbruck, Austria, [ISBN 978-0-88986-629-4], pp. 598-604. 2007
http://www.actapress.com/Abstract.aspx?paperId=29513
A21-c5 Pengfei Zhou; Haigui Kang; Li Lin, A Fuzzy Model for Scheduling Equipments Handling Outbound
Container in Terminal, The Sixth World Congress on Intelligent Control and Automation (WCICA 2006),
21-23 June 2006, vol. 2, pp. 7267-7271. 2006
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A21-c4 D.Dubois, E.Kerre, R.Mesiar and H.Prade, Fuzzy interval analysis, in: Didier Dubois and Henri Prade
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M.; Gupta, Madan M. eds., Uncertainty Analysis in Engineering and Sciences Fuzzy Logic, Statistics,
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Concept, New York: Springer, 2012. 173 p.
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Software and Applications with Fuzzy Set Techniques, Imperial College Press, [ISBN 9781860947933],
2007.
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• Juan Carlos Figueroa-Garcia, Fuzzy Linear Programming with Interval Type-2 fuzzy constraints, Universidad Nacional de Colombia, Facultad de Ingenieria, Departamento de Ingenieria Industrial y de Sistemas,
Bogota, Colombia. 2014
http://www.bdigital.unal.edu.co/46408/1/02300639.2014.pdf
• Lisy Cherian, Optimization in Fuzzy Environment. Union Christian College, Mahatma Gandhi University,
India. 2008
http://shodhganga.inflibnet.ac.in/handle/10603/22561
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• Luiza Amalia Pinto Cantao, Programacao Nao-Linear com Parametros Fuzzy: Teoria e Algoritmos, Universidade Estadual de Campinas, UNICAMP, Brasil. 2003
• Kenneth David Jamison, Modeling Uncertainty Using Probabilistic Based Possibility Theory with Applications to Optimization, University of Colorado at Denver. 1998
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[A22] Robert Fullér and Eberhard Triesch, A note on law of large numbers for fuzzy variables, FUZZY SETS
AND SYSTEMS, 55(1993) 235-236. [Zbl.782.60004]. doi 10.1016/0165-0114(93)90136-6
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A22-c6 Dug Hun Hong, The law of large numbers and renewal process for T-related weighted fuzzy numbers
on Rq , INFORMATION SCIENCES, 228(2013), pp. 45-60. 2013
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A22-c5 Mila Stojakovic, Zoran Stojakovic, Series of fuzzy sets, FUZZY SETS AND SYSTEMS, Volume 160,
Issue 21, pp. 3115-3127. 2009
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A22-c4 Dug Hun Hong and Chul H. Ahn, Equivalent conditions for laws of large numbers for T-related L-R
fuzzy numbers, FUZZY SETS AND SYSTEMS, 136(2003) 387-395. 2003
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272
In 1982, Badard [1] proved a law of large numbers for fuzzy numbers with common spread when
T (u, v) = uv. In 1991, Williamson [27] generalized law of large numbers for fuzzy numbers, but
his result was shown to be incorrect by Fullér and Triesch [A22]. (page 387)
A22-c3 Hong DH, Ro PI The law of large numbers for fuzzy numbers with unbounded supports, FUZZY SETS
AND SYSTEMS, 116 (2): 269-274 DEC 1 2000
http://dx.doi.org/10.1016/S0165-0114(98)00188-2
We note that Williamson [12] tried to generalize Badard’s results under a general t-norm extension
principle. But his theorem is not valid (see [A22]). (page 269)
in proceedings and edited volumes
A22-c2 D.Dubois, E.Kerre, R.Mesiar and H.Prade, Fuzzy interval analysis, in: Didier Dubois and Henri Prade
eds., Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, Volume 7, Kluwer Academic
Publishers, [ISBN 0-7923-7732-X], 2000, 483-581. 2000
Fullér and Triesch give an example of convergence to non-crisp intervals. (page 529)
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A22-c1 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
[A23] Robert Fullér and Tibor Keresztfalvi, A note on t-norm-based operations on fuzzy numbers, Supplement to
Kybernetika, 28(1992) 45-49. [MR: 94d:04007] [Zbl.875.04008]
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A23-c3 M.F.Kawaguchi and T.Da-te, Properties of fuzzy arithmetic based on triangular norms, Journal of Japan
Society for Fuzzy Theory and Systems, 5(1993) 1113-1121 (in Japanese). Japanese Journal of Fuzzy Theory
and Systems, 5(1993) 677-687 (English Translation version). 1993
in proceedings and edited volumes
A23-c2 M.F.Kawaguchi and T. Da-Te, A calculation method for solving fuzzy arithmetic equations with triangular norms, in: Proc. of Second IEEE international Conference on Fuzzy Systems, 1993 470-476. 1993
http://ieeexplore.ieee.org/iel2/1022/7759/00327513.pdf?arnumber=327513
in books
A23-c1 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
[A24] Robert Fullér and Tibor Keresztfalvi, t-Norm-based addition of fuzzy intervals, FUZZY SETS AND SYSTEMS, 51(1992) 155-159. [MR: 93k:04004]. doi 10.1016/0165-0114(92)90188-A
in journals
2016
A24-c57 Lucian Coroianu, Necessary and sufficient conditions for the equality of the interactive and noninteractive sums of two fuzzy numbers, FUZZY SETS AND SYSTEMS, 283(2016), pp. 40-55. 2016
http://dx.doi.org/10.1016/j.fss.2014.10.026
2015
A24-c56 Dug Hun Hong, The Existence of T-iid Random Fuzzy Variables and its Law of Large Numbers,
INTERNATIONAL JOURNAL OF MATHEMATICAL ANALYSIS, 9: (49) pp. 2407-2418. 2015
http://dx.doi.org/10.12988/ijma.2015.58192
273
A24-c55 Chun Yong Wang, Bao Qing Hu, Generalized extended fuzzy implications, Fuzzy Sets and Systems,
268(2015), pp. 93-109. 2015
http://dx.doi.org/10.1016/j.fss.2014.05.010
2012
A24-c54 Z. Makó, Real vector space of LR-fuzzy intervals with respect to the shape-preserving t-norm-based
addition, FUZZY SETS AND SYSTEMS, 200(2012), pp. 136-149. 2012
http://dx.doi.org/10.1016/j.fss.2012.02.014
2009
A24-c53 Dug Hun Hong, A NOTE ABOUT OPERATIONS LIKE T-W (THE WEAKEST t-NORM) BASED
ADDITION ON FUZZY INTERVALS, KYBERNETIKA, 45 (3): 541-547 2009
http://www.kybernetika.cz/content/2009/3/541
A24-c52 Claudio De Capua, Emilia Romeo, A t-Norm-Based Fuzzy Approach to the Estimation of Measurement Uncertainty, IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, 58(2009),
pp.350-355. 2009
http://dx.doi.org/10.1109/TIM.2008.2003339
A24-c51 Janusz T. Starczewski, Extended triangular norms, INFORMATION SCIENCES, 179(2009), pp. 742757. 2009
http://dx.doi.org/10.1016/j.ins.2008.11.009
This result was inspired by works [A24,12] on the addition of fuzzy intervals. (page 752)
A24-c50 Z. Makó, Real vector space with scalar product of quasi-triangular fuzzy numbers, ACTA UNIVERSITATIS SAPIENTIAE, MATHEMATICA, 1(2009), number 1, pp. 51-71. 2009
http://www.acta.sapientia.ro/acta-math/C1-1/MATH1-5.PDF
2008
A24-c49 Dug Hun Hong, A convexity problem and a new proof for linearity preserving additions of fuzzy
intervals, FUZZY SETS AND SYSTEMS, 159(2008) pp. 3388-3392. 2008
http://dx.doi.org/10.1016/j.fss.2008.05.020
2007
A24-c48 Hong DH, Hwang C, Kim KT, T-sum of sigmoid-shaped fuzzy intervals INFORMATION SCIENCES
177 (18): 3831-3839 SEP 15 2007
http://dx.doi.org/10.1016/j.ins.2007.03.023
A24-c47 Hong DH, T-sum of bell-shaped fuzzy intervals, FUZZY SETS AND SYSTEMS 158 (7): 739-746
APR 1 2007
http://dx.doi.org/10.1016/j.fss.2006.10.021
2006
A24-c46 József Dombi and Norbert Győrbı́ró, Addition of sigmoid-shaped fuzzy intervals using the Dombi
operator and infinite sum theorems, FUZZY SETS AND SYSTEMS, 157(2006) 952-963. 2006
http://dx.doi.org/10.1016/j.fss.2005.09.011
Fullér has studied the sup-T sum with triangular fuzzy intervals [A32,A30] and in a more general
context [A24]. These results were developed further and extended by Hong [11-13] and Mesiar
[15]. (page 953)
2004
A24-c45 Hong DH On types of fuzzy numbers under addition KYBERNETIKA, 40 (4): 469-476. 2004
274
http://kybernetika.utia.cas.cz/pdf_article/40_4_654_full.pdf
2003
A24-c44 Dug-Hun Hong, Notes on the compatibility between defuzzification and t-norm based fuzzy arithmetic
operations, JOURNAL OF FUZZY LOGIC AND INTELLIGENT SYSTEMS, 13(2003), number 2, pp.
231-236. 2003
http://dx.doi.org/10.5391/JKIIS.2003.13.2.231
A24-c43 Dug Hun Hong, T-sum of L-R fuzzy numbers with unbounded supports, Commun. Korean Math.
Soc., 18 (2003), no. 2, 385–392. 2003
The next result on the sum of L-R fuzzy numbers based on an Archimedean continuous t-norm T
is due to Fullér and Keresztfalvi [A24]. (page 387)
2002
A24-c42 Dug Hun Hong, On shape-preserving additions of fuzzy intervals, JOURNAL OF MATHEMATICAL
ANALYSIS AND APPLICATIONS, 267 (1): 369-376 MAR 1 2002
2001
A24-c41 Dug Hun Hong, Some results on the addition of fuzzy intervals, FUZZY SETS AND SYSTEMS,
122(2001) 349-352. 2001
http://dx.doi.org/10.1016/S0165-0114(00)00005-1
A24-c40 Seok Yoon Hwang and Hyo Sam Lee, Nilpotent t-norm-based sum of fuzzy intervals, FUZZY SETS
AND SYSTEMS, 123(2001) 73-80. 2001
http://dx.doi.org/10.1016/S0165-0114(01)00005-7
A24-c39 Dug Hun Hong, Shape preserving multiplications of fuzzy numbers, FUZZY SETS AND SYSTEMS,
123(2001) 81-84. 2001
http://dx.doi.org/10.1016/S0165-0114(00)00107-X
2000
A24-c38 Klement EP, Mesiar R, Pap E Generated triangular norms KYBERNETIKA, 36 (3): 363-377. 2000
http://dml.cz/dmlcz/135356
1998
A24-c37 A.Kolesárová, Triangular norm-based addition preserving linearity of T-sums of linear fuzzy intervals,
MATHWARE & SOFT COMPUTING, 5(1998) 91-98. 1998
A24-c36 Hwang SY, Hwang JJ, An JH The triangular norm-based addition of fuzzy intervals APPLIED MATHEMATICS LETTERS, 11 (4): 9-13 JUL 1998
http://dx.doi.org/10.1016/S0893-9659(98)00048-2
1997
A24-c35 B. De Baets and A. Marková-Stupňanová, Analytical expressions for addition of fuzzy intervals,
FUZZY SETS AND SYSTEMS, 91(1997) 203-213. 1997
http://dx.doi.org/10.1016/S0165-0114(97)00141-3
The first results for an arbitray continuous Archimedean t-norm are due to Fullér and Keresztfalvi
[A24].
Propostion 7. (Fullér and Keresztfalvi [A24]). Consider a continuous Archimedean t-norm T
with additive generator f and n LR-fuzzy intervals Ai = (li , ri , α, β)LR , i = 1, . . . , n. l f f is
275
twice differentiable
and strictly convex, and L and R are twice differentiable and concave, then
Ln
the T -sum T i=1 Ai is given by

!!!

l−x

(−1)

if l − nα ≤ x ≤ l,
nf L
f



nα




n

M
1
if l ≤ x ≤ r,
!!!
Ai (x) =

x−r

T i=1


f (−1) nf R
if r ≤ x ≤ r + nβ,


nβ





0
elsewhere,
where l =
Pn
i=1 li
and r =
Pn
i=1 ri .
(page 207)
A24-c34 R.Mesiar, Triangular-norm-based addition of fuzzy intervals, FUZZY SETS AND SYSTEMS, 91(1997)
231-237. 1997
http://dx.doi.org/10.1016/S0893-9659(98)00048-2
A24-c33 D.H.Hong and C. Hwang, A T-sum bound of LR-fuzzy numbers, FUZZY SETS AND SYSTEMS,
91(1997) 239-252. 1997
The exact output of a T -sum of some LR-fuzzy numbers in an analytical form was found only
for some special cases. For Archemedean t-norm T with additive generator f , the most general
published result is due to Hong and Hwang [9], generalizing the earlier results of Fullér and
Keresztfalvi [A24]. (page 240)
A24-c32 A. Marková-Stupňanová, Idempotents of T-addition of fuzzy numbers, Tatra Mountains Mathematical
Publications 12(1997), 65-72. [MR: 98k:04005] 1997
http://tatra.mat.savba.sk/Full/12/12markov.ps
A24-c31 D.H.Hong and S.Y.Hwang, The convergence of T-product of fuzzy numbers, FUZZY SETS AND
SYSTEMS, 85(1997) 373-378. 1997
http://dx.doi.org/10.1016/0165-0114(95)00333-9
Recently, t-norm-based addition of fuzzy numbers and its convergence have been studied [A32,
A30, A28, A24, 6, 7, 9]. (page 373)
A24-c30 A.Markova, T-sum of L-R fuzzy numbers, FUZZY SETS AND SYSTEMS, 85(1997) 379-384. 1997
http://dx.doi.org/10.1016/0165-0114(95)00370-3
The next result on the sum of L-R fuzzy numbers based on an Archimedean continous t-norm T
is due to Fullér and Keresztfalvi [A24]. (page 380)
A24-c29 R.Mesiar, Shape preserving additions of fuzzy intervals, FUZZY SETS AND SYSTEMS, 86 73-78.
1997
http://dx.doi.org/10.1016/0165-0114(95)00401-7
Some results on this topic and applications can be found e.g. in [2, A24-7, 11-13].
A24-c28 S.Y.Hwang and D.H.Hong, The convergence of T-sum of fuzzy numbers on Banach spaces, APPLIED
MATHEMATICS LETTERS, 10 No. 4, 129-134. 1997
http://dx.doi.org/10.1016/S0893-9659(97)00072-4
Recently, Houg and Hwang [1] determined the exact membership function of the t-norm-based
sum of fuzzy numbers, in the case of Archimedean t-norm having convex additive generator function and fuzzy numbers with concave shape functions, which is the generalization of Fullér and
Keresztfalvi’s result [A24]. (page 129)
1996
276
A24-c27 R.Mesiar, A note to the T-sum of L-R fuzzy numbers, FUZZY SETS AND SYSTEMS, 79(1996)
259-261. 1996
http://dx.doi.org/10.1016/0165-0114(95)00178-6
1995
A24-c26 A. Kolesárová, Triangular norm-based addition of linear fuzzy numbers, Tatra Mountains Mathematical Publications, 6(1995) 75-81. 1995
http://tatra.mat.savba.sk/paper.php?id_paper=193
A24-c25 D.H.Hong, A note on t-norm-based addition of fuzzy intervals, FUZZY SETS AND SYSTEMS,
75(1995) 73-76. 1995
http://dx.doi.org/10.1016/0165-0114(94)00329-6
We generalize a result of Fullér and Keresztfalvi (1992) regarding the computation of t-normbased additions of LR-fuzzy intervals, the proof of which is new and simple. (page 73)
A24-c24 A.Markova, Addition of L-R fuzzy numbers, Bulletin for Studies and Exchanges on Fuzziness and its
Applications, 63(1995) 25-29. 1995
1994
A24-c23 D.H.Hong and S.Y.Hwang, On the convergence of T-sum of L-R fuzzy numbers, FUZZY SETS AND
SYSTEMS, 63(1994) 175-180. 1994
http://dx.doi.org/10.1016/0165-0114(94)90347-6
A24-c22 D.H.Hong and S.Y.Hwang, On the compositional rule of inference under triangular norms, FUZZY
SETS AND SYSTEMS, 66(1994) 25-38. 1994
http://dx.doi.org/10.1016/0165-0114(94)90299-2
A24-c21 M.F.Kawaguchi and T.Da-te, Some algebraic properties of weakly non-interactive fuzzy numbers,
FUZZY SETS AND SYSTEMS 68(1994) 281-291. 1994
http://dx.doi.org/10.1016/0165-0114(94)90184-8
Nevertheless, we expect that the concrete characteristics of each t-norm would make it possible
to cope with such a problem to a certain extent. For instance, Fullér et al. illustrated the sums
of triangular fuzzy numbers based on various t-norms: algebraic product, Hamacher product,
Yager’s parametrized t-norm, etc. [A32, A30, A24]. Their results help us to evaluate a fuzzy
linear expression of which either coefficients or variables are fuzzy numbers. (page 290)
1993
A24-c20 M.F.Kawaguchi and T.Da-te, Properties of fuzzy arithmetic based on triangular norms, Journal of
Japan Society for Fuzzy Theory and Systems, 5(1993) 1113-1121 (in Japanese). Japanese Journal of Fuzzy
Theory and Systems, 5(1993) 677-687 (English Translation version). 1993
in proceedings and edited volumes
2016
A46-c2 Andrea Sgarro, Laura Franzoi, (Ir)relevant T-norm Joint Distributions in the Arithmetic of Fuzzy Quantities: 16th International Conference, IPMU 2016, Eindhoven, The Netherlands, June 20 - 24, 2016, Proceedings, Part II In: Joao Paulo Carvalho, Marie-Jeanne Lesot, Uzay Kaymak, Susana Vieira, Bernadette
Bouchon-Meunier, Ronald R Yager eds., Information Processing and Management of Uncertainty in KnowledgeBased Systems, Communications in Computer and Information Science, vol. 611, Springer, 2016. (ISBN
978-3-319-40580-3) pp. 3-11. 2016
http://dx.doi.org/10.1007/978-3-319-40581-0 1
2015
277
C17-c4 Luciana Takata Gomes, Laécio Carvalho de Barros, Barnabas Bede, Basic Concepts, In: Fuzzy Differential Equations in Various Approaches. Springer, SpringerBriefs in Mathematics, (ISBN 978-3-31922574-6) pp. 11-40. 2015
http://dx.doi.org/10.1007/978-3-319-22575-3_2
2014
A24-c11 L T Kóczy, A Note on Hamacher-Operators, Advances in Soft Computing, 159 Intelligent Robotics
and Control, Topics in Intelligent Engineering and Informatics vol 8/2014, Springer Verlag, [ISBN 978-3319-05944-0], pp. 159-163. 2014
http://dx.doi.org/10.1007/978-3-319-05945-7_10
2013
A24-c10 Janusz T Starczewski, Algebraic Operations on Fuzzy Valued Fuzzy Sets, in: Advanced Concepts in
Fuzzy Logic and Systems with Membership Uncertainty, Studies in Fuzziness and Soft Computing, vol.
284/2013, Springer, [ISBN 978-3-642-29520-1], pp. 33-76. 2013
http://dx.doi.org/10.1007/978-3-642-29520-1_2
2004
A24-c9 Claudio De Capua and Emilia Romeo, A t-Norm Based Fuzzy Approach to the Estimation of Measurement Uncertainty, Instrumentation and Measurement Technology Conference (IMTC 2004) Como, Italy,
18-20 May 2004, [doi 10.1109/IMTC.2004.1351034], pp. 229-233. 2004
http://dx.doi.org/10.1109/IMTC.2004.1351034
2000
A24-c8 D.Dubois, E.Kerre, R.Mesiar and H.Prade, Fuzzy interval analysis, in: Didier Dubois and Henri Prade
eds., Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, Volume 7, Kluwer Academic
Publishers, [ISBN 0-7923-7732-X], 2000, 483-581. 2000
A closed form solution of the fuzzy addition in the case of fuzzy intervals was provided by Dubois
and Prade (1981) for the three basic triangular norms other than the minimum. Several other
results were obtained since then by Fullér and Keresztfalvi (1992), Kawaguchi and Da-te (1993,
1994), . . . (page 526)
1998
A24-c7 A. Marková-Stupňanová, Idempotent fuzzy intervals, in: Proceedings of IPMU’98 Conference, (July
6-10, 1998, Paris, La Sorbonne), [ISBN 2-842-54-013-1], 1998 255-258. 1998
We recall a formula for the T -sum based on the continuous Archimedean t-norms for special type
of L-R fuzzy numbers introduced by Fullér and Keresztfalvi [A24] and generalized by Mesiar
. . . (page 257)
1996
A24-c6 D.H.Hong and C. Hwang, Upper bound of T-sum of LR-fuzzy numbers, in: Proceedings of IPMU’96
Conference, (July 1-5, 1996, Granada, Spain), 1996 343-346. 1996
A24-c5 B. De Baets and A. Markova, Addition of LR-fuzzy intervals based on a continuous t-norm, in: Proceedings of IPMU’96 Conference, (July 1-5, 1996, Granada, Spain), pp. 353-358. 1996
1993
278
A24-c4 M.F.Kawaguchi and T. Da-Te, A calculation method for solving fuzzy arithmetic equations with triangular norms, in: Proceedings of Second IEEE international Conference on Fuzzy Systems, 1993 470-476.
1993
http://ieeexplore.ieee.org/iel2/1022/7759/00327513.pdf?
in books
A24-c4 Adrian I Ban, Lucian Coroianu, Przemyslaw Grzegorzewski, FUZZY NUMBERS: APPROXIMATIONS, RANKING AND APPLICATIONS, Institute of Computer Science, Polish Academy of Sciences,
2015. Information technologies: research and their interdisciplinary applications, vol. 9, (ISBN 978-8363159-21-4). 2015
A24-c3 E. P. Klement, Radko Mesiar, Endre Pap, Triangular Norms, Springer, [ISBN 0792364163], 2000.
A24-c2 Jorma K. Mattila, Text Book of Fuzzy Logic, Art House, Helsinki, [ISBN 951-884-152-7], 1998.
A24-c1 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
[A25] Robert Fullér and Brigitte Werners, The compositional rule of inference with several relations, TATRA
MOUNTAINS MATHEMATICAL PUBLICATIONS, 1(1992) 39-44. [Zbl.788.68132]
in journals
A25-c3 M Shahjalal, Abeda Sultana, Nirmal Kanti Mitra, A F M Khodadad Khan, Compositional Rule of Inference and Adaptive Fuzzy Rule Based Scheme with Applications Annals of Pure and Applied Mathematics
3(2013), number 2, pp. 155-168. 2013
http://www.researchmathsci.org/apamart/apam-v3n2-7.pdf
A25-c2 B. Jayaram, On the Law of Importation (x ∧ y) −→ z ≡ (x −→ (y −→ z)) in Fuzzy Logic, IEEE
Transactions on Fuzzy Systems, vol.16, no.1, pp.130-144, Feb. 2008
http://dx.doi.org/10.1109/TFUZZ.2007.895969
in books
A25-c1 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
[A26] Robert Fullér and Hans-Jürgen Zimmermann, On computation of the compositional rule of inference under
triangular norms, FUZZY SETS AND SYSTEMS, 51(1992) 267-275. [MR: 93k:03026] [Zbl.782.68110].
doi 10.1016/0165-0114(92)90017-X
in journals
A26-c27 M Štepnicka, B Jayaram, On the Suitability of the Bandler-Kohout Subproduct as an Inference Mechanism, IEEE TRANSACTIONS ON FUZZY SYSTEMS, 18(2010), number 2, pp. 285-298. 2010
http://dx.doi.org/10.1109/TFUZZ.2010.2041007
There are many works that have proposed modifications to the classical CRI in an attempt to
enhance the efficiency in its inferencing (see, for example, the works of Fullér and coauthors
[48]-[50] and Moser and Navara [51]-[53]). (page 295)
A26-c26 B. Jayaram, On the Law of Importation (x ∧ y) −→ z ≡ (x −→ (y −→ z)) in Fuzzy Logic, IEEE
Transactions on Fuzzy Systems, vol.16, no.1, pp. 130-144, Feb. 2008
http://dx.doi.org/10.1109/TFUZZ.2007.895969
A26-c25 Hong DH, Hwang C, Kim KT T-sum of sigmoid-shaped fuzzy intervals INFORMATION SCIENCES,
177 (18): 3831-3839 SEP 15 2007
http://dx.doi.org/10.1016/j.ins.2007.03.023
A26-c24 Hong DH, T-sum of bell-shaped fuzzy intervals, FUZZY SETS AND SYSTEMS, 158 (7): 739-746
APR 1 2007
http://dx.doi.org/10.1016/j.fss.2006.10.021
279
A26-c23 Hong DH On types of fuzzy numbers under addition KYBERNETIKA, 40 (4): 469-476. 2004
http://kybernetika.utia.cas.cz/pdf_article/40_4_654_full.pdf
A26-c22 Dug-Hun Hong, Notes on the compatibility between defuzzification and t-norm based fuzzy arithmetic
operations, JOURNAL OF FUZZY LOGIC AND INTELLIGENT SYSTEMS, 13(2003), number 2, pp.
231-236. 2003
http://dx.doi.org/10.5391/JKIIS.2003.13.2.231
A26-c21 Dug Hun Hong, T-sum of L-R fuzzy numbers with unbounded supports, Commun. Korean Math.
Soc., 18 (2003), no. 2, pp. 385-392. 2003
A26-c20 Hong DH, On shape-preserving additions of fuzzy intervals, JOURNAL OF MATHEMATICAL
ANALYSIS AND APPLICATIONS, 267 (1): 369-376, MAR 1 2002
A26-c19 Dug Hun Hong, Some results on the addition of fuzzy intervals FUZZY SETS AND SYSTEMS,
122(2001), pp. 349-352. 2001
http://dx.doi.org/10.1016/S0165-0114(00)00005-1
A26-c18 Seok Yoon Hwang and Hyo Sam Lee, Nilpotent t-norm-based sum of fuzzy intervals, FUZZY SETS
AND SYSTEMS, 123(2001), pp. 73-80. 2001
http://dx.doi.org/10.1016/S0165-0114(01)00005-7
In particular if α1 = α2 , β1 = β2 then Ã∗ = Ã1 ⊕T Ã2 , which generalizes the results by Fullér
and Zimmermann [A24, A26]. (page 74)
A26-c17 Dug Hun Hong Shape preserving multiplications of fuzzy numbers, FUZZY SETS AND SYSTEMS,
123(2001), pp. 81-84. 2001
http://dx.doi.org/10.1016/S0165-0114(00)00107-X
A26-c16 D.H.Hong and C. Hwang, A T-sum bound of LR-fuzzy numbers, FUZZY SETS AND SYSTEMS,
91(1997) 239-252. 1997
http://dx.doi.org/10.1016/S0165-0114(97)00144-9
Now, in the case of different spreads, we are naturally asked about how to determine the exact
membership function. Fullér and Zimmermann [A26] mentioned in their remark 1 that it seems
to be very difficult and complicated to determine the exact membership function of T -sum of
LR-fuzzy numbers. (page 241)
We also consider the compositional rule of inference under triangular norms stated by Fullér and
Zimmermann [A26]. (page 252)
A26-c15 A.Markova, T-sum of L-R fuzzy numbers, FUZZY SETS AND SYSTEMS, 85(1997) 379-384. 1997
http://dx.doi.org/10.1016/0165-0114(95)00370-3
Using our results, we guarantee the validity of Fullér-Zimmermann composition law for f ◦ φ1
and f ◦ φ2 convex . . . (page 383)
A26-c14 R.Mesiar, Shape preserving additions of fuzzy intervals, FUZZY SETS AND SYSTEMS, 86(1997),
pp. 73-78. 1997
http://dx.doi.org/10.1016/0165-0114(95)00401-7
Some applications of above results are expected also in the domain of compositional rules of
inference under nilpotent t-norms, see e.g. [A26]. (page 78)
A26-c13 A.Markova, Addition of L-R fuzzy numbers, Bulletin for Studies and Exchanges on Fuzziness and its
Applications, 63(1995), pp. 25-29. 1995
A26-c12 D.H.Hong and S.Y.Hwang, On the compositional rule of inference under triangular norms, FUZZY
SETS AND SYSTEMS, 66(1994), pp. 25-38. 1994
http://dx.doi.org/10.1016/0165-0114(94)90299-2
280
The aim of this paper is to provide a close upper bound of the membership function for the compositional rule of inference under Archimedean t-norm, where both the observation and the relation
parts are given by Hellendoorn’s φ-function (1980). In particular, if the left and right spreads of
the observation part is the same as those of the relation part, then this upper bound is the exact
membership function, which generalizes the earlier results by Fullér and Zimmermann (1992) in
that the assumption of twice differentiability is deleted. (page 25)
Fullér and Zimmermann [A26] wrote a paper which deals with the derivation of exact calculation
formulas for the compositional rule of inference, which has the global scheme [7]
Observation: x has property P
Relation:
x
and y have relation W
Conclusion:
y
has property Q
where the membership function of the conclusion Q is defined by sup-t-norm composition of P
and W :
Q(y) = sup t-norm(P (x), W (x, y)).
x
(page 26)
In [6] Hellendoorn showed the closure property of the compositional rule of inference under supmin-norm composition and prsented exact calculation formulas for the membership function of
the conclusion when both the observation and relation parts are given by S-, π-, or φ-functions.
Fullér and Zimmermann’s results are connected with those presented in [6] and they generalize
them as follows:
Theorem 1.1 [A26] Let T be an Archimedean t-norm with additive generator f and let P (x) =
φ(x; a, b, c, d) and W (x, y) = φ(y − x; a + u, b + u, c + v, d + v). If φ1 and φ2 are twice
differentiable, concave functions, and f is a twice differentiable, strictly convex function, then

1
if 2b + u ≤ y ≤ 2c + v




y
−
2a
−
u


 f [−1] 2f φ1
if 2a + u ≤ y ≤ 2b + u

2(b − a)
Q(y) =

y − 2c − v


if 2c + v ≤ y ≤ 2d + v
f [−1] 2f φ2


2(d − c)



0
otherwise.
(page 26)
From Theorem 2.4 we know that if the left and right spreads of P are equal to the left and right
spreads of W , respectively, then the exact membership function of the conlusion Q can be determined without the condition of differentiability of φ1 , φ2 and f in Fullér and Zimmermann’s
theorem [A26]. (page 29)
in proceedings and edited volumes
A26-c10 M.Štepnicka and B. Jayaram, On Computational Aspects of the BK-Subproduct Inference Mechanism,
18th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2009, Jeju Island, Korea, August 2024, 2009, pp. 1181-1186. 2009
http://dx.doi.org/10.1109/FUZZY.2009.5277076
A26-c9 Inma P. Cabrera, Pablo Cordero, and Manuel Ojeda-Aciego, Fuzzy Logic, Soft Computing, and Applications, in: Joan Cabestany; Francisco Sandoval; Alberto Prieto; Juan M. Corchado eds., Bio-Inspired
Systems: Computational and Ambient Intelligence, Lecture Notes in Computer Science, vol. 5517/2009,
Springer, [ISBN 978-3-642-02477-1], 2009, pp. 236-244. 2009
http://dx.doi.org/10.1007/978-3-642-02478-8_30
A26-c8 D.Dubois, E.Kerre, R.Mesiar and H.Prade, Fuzzy interval analysis, in: Didier Dubois and Henri Prade
eds., Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, Volume 7, Kluwer Academic
Publishers, [ISBN 0-7923-7732-X], 2000, 483-581. 2000
281
A26-c7 D.H.Hong and C. Hwang, Upper bound of T-sum of LR-fuzzy numbers, in: Proc. of IPMU’96 Conference (July 1-5, 1996, Granada, Spain), 1996 343-346. 1996
in books
A26-c6 Da Ruan, Etienne E. Kerre, Fuzzy If-then Rules in Computational Intelligence: Theory and Applications, Kluwer, [ISBN 9780792378204], 2000.
A26-c5 E. P. Klement, Radko Mesiar, Endre Pap, Triangular Norms, Springer, [ISBN 978-0-7923-6416-0],
2000.
http://www.springer.com/philosophy/logic+and+philosophy+of+language/book/978-0-7923-6416-0
A26-c4 Jonathan S. Golan, Semirings and Their Applications, Springer, [ISBN: 978-0-7923-5786-5], 1999.
http://www.springer.com/mathematics/algebra/book/978-0-7923-5786-5
A26-c3 Jonathan S. Golan, Power Algebras over Semirings, Springer, [ISBN 978-0-7923-5834-3], 1999.
http://www.springer.com/mathematics/algebra/book/978-0-7923-5834-3
A26-c2 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
A26-c1 G.J.Klir and B.Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, [ISBN
0-13-101171-5], 1995.
[A27] Mario Fedrizzi and Robert Fullér, Stability in possibilistic linear programming problems with continuous
fuzzy number parameters, FUZZY SETS AND SYSTEMS, 47(1992) 187-191. [MR: 93g:90088]
[Zbl.808.90130]. doi : 10.1016/0165-0114(92)90177-6
A27-c12 Rafik Aliev, Alex Tserkovny, Systemic approach to fuzzy logic formalization for approximate reasoning, INFORMATION SCIENCES, 181(2011), pp. 1045-1059. 2011
http://dx.doi.org/10.1016/j.ins.2010.11.021
A27-c11 Rasoul Dadashzadeh; S. B. Nimse, ON STABILITY IN MULTIOBJECTIVE LINEAR PROGRAMMING PROBLEMS WITH SYMMETRIC TRAPEZOIDAL FUZZY NUMBERS, ANNALS OF ORADEA
UNIVERSITY - MATHEMATICS FASCICOLA, Tom XIV(2007), pp. 5-14. 2007
http://stiinte.uoradea.ro/en/pdfs/2007/1.pdf
A27-c10 Rybkin VA, Yazenin AV, On the problem of stability in possibilistic optimization, INTERNATIONAL
JOURNAL OF GENERAL SYSTEMS, 30 (1), pp. 3-22. 2001
http://dx.doi.org/10.1080/03081070108960695
A27-c9 Xu Jiuping, A kind of fuzzy linear programming problems based on interval-valued fuzzy sets, Applied
Mathematics - A Journal of Chinese Universities, vol. 15, pp. 65-72. 2000
http://dx.doi.org/10.1007/s11766-000-0010-y
A27-c8 S. Jenei, Continuity in approximate reasoning, Annales Univ. Sci. Budapest, Sect. Comp., 15(1995)
233-242. 1995
Further investigations have been performed for stability of fuzzy linear systems and fuzzy linear
programming problems in [A27], [A34], [A31], [8], [A35].
A27-c7 B.Julien, An extension to possibilistic linear programming, FUZZY SETS AND SYSTEMS, 64(1994)
195-206. 1994
http://dx.doi.org/10.1016/0165-0114(94)90333-6
The approach deals with imprecise parameters treated as fuzzy variables with possibility distributions assigned to them in the form of fuzzy numbers. A fuzzy number is a fuzzy set which is
normal, continouos, fuzzy convex and compactly supported [A27].
in proceedings and edited volumes
A27-c6 V.A.Rybkin and A.V.Yazenin, Regularization and stability of possibilistic linear programming problems, in: Proceedings of the Sixth European Congress on Intelligent Techniques and Soft Computing (EUFIT’98), Aachen, September 7-10, 1998, Verlag Mainz, Aachen, Vol. I, 1998 37-41. 1998
282
The criterion of stability based on uniform metric is given in [A27, 6].
A27-c5 T. Tanino, Sensitivity Analysis in MCDM, in: Gal, Tomas; Stewart, Theodor J.; Hanne, Thomas (Eds.)
Multicriteria Decision Making Advances in MCDM Models, Algorithms, Theory and Applications Series:
International Series in Operations Research & Management Science , Vol. 21, Springer, [ISBN 978-0-79238534-9], 1999 pp. 7-1 – 7-29. 1999
A27-c4 Alexander V. Yazenin, Vladimir A. Rybkin, Strong and Weak Stability in Possibilistic Linear Programming, in: Proceedings of the Seventh European Congress on Intelligent Techniques and Soft Computing
(EUFIT’99), Aachen, September 13-16, 1999 Verlag Mainz, Aachen, [ISBN 3-89653-808-X], 4 pages,
(Proceedings on CD-Rom). 1999
in books
A27-c4 Rafik Aziz Aliev, Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions, Studies in
Fuzziness and Soft Computing, vol. 293/2013, Springer, [ISBN 978-3-642-34894-5]. 2013
http://dx.doi.org/10.1007/978-3-642-34895-2
A27-c3 Pedro Salinas, El defensor, (Translated by Juan Marichal), Springer, [ISBN 842064532X], 2002.
A27-c2 Y.J.Lai and C.L.Hwang, Fuzzy Multiple Objective Decision Making, Lecture Notes in Economics and
Mathematical Systems, No. 404, Springer Verlag, [ISBN: 978-3-540-57595-5], Berlin 1994.
A27-c1 H. Rommelfanger, Fuzzy Decision Support-Systeme, Springer-Verlag, Heidelberg, 1994 [ISBN 3-54057793-9] (Second Edition).
[A28] Robert Fullér, A law of large numbers for fuzzy numbers, FUZZY SETS AND SYSTEMS, 45(1992) 299303. [MR 92j:04003] [Zbl.748.60003]. doi 10.1016/0165-0114(92)90147-V
in journals
2016
A28-c43 Yao K, Gao J, Law of Large Numbers for Uncertain Random Variables, IEEE TRANSACTIONS ON
FUZZY SYSTEMS, 24: (3) pp. 615-621. 2016
http://dx.doi.org/10.1109/TFUZZ.2015.2466080
A28-c42 Dug Hun Hong, Blackwell type theorem for general T-related and identically distributed fuzzy variables, FUZZY OPTIMIZATION AND DECISION MAKING (to appear). 2016
http://dx.doi.org/10.1007/s10700-016-9234-z
A28-c41 Dug Hun Hong, Renewal and Renewal Reward Theorems for T-Independent L-R Fuzzy Variables,
APPLIED MATHEMATICAL SCIENCES, 10: (1) pp. 23-35. 2016
http://dx.doi.org/10.12988/ams.2016.510646
2014
A28-c40 T. Pedro, Law of large numbers for the possibilistic mean value, FUZZY SETS AND SYSTEMS,
245(2014), pp. 116-124. 2014
http://dx.doi.org/10.1016/j.fss.2013.10.011
By analogy to the probabilistic case, we can say that Sn → Y in distribution (under the possibilistic mean value). As will be shown, this mode of convergence implies the law of large number
with convergence in necessity in e.g. [A28]. (page 117)
2013
A28-c39 P. Terán, Algebraic, metric and probabilistic properties of convex combinations based on the t-normed
extension principle: The strong law of large numbers FUZZY SETS AND SYSTEMS, 223(2013), pp. 1-25.
2013
http://dx.doi.org/10.1016/j.fss.2013.01.006
283
A28-c38 Dug Hun Hong, The law of large numbers and renewal process for T-related weighted fuzzy numbers
on Rq , INFORMATION SCIENCES, 228(2013), pp. 45-60. 2013
http://dx.doi.org/10.1016/j.ins.2012.12.016
2011
A28-c37 Shuming Wang; Junzo Watada, Some properties of T -independent fuzzy variables, MATHEMATICAL AND COMPUTER MODELLING, 53(2011), issues 5-6, pp. 970-984. 2011
http://dx.doi.org/10.1016/j.mcm.2010.11.006
Fullér [A28] proved a law of large numbers for T -related symmetric triangular fuzzy variables
with common spread by using necessity measure, where T (u, v) ≤ uv/(u + v − uv) for all
0 ≤ u, v ≤ 1. Triesch [28] extended the results of Fullér [A28], a nd studied some laws of large
numbers for sequences of mutually T -related LR fuzzy numbers, respectively, where T belongs
to a class of continuous Archimedean t-norms. Also utilizing necessity measure and continuous
Archimedean t-norms, Hong and Ro [29] further generalized the results of [28] to fuzzy numbers
with unbounded supports. Developing the ideas of [29], this paper further discusses the limit
theorems for the sum of T -independent fuzzy variables. (page 971)
2010
A28-c36 Dug Hun Hong, Blackwell’s Theorem for T-related fuzzy variables, INFORMATION SCIENCES
180:(2010), issue 9, pp. 1769-1777. 2010
http://dx.doi.org/10.1016/j.ins.2010.01.006
Many different types of the law of large numbers for T-related fuzzy variables have been studied
by a number of authors, such as, Badard [1], Fullér [A28], Triesch [17], Markov [13], Hong [4],
Hong and Lee [6], Hong and Ro [5], and Hong and Ahn [7]. (page 1769)
2006
A28-c35 Yanju Chen, Yan-Kui Liu A strong law of large numbers in credibility theory, WORLD JOURNAL
OF MODELLING AND SIMULATION, Vol. 2 (2006) No. 5, pp. 331-337. 2006
http://www.worldacademicunion.com/journal/1746-7233WJMS/wjmsvol2no5paper06.pdf
Fullér [A28] studied a law of large numbers for symmetric triangular fuzzy variables when T (u.v) ≤
uv/(u + v − uv). (page 331)
A28-c34 Hong DH, Renewal process with T-related fuzzy inter-arrival times and fuzzy rewards, INFORMATION SCIENCES, 176 (16): 2386-2395 AUG 22 2006
http://dx.doi.org/10.1016/j.ins.2005.06.008
Following Fullér (see [A28]), we say that ξ1 , ξ2 , . . . , ξn , . . . , obey the law of large numbers if for
all > 0 the quantity Nes(mn − < (ξ1 + ξ2 + · · · + ξn )/n < mn + ) tends to 1 as n → ∞.
(page 2388)
2003
A28-c33 Dug Hun Hong and Chul H. Ahn, Equivalent conditions for laws of large numbers for T-related L-R
fuzzy numbers, FUZZY SETS AND SYSTEMS, 136(2003) 387-395. 2003
http://dx.doi.org/10.1016/S0165-0114(02)00217-8
Abstract. In this paper, we give some necessary and sufficient conditions for laws of large numbers for sequence of mutually T-related L-R fuzzy numbers when T is an continuous Archimedean
t-norm and diameter of support of the fuzzy numbers is not uniformly bounded. We also consider
some necessary and sufficient conditions for laws of large numbers for L-R fuzzy random numbers, and generalize earlier results of Fullér (Fuzzy Sets and Systems 45 (1992) 299-303), Triesch
(Fuzzy Sets and Systems 58 (1993) 339-342) and Hong and Lee (Fuzzy Sets and Systems 121
(2001) 537-543).
284
..
.
In 1982, Badard [1] proved a law of large numbers for fuzzy numbers with common spread when
T (u, v) = uv. In 1991, Williamson [27] generalized law of large numbers for fuzzy numbers, but
his result was shown to be incorrect by Fullér and Triesch [A22]. In 1992, Fullér [A28] proved a
law of large numbers for sequence of mutually T-related symmetric triangular fuzzy numbers with
common spreads if T (u, v) ≤ H0 (u, v) := uv/(u + v − uv) for all 0 ≤ u, v ≤ 1. (page 387)
Strong laws of large numbers for sums of independent fuzzy random variables have been studied
by several people. A SLLN for sums of independent and identically distributed (i.i.d.) fuzzy
random variables was obtained by Kruse [18], and a SLLN for sums of independent fuzzy random
variables by Miyakoshi and Shimbo [21]. Also, Klement et al. [ 17] proved some limit theorems
which includes a SLLN, and Inoue [16] obtained a SLLN for sums of independent tight fuzzy
random sets, Hong and Kim [12] studied Marcinkiewicz-type law of large numbers for fuzzy
random variables under additional assumption. On the other hand, Näther et al. [22] considered
a linear regression model when centers and spreads are random variables. In this paper, we also
consider laws of large numbers for T-related L-R fuzzy numbers when centers and spreads are
i.i.d. random variables and generalize the result of Fullér [A28]. (page 388)
A28-c32 Dug Hun Hong, T-sum of L-R fuzzy numbers with unbounded supports, COMMUNICATIONS OF
THE KOREAN MATHEMATICAL SOCIETY, 18 (2003), no. 2, 385-392. 2003
2001
A28-c31 Dug Hun Hong and Jaejin Lee A convergence of geometric mean for T-related fuzzy numbers FUZZY
SETS AND SYSTEMS, 121(2001) 537-543. 2001
http://dx.doi.org/10.1016/S0165-0114(99)00136-0
Fullér [A28] studied a convergence of arithmetic mean for sequences of mutually T-related symmetrict riangular fuzzynumbers with common spread if T (u, v) ≤ H0 (u, v) := uv/(u + v − uv)
for all 0 ≤ u, v ≤ 1. Triesch [11] and Fullér [C47] generalize Fullér’s results for certain sequences
of L-R fuzzy numbers with uniformly bounded spreads if T belongs to the class of Archimedian
t-norms. Hong and Kim [9] generalized Triesch’s results for sequences of fuzzy numbers in a
Banach space and Hong [7] provided a general law of large numbers fo rarrays of L-R fuzzy
numbers. Recently, Hong and Hwang [8] provided new results regarding the effective practical
computation of t-norm-based products of R-type fuzzy numbers and their limit. Then it is natural
to ask about convergence of geometric mean for fuzzy numbers. (page 537)
Now we can also ask the same type of conjecture as in Fullér’s paper [A28]: Suppose we are given
an Archimedean t-norm and a sequence ã1 , ã2 , . . . , ãn , . . . of fuzzy numbers such that for all n,
the diameter of the support of ãn is bounded by the same constant C independent of n. Then (2)
in Theorem 1 holds. (page 542)
2000
A28-c30 Hong DH, Lee J, On the law of large numbers for mutually T-related L-R fuzzy numbers, FUZZY
SETS AND SYSTEMS, 116 (2): 263-267 DEC 1 2000
http://dx.doi.org/10.1016/S0165-0114(98)00071-2
Recently, Fullér [A28] proved a law of large numbers for sequences of mutually T-related symmetric triangular fuzzy numbers with common spread if T (u, v) ≤ H0 (u, v) := uv/(u + v − uv)
for all 0 ≤ u, v ≤ 1. Triesch [10], Hong [5], Hong and Hwang [7] and Fullér [4] generalize
Fullér’s results for certain sequences of L-R fuzzy numbers with uniformly bounded spreads if
T belongs to the class of Archimedean t-norms. Hong and Kim [8] generalized Triesch’s results
for sequences of fuzzy numbers in a Banach space and Hong [6] provided a general law of large
numbers for arrays of L-R fuzzy numbers. Triesch stated in concluding remarks at the end of
[11] that there could be laws of large numbers for interesting classes of t-norms and sequences
of fuzzy numbers where the diameter of the support of fuzzy numbers is not uniformly bounded.
The object of this paper is to study a law of large numbers concern- ing the Triesch’s statement
and generalize results of Fullér [A28] and Triesch [11]. (page 263)
285
A28-c29 Hong DH, Ro PI, The law of large numbers for fuzzy numbers with unbounded supports, FUZZY
SETS AND SYSTEMS, 116 (2): 269-274 DEC 1 2000
http://dx.doi.org/10.1016/S0165-0114(98)00188-2
Recently, Fullér [A28], Triesch [11], Hong [6], Hong and Kim [8] studied laws of large numbers
for fuzzy numbers. (page 269)
A28-c28 Markova-Stupnanova A T-law of large numbers for fuzzy numbers, KYBERNETIKA, 36 (3): 379388. 2000
http://www.kybernetika.cz/content/2000/3/379
Fuller [2] introduced the law of large numbers for special LR-fuzzy numbers and t-norms bounded
by the Hamacher product t-norm.
Theorem 1. (The law of large numbers, [2]) (page 381)
1998
A28-c27 L.C.Jang and J.S.Kwon, A note on law of large numbers for fuzzy numbers in a Banach space, FUZZY
SETS AND SYSTEMS, 98(1998) 77-81. 1998
http://dx.doi.org/10.1016/S0165-0114(96)00391-0
Fullér [A28] proved a law of large numbers for sequences of symmetric triangular fuzzy numbers
with common spread and Triesch [3] generalizes Fullér’s result for sequences of L-R fuzzy numbers with bounded spreads. In this paper, we study a law of large numbers for sequences of fuzzy
numbers in a Banach space to generalize earlier results mentioned above. The fuzzy numbers considered need not have (uniformly) bounded supports. Our condition relates the additive generator
of t-norm and shape functions of fuzzy numbers involved. (page 77)
A28-c26 A. Marková-Stupňanová, The law of large numbers for fuzzy numbers, Bulletin for Studies and Exchanges on Fuzziness and its Applications, 75(1998) 53-59. 1998
Fullér [A28] introduced the law of large numbers for special LR-fuzzy numbers and Hamacher
t-norm. (page 54)
A28-c25 A. Marková-Stupňanová, A note on the recent results on the law of large numbers for fuzzy numbers,
Bulletin for Studies and Exchanges on Fuzziness and its Applications, 76(1998) 12-18.
Fullér [A28] proved a law of large numbers for sequences of symmetric triangular fuzzy numbers
with common spread. (page 12)
1997
A28-c24 D.H.Hong and S.Y.Hwang, The convergence of T-product of fuzzy numbers, FUZZY SETS AND
SYSTEMS, 85(1997) 373-378. 1997
http://dx.doi.org/10.1016/0165-0114(95)00333-9
Recently, t-norm-based addition of fuzzy numbers and its convergence have been studied [A32,
A30, A28, A24, 6, 7, 9]. (page 373)
A28-c23 A.Markova, T-sum of L-R fuzzy numbers, FUZZY SETS AND SYSTEMS, 85(1997) 379-384. 1997
http://dx.doi.org/10.1016/0165-0114(95)00370-3
(i) Fullér’s theorem [A28] on the law of large numbers is valid for each t-norm T with additive
generator f and L-R fuzzy numbers such that both f ◦ L and f ◦ R are convex. Consequently, the
same is true, for given shapes L, R, for each t-norm T ∗ ≤ T . Note that Fullér’s result concerns
Hamacher’s t-norm . . . (page 383)
A28-c22 D.H.Hong and C. Hwang, A T-sum bound of LR-fuzzy numbers, FUZZY SETS AND SYSTEMS,
91(1997) 239-252. 1997
http://dx.doi.org/10.1016/S0165-0114(97)00144-9
286
As applications, we can consider Fullér’s theorem [A28] on the law of large numbers. His result
was generalized by Triesch [18], Hong [7] and Hong and Kim [10]. But, in these results the
uniform boundedness of supports of LR-fuzzy numbers is assumed. Triesch [19] stated that there
could be laws of large numbers for interesting classes of t-norm and sequences of fuzzy numbers
where the diameter of the support of fuzzy numbers is not uniformly bounded. Using the idea of
Theorem 5, Hong and Lee [11] have s tudied a law of large numbers without assuming uniform
boundedness and generalized results of Fullér [A28] and Triesch [19]. (page 251)
A28-c21 K.-L. Zhang and K. Hirota, On fuzzy number lattice (R̃, ≤), FUZZY SETS AND SYSTEMS, 92(1997)
113-122. 1997
http://dx.doi.org/10.1016/S0165-0114(96)00164-9
1996
A28-c20 D.H.Hong and Y.M.Kim, A law of large numbers for fuzzy numbers in a Banach space, FUZZY SETS
AND SYSTEMS, 77(1996) 349-354. 1996
http://dx.doi.org/10.1016/0165-0114(95)00048-8
Recently, Fullér [A28] proves a law of large numbers for sequences of symmetric triangular fuzzy
numbers with common spread and Triesch [9] generalizes Fullér’s results for sequences of L-R
fuzzy numbers with bounded spreads. The object of this paper is to consider fuzzy numbers in a
Banach space and to generalize earlier results of Fullér and Triesch. (page 349)
A28-c19 Hong DH A convergence theorem for arrays of L - R fuzzy numbers INFORM SCIENCES 88 (1-4):
169-175 JAN 1996
http://dx.doi.org/10.1016/0020-0255(95)00160-3
1995
A28-c18 A.Markova, Addition of L-R fuzzy numbers, Bulletin for Studies and Exchanges on Fuzziness and its
Applications, 63(1995) 25-29. 1995
1994
A28-c17 D.H.Hong, A note on the law of large numbers for fuzzy numbers, FUZZY SETS AND SYSTEMS
64(1994), No. 1, 59-61. [MR 95e:03152]
http://dx.doi.org/10.1016/0165-0114(94)90006-X
Abstract: We prove Fullér’s open question [Fuzzy Sets and Systems, 45(1992) 299-303]: We
construct a t-norm T showing Fullér’s theorem on . . . (page 59).
A28-c16 D.H.Hong, A note on the law of large numbers for fuzzy numbers, FUZZY SETS AND SYSTEMS,
68(1994), No. 2, 243-243. [MR 1 321 502]
http://dx.doi.org/10.1016/0165-0114(94)90050-7
1993
A28-c15 E.Triesch, Characterisation of Archimedean t-norms and a law of large numbers, FUZZY SETS AND
SYSTEMS, 58(1993) 339-342. 1993
http://dx.doi.org/10.1016/0165-0114(93)90507-E
Abstract: We study a law of large numbers for mutually T -related fuzzy numbers where T is an
Archimedean t-norm and extend earlier results of Fullér in this area. In particular, we show that
the class of Archimedean t-norms can be characterized by the validity of a very general law of
large numbers for sequences of L-R fuzzy numbers. numbers. (page 339)
Following Fullér (see [A28]), we say that ξ1 , ξ2 , . . . , ξn , . . . , obeys the law of large numbers if for
all > 0 the quantity Nes(mn − < (ξ1 +ξ2 +· · ·+ξn )/n < mn +) tends to 1 for n → ∞. Fullér
proves a law of large numbers for sequences of symmetric triangular fuzzy numbers with common
spread of limn→∞ mn exists and T (u.v) ≤ H0 (u, v) := uv/(u + v − uv) for all 0 ≤ u, v ≤ 1. In
287
[C27], the result is extended to certain sequences of L-R fuzzy numbers if T belongs to a subclass
of the class of Archimedean t-norms. Fullér proposes the following conjecture at the end of [A28]:
Suppose we are given an Archimedean t-norm and a sequence ξ1 , ξ2 , . . . , ξn , . . . such that, for all
n, the diameter of the support of ξn is bounded by the same constant C independent of n. Then
ξ1 , ξ2 , . . . , ξn , . . . obeys the law of large numbers. (pages 339-340)
in proceedings and edited volumes
A28-c14 Lanzhen Yang, Minghu Ha, Laws of large numbers for uncertain variables, Proceedings of the 6th
International Conference on Biomedical Engineering and Informatics (BMEI). IEEE Computer Society
Press, [ISBN 978-1-4799-2760-9], pp. 765-772. 2013
http://dx.doi.org/10.1109/BMEI.2013.6747043
A28-c13 Baogui Xin; Tong Chen; Wei Yu; Weak Laws of Large Numbers for fuzzy variables based on credibility measure, Seventh International Conference on Fuzzy Systems and Knowledge Discovery (FSKD),
10-12 August 2010, Yantai, Shandong, China, [ISBN 978-1-4244-5931-5], pp. 377-381. 2010
http://dx.doi.org/10.1109/FSKD.2010.5569638
A lot of researches have been reported in the area of WLLN for fuzzy numbers based on fuzzy
sets theory such as Fuller [A28] , Triesch [8], Hong [9], Hong and Kim [10], Jang and Kwon [11],
Hong and Ro [12], Taylor, Seymour and Chen [13], and in the area of WLLN for fuzzy random
variables based on credibility measure such as Yang and Liu [14], but all of them are essentially
different from WLLN for fuzzy variables based on credibility measure. (page 377)
A28-c12 Pedro Terán, On Convergence in Necessity and Its Laws of Large Numbers, in: Didier Dubois et al
eds., Soft Methods for Handling Variability and Imprecision, Advances in Soft Computing, vol. 48/2010,
Springer, [ISBN 978-3-540-85026-7], pp. 289-296. 2010
http://dx.doi.org/10.1007/978-3-540-85027-4_35
A28-c11 Shu-Ming Wang, Junzo Watada, On laws of large numbers for L-R fuzzy variables, 2008 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, July 12-15, 2008, Kunming, China, [ISBN: 978-1-4244-2095-7], pp. 3750-3755. 2008
http://dx.doi.org/10.1109/ICMLC.2008.4621057
In recent years, a lot of researches have been reported on the convergent properties of sum of T independent fuzzy variables or fuzzy numbers, and various forms of laws of large numbers were
proposed [4, 6, 7, 20]. Among them, Fuller [A28] proved a law of large numbers for T -related
symmetric triangular fuzzy variables with common spread (page 3750)
A28-c10 Guo-Chun Zhang, Shu-Ming Wang, Xiao-Dong Dai, The Convergent Results about the Sum of Fuzzy
Variables and the Law of Large Numbers, International Conference on Machine Learning and Cybernetics,
19-22 Aug. 2007, vol.2, pp.1209-1214. 2007
http://dx.doi.org/10.1109/ICMLC.2007.4370328
In credibility theory, fuzzy variable introduced by Kaufmann [10] is a critical concept. In recent
years, a lot of work has been done on the properties about the sum of fuzzy variables or fuzzy
numbers, and various forms of law of large numbers for fuzzy variables were proposed. Badard
[1] studied the behavior of arithmetical mean for T -independent fuzzy numbers where T =”min”
and T =classical product; Fullér [A28] proved a law of large numbers for T -independent fuzzy
numbers with common spread if T (x, y) ≤ xy/(x + y − xy) for all 0 ≤ x, y ≤ 1; Triesch [21],
Hong and Hwang [4] generalized Fullér’s results for certain sequence of L - R fuzzy numbers if T
is a Archimedean t-norm; Hong and Lee [5] studied the law of large numbers for T -independent
L - R fuzzy numbers where T is an Archimedean t-norm and the diameter of the support of the
fuzzy numbers is not uniformly bounded, this generalized Triesch’s results.
..
.
This paper studies the convergent properties on the sum of T-independent fuzzy variables based on
credibility theory and the convex hull of a function, and finally gives a strong law of large numbers
for fuzzy variables. (page 1209)
288
A28-c9 YJ Chen, TG Fan, FF Hao, The convergence theorems for sequence of fuzzy variables, Proceedings of
the 5th International Conference on Machine Learning and Cybernetics, Aug. 13-16, 2006, Vols 1-7, pp.
1889-1894. 2006
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04370350
A28-c8 Dick, S. and Kandel, A. Granular computing in neural networks, in: Granular Computing: An Emerging
Paradigm, W. Pedrycz, Ed. Physica-Verlag GmbH, Heidelberg, Germany, 275-305. 2001
A28-c7 M. Oussalah, New Formulations of Law of Large Numbers and Its Convergence in the Framework of
Possibility Theory, In: Da Ruan ed., Intelligent Techniques and Soft Computing in Nuclear Science and
Engineering: Proceedings of the 4th International Flins Conference Bruges, Belgium, World Scientific,
[ISBN 9789810243562], pp. 80-86. 2000
A28-c6 D.Dubois, E.Kerre, R.Mesiar and H.Prade, Fuzzy interval analysis, in: Didier Dubois and Henri Prade
eds., Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, Volume 7, Kluwer Academic
Publishers, [ISBN 0-7923-7732-X], 2000, 483-581. 2000
A28-c5 E. Pap, The law of large numbers in representation on uncertainty, in: B.De Baets, J. Fodor and
L. T. Kóczy eds., Proceedings of the Fourth Meeting of the Euro Working Group on Fuzzy Sets and Second
International Conference on Soft and Intelligent Computing (Eurofuse-SIC’99), Budapest, Hungary, 25-28
May 1999, Technical University of Budapest, [ISBN 963 7149 21X], 1999 459-464. 1999
Following Fullér [A28] we say that ã1 = (a1 , α), ã2 = (a2 , α), . . . obeys the law of large numbers
if
1
lim (ã1 ⊕T · · · ⊕T ãn )(z) = χa (z)
n→∞ n
where
a1 + · · · + an
a = lim
n→∞
n
(page 460)
Fullér proves a law of large numbers if T ≤ T0H , where T0H is the Hamacher norm with parameter
0; and for TM (where TM is min-t-norm) the law of large numbers is not valid. Triesch [12]
generalized Fullér’s result for sequences of LR-fuzzy numbers with bounded spreads. Hong and
Kim [5] generalized earlier results of Fullér and Triesch and gave law of large numbers in Banach
space. Fullér suggests the question: Does the law of large numbers valid for t-norm T such that
T0H ≤ T ≤ TM ? (page 461)
A28-c4 D.H.Hong and C. Hwang, Upper bound of T-sum of LR-fuzzy numbers, in: Proceedings of IPMU’96
Conference (July 1-5, 1996, Granada, Spain), 1996 343-346.
A28-c3 D.Dubois, H.Prade and R.R.Yager eds., Readings in Fuzzy Sets for Intelligent Systems, Morgan Kaufmann Publisher, San Mateo, 1993, page 24.
Studies the limit of the arithmetic mean of identical fuzzy numbers under various t-norm based
extension principles. (page 24)
in books
A28-c2 Jorma K. Mattila, Text Book of Fuzzy Logic, Art House, Helsinki, [ISBN 951-884-152-7], 1998.
A28-c1 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
[A29] Robert Fullér, On the generalized method-of-case inference rule, Annales Univ. Sci. Budapest, Sectio
Computatorica, 12(1991) 107-113. [MR: 93b:03036] [Zbl.895.68134]
in books
[A29-c1] R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
[A30] Robert Fullér, On Hamacher-sum of triangular fuzzy numbers, FUZZY SETS AND SYSTEMS 42(1991)
205-212. [MR 92d:04003] [Zbl.734.04004]. doi 10.1016/0165-0114(91)90146-H
289
in journals
A30-c16 L N Zhang, F P Wu, L L Yu, X Wang, Grey Clustering Evaluation Model Based on D-S Evidence
Theory to Evaluate the Scheme of Basin Initial Water Rights Allocation, The Open Cybernetics & Systemics
Journal, 2015(2015), number 9, pp. 7-16. 2015
http://dx.doi.org/10.2174/1874110X01509010007
A30-c16 SALIH AYTAR, A NEIGHBOURHOOD SYSTEM OF FUZZY NUMBERS AND ITS TOPOLOGY,
Commun. Fac. Sci. Univ. Ankara, Ser. A1, Math. Stat. Volume 62, Number 1, pp. 73-83. 2013
http://communications.science.ankara.edu.tr/A1/yayinlar/A1-2013-62-1-7.pdf
In 1991 Fuller [9] calculated the membership function of the product-sum of triangular fuzzy
numbers. Later Hong and Hwang [13] determined the exact membership function of the t-normbased sum of fuzzy numbers. In 1997 Hwang and Hong [14] have studied the membership function
of the t-norm-based sum of fuzzy numbers on Banach spaces, which generalizes earlier results
Fuller [9] and Hong and Hwang [13]. These papers are important ones related to the theory of
convergence. (page 74)
A30-c15 L N Zhang, F P Wu, P Jia, Grey Evaluation Model Based on Reformative Triangular Whitenization
Weight Function and Its Application in Water Rights Allocation System, THE OPEN CYBERNETICS &
SYSTEMICS JOURNAL, 7(2013), pp. 1-10. 2013
http://dx.doi.org/10.2174/1874110X20130521001
A30-c14 József Dombi and Norbert Győrbı́ró, Addition of sigmoid-shaped fuzzy intervals using the Dombi
operator and infinite sum theorems, FUZZY SETS AND SYSTEMS, 157(2006) 952-963. 2006
http://dx.doi.org/10.1016/j.fss.2005.09.011
Fullér has studied the sup-T sum with triangular fuzzy intervals [A32,A30] and in a more general
context [A24]. These results were developed further and extended by Hong [11-13] and Mesiar
[15]. (page 953)
A30-c13 Sato-Ilic M, Sato Y Asymmetric aggregation operator and its application to fuzzy clustering model,
COMPUTATIONAL STATISTICS & DATA ANALYSIS, 32 (3-4): 379-394, JAN 28 2000
http://dx.doi.org/10.1016/S0167-9473(99)00091-2
A30-c12 Sato-Ilic M, Sato Y A general fuzzy clustering model based on asymmetric aggregation operators
IETE JOURNAL OF RESEARCH, 44 (4-5): 207-218 JUL-OCT 1998
A30-c11 S.Y.Hwang and D.H.Hong, The convergence of T-sum of fuzzy numbers on Banach spaces, APPLIED
MATHEMATICS LETTERS, vol. 10, No. 4, 129-134. 1997
http://dx.doi.org/10.1016/S0893-9659(97)00072-4
The purpose of this paper is to study the membership function of the t-norm-based sum of fuzzy
numbers on Banach spaces, which generalizes earlier results by Fullér [A30] and Hong and Hwang
[1]. (page 129)
A30-c10 D.H.Hong and S.Y.Hwang, The convergence of T-product of fuzzy numbers, FUZZY SETS AND
SYSTEMS, 85(1997) 373-378. 1997
http://dx.doi.org/10.1016/0165-0114(95)00333-9
Recently, t-norm-based addition of fuzzy numbers and its convergence have been studied [A32,
A30, A28, A24, 6, 7, 9]. (page 373)
A30-c9 Mika Sato, Yoshiharu Sato A general fuzzy clustering model based on aggregation operators BEHAVIORMETRIKA, 22: (2) 115-128 (1995)
http://dx.doi.org/10.2333/bhmk.22.115
A30-c8 D.H.Hong and S.Y.Hwang, On the convergence of T-sum of L-R fuzzy numbers, FUZZY SETS AND
SYSTEMS, 63(1994) 175-180. 1994
http://dx.doi.org/10.1016/0165-0114(94)90347-6
290
Abstract: This paper presents the membership function of infinite (or finite) sum (defined by the
sup-t-norm convolution) of L-R fuzzy numbers under the conditions of the convexity of additive
generators and the concavity of L, R. As an application, we shall calculate the membership
function of the limit distribution of the Hamacher sum (Hr -sum) for 0 ≤ r ≤ 2, which generalizes
Fullér’s results [A32, A30] in the case r ∈ {0, 1, 2}. (page 175)
Fullér [A32, A30] obtained the following result.
Theorem 1. Let r = 0,
2 and let ãi = (ai , α, α)LR be L-R fuzzy numbers with L(x) = R(x) =
P1,
∞
1 − x such that A = i=1 exists and it is finite. Then the pointwise limits of the partial product
sums Ãn := ã1 + · · · = ãn for n → ∞ exist and are given by

1



if r = 0,


1
+
|A
− z|/α


lim Ãn (z) =
exp(−|A − z|/α)
if r = 1,
n→∞




2


if r = 2.

1 + exp(−2|A − z|/α)
In this paper, we determine the exact limit distributions of T-sum Ãn under very mild conditions,
which generalize earlier results by Fullér [A32, A30]. (page 176)
A30-c7 M.F.Kawaguchi and T.Da-te, Some algebraic properties of weakly non-interactive fuzzy numbers,
FUZZY SETS AND SYSTEMS, 68(1994) 281-291. 1994
http://dx.doi.org/10.1016/0165-0114(94)90184-8
A30-c6 M.F.Kawaguchi and T.Da-te, Properties of fuzzy arithmetic based on triangular norms, Journal of Japan
Society for Fuzzy Theory and Systems, 5(1993) 1113-1121 (in Japanese). Japanese Journal of Fuzzy Theory
and Systems, 5(1993) 677-687 (English Translation version). 1993
in proceedings and edited volumes
A30-c5 M. Sato-Ilic, Fuzzy clustering for uncertainty data, in: Proceedings of the 1999 IEEE International
Conference on Systems, Man, and Cybernetics, [doi 10.1109/ICSMC.1999.814117], vol.1, pp. 359-364.
1999
A30-c4 M. Sato and Y. Sato, A generalized fuzzy clustering model based on aggregation operators and its
applications, in: B. Bouchon-Meunier ed., Aggregation and Fusion of Imperfect Information, (Studies in
Fuzziness and Soft Computing, ed., J. Kacprzyk. Vol. 12) Physica-Verlag, 1998 261-278. 1998
A30-c3 M. Sato and Y. Sato, A generalized fuzzy clustering model based on fuzzy aggregation operators, in:
Proceedings of Sixth IFSA World Congress, July 22-28, 1995, Sao Paulo. 1995
in books
A30-c2 Jorma K. Mattila, Text Book of Fuzzy Logic, Art House, Helsinki, [ISBN 951-884-152-7], 1998.
A30-c1 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
[A31] Robert Fullér, Well-posed fuzzy extensions of ill-posed linear equality systems, Fuzzy Systems and Mathematics, 5(1991) 43-48.
in journals
A31-c3 D A Molodtsov, D V Kovkov, Stability and Approximation of Maximin Problems, AUTOMATION
AND REMOTE CONTROL, 75: (3) pp. 447-457. (2014)
http://dx.doi.org/10.1134/S0005117914030035
A31-c2 S.Jenei, Continuity in approximate reasoning, Annales Univ. Sci. Budapest, Sect. Comp., 15(1995)
233-242. 1995
in books
291
A31-c1 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
[A32] Robert Fullér, On product-sum of triangular fuzzy numbers, FUZZY SETS AND SYSTEMS 41(1991)
83-87. [MR 92c:04008] [Zbl.725.04002]. doi 10.1016/0165-0114(91)90158-M
in journals
2015
A32-c37 Zhi-Yuan Feng, Johnson T -S Cheng, Yu-Hong Liu, I-Ming Jiang, Options pricing with time changed
Lévy processes under imprecise information, Fuzzy Optimization and Decision Making, 14: (1) pp. 97-119.
2015
http://dx.doi.org/10.1007/s10700-014-9191-3
2013
A32-c36 Shruti Garg, G Sahoo, Crack Classification and Interpolation of Old Digital Paintings, Journal of
Computer Sciences and Applications, 1(2013), number 5, pp. 85-90. 2013
http://dx.doi.org/10.12691/jcsa-1-5-2
2012
A32-c36 Suchismita Das, Shruti Garg, G Sahoo, Comparison of Content Based Image Retrieval Systems Using
Wavelet and Curvelet Transform, The International Journal of Multimedia & Its Applications, 4: (4) pp.
137-154. 2012
http://dx.doi.org/10.5121/ijma.2012.4412
2011
A32-c35 Daniel M. Batista, Nelson L.S. da Fonseca, Robust scheduler for grid networks under uncertainties
of both application demands and resource availability, COMPUTER NETWORKS, 55(2011), issue 1, pp.
3-19. 2011
http://dx.doi.org/10.1016/j.comnet.2010.07.009
2009
A32-c35 Weidong Xu, Chongfeng Wu, Weijun Xu, Hongyi Li, A jump-diffusion model for option pricing under
fuzzy environments, INSURANCE: MATHEMATICS AND ECONOMICS, 44(2009), pp. 337-344. 2009
http://dx.doi.org/10.1016/j.insmatheco.2008.09.003
2006
A32-c34 J. Dombi, N. Győrbı́ró, Addition of sigmoid-shaped fuzzy intervals using the Dombi operator and
infinite sum theorems, FUZZY SETS AND SYSTEMS 157 (7): 952-963 APR 1 2006
http://dx.doi.org/10.1016/j.fss.2005.09.011
Fullér has studied the sup-T sum with triangular fuzzy intervals [A32,A30] and in a more general
context [A24]. These results were developed further and extended by Hong [11-13] and Mesiar
[15]. (page 953)
2004
A32-c33 Hong DH, On types of fuzzy numbers under addition, KYBERNETIKA 40 (4): 469-476 2004
http://kybernetika.utia.cas.cz/pdf_article/40_4_654_full.pdf
2003
292
A32-c32 Dug Hun Hong, T-sum of L-R fuzzy numbers with unbounded supports, Commun. Korean Math.
Soc., 18 (2003), no. 2, 385–392. 2003
2001
A32-c31 Dug Hun Hong, Some results on the addition of fuzzy intervals FUZZY SETS AND SYSTEMS,
122(2001) 349-352. 2001
http://dx.doi.org/10.1016/S0165-0114(00)00005-1
1997
A32-c30 Guojun Wang, Uniformity of triangular fuzzy number space, Pure and Applied Mathematics 13(1997),
number 2, pp. 1-5 (in Chinese). 1997
A32-c30 D.H.Hong and S.Y.Hwang, The convergence of T-product of fuzzy numbers, FUZZY SETS AND
SYSTEMS, 85(1997) 373-378. 1997
http://dx.doi.org/10.1016/0165-0114(95)00333-9
Recently, t-norm-based addition of fuzzy numbers and its convergence have been studied [A32,
A30, A28, A24, 6, 7, 9]. (page 373)
A32-c29 A.Markova, T-sum of L-R fuzzy numbers, FUZZY SETS AND SYSTEMS, 85(1997) 379-384. 1997
http://dx.doi.org/10.1016/0165-0114(95)00370-3
A32-c28 S.Y.Hwang and D.H.Hong, The convergence of T-sum of fuzzy numbers on Banach spaces, APPLIED
MATHEMATICS LETTERS, 10(1997) 129-134. 1997
http://dx.doi.org/10.1016/S0893-9659(97)00072-4
In 1991, Fullér calculated the membership function of the product-sum of triangular fuzzy numbers, and he asked for conditions on which the product-sum of L-R fuzzy numbers has the same
membership function. The answer for this question was given by Triesch [2] and Hong [3], which
is the conditions that log L and log R are concave functions. Recently, Houg and Hwang [1] determined the exact membership function of the t-norm-based sum of fuzzy numbers, in the case of
Archimedean t-norm having convex additive generator function and fuzzy numbers with concave
shape functions, which is the generalization of Fullér and Keresztfalvi’s result [4]. The purpose
of this paper is to study the membership function of the t-norm-based sum of fuzzy numbers on
Banach spaces, which generalizes earlier results by Fullér [5] and Hong and Hwang [1]. The idea
follows from Hong and Hwang’s paper [1]. (page 129)
A32-c27 D.H.Hong and C. Hwang, A T-sum bound of LR-fuzzy numbers, FUZZY SETS AND SYSTEMS,
91(1997), pp. 239-252. 1997
http://dx.doi.org/10.1016/S0165-0114(97)00144-9
A32-c26 K.-L. Zhang and K. Hirota, On fuzzy number lattice (R̃, ≤), FUZZY SETS AND SYSTEMS, 92(1997),
pp. 113-122. 1997
http://dx.doi.org/10.1016/S0165-0114(96)00164-9
1995
A32-c25 A.Markova, Addition of L-R fuzzy numbers, Bulletin for Studies and Exchanges on Fuzziness and its
Applications, 63(1995), pp. 25-29. 1995
1994
A32-c24 D.H.Hong, A note on product-sum of L-R fuzzy numbers, FUZZY SETS AND SYSTEMS, 66(1994),
pp. 381-382. 1994
http://dx.doi.org/10.1016/0165-0114(94)90106-6
Triesch (1993) provided a partial answer to Fullér’s (1991) question about the membership function of the finite sum (defined via sup-product-norm convolution) of L-R fuzzy numbers. In this
short note, we prove the other half. (page 381)
293
Fullér [A32] asks for conditions on L-R fuzzy numbers ãi = (ai , α, β)LR , i = 1, 2, . . . , n which
imply that partial product sums are given by the formula

An − z


n

if An − nα ≤ z ≤ An ,
L

nα
Ãn (z) =

z − An


if An ≤ z ≤ An + nβ
 Rn
nβ
Pn
where An = i=1 ai . (page 381)
A32-c23 M.F.Kawaguchi and T.Da-te, Some algebraic properties of weakly non-interactive fuzzy numbers,
FUZZY SETS AND SYSTEMS, 68(1994) 281-291. 1994
http://dx.doi.org/10.1016/0165-0114(94)90184-8
A32-c22 D.H.Hong and S.Y.Hwang, On the convergence of T-sum of L-R fuzzy numbers, FUZZY SETS AND
SYSTEMS 63(1994) 175-180. 1994
http://dx.doi.org/10.1016/0165-0114(94)90347-6
1993
A32-c21 E.Triesch, On the convergence of product-sum series of L-R fuzzy numbers, FUZZY SETS AND
SYSTEMS, 53(1993) 189-192. 1993
http://dx.doi.org/10.1016/0165-0114(93)90172-E
A32-c20 Jin Bai Ki On product-sum of fuzzy complex numbers of elliptic type, THE JOURNAL OF FUZZY
MATHEMATICS, Vol.1, No.3 (1993) 611-617. 1993
A32-c19 M.F.Kawaguchi and T.Da-te, Properties of fuzzy arithmetic based on triangular norms, Journal of
Japan Society for Fuzzy Theory and Systems, 5(1993) 1113-1121 (in Japanese). Japanese Journal of Fuzzy
Theory and Systems, 5(1993) 677-687 (English Translation version). 1993
in proceedings and edited volumes
A32-c9 Mencattini A, Salmeri M, Lojacono R., On a generalized T-norm for the representation of uncertainty
propagation in statistically correlated measurements by means of fuzzy variables, In: 2007 IEEE International Workshop on Advanced Methods for Uncertainty Estimation in Measurement, Trento; Italy , pp.
10-15. 2007
http://dx.doi.org/10.1109/AMUEM.2007.4362562
A32-c8 M. Nachtegael, S. Schulte, V. De Witte, T. Mélange; E. E. Kerre, Image Similarity - From Fuzzy Sets
to Color Image Applications, in: Advances in Visual Information Systems, Lecture Notes in Computer
Science, vol. 4781, pp. 26-37. 2007
http://dx.doi.org/10.1007/978-3-540-76414-4_4
A32-c7 M. Nachtegael, D. Van der Weken, V. De Witte, S. Schulte T. Mélange, E.E. Kerre, Color Image
Retrieval Using Fuzzy Similarity Measures and Fuzzy Partitions , in: Proceedings of the 2007 IEEE International Conference on Image Processing (ICIP’2007), September 16-19, 2007, San Antonio, Texas, [file
name: 04379511], pp. VI-13 - VI-16. 2007
A32-c6 A. Danak, A.R. Kian, Fuzzy contributive games: an extension to the game of civic duty In: 17th IEEE
International Conference on Tools with Artificial Intelligence (ICTAI 05), 14-16 November 2005, Hong
Kong, China, pp. 561-566. 2005
http://dx.doi.org/10.1109/ICTAI.2005.67
A32-c5 D.Dubois, E.Kerre, R.Mesiar and H.Prade, Fuzzy interval analysis, in: Didier Dubois and Henri Prade
eds., Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, Volume 7, Kluwer Academic
Publishers, [ISBN 0-7923-7732-X], 2000, 483-581. 2000
A32-c4 D.H.Hong and C. Hwang, Upper bound of T-sum of LR-fuzzy numbers, in: Proceedings of IPMU’96
Conference (July 1-5, 1996, Granada, Spain), 1996 343-346. 1996
294
in books
A32-c3 Elisabeth Rakus-Andersson, Fuzzy and Rough Techniques in Medical Diagnosis and Medication, Studies in Fuzziness and Soft Computing series, vol. 212/2007, Springer, [ISBN 978-3-540-49707-3], 2007.
A32-c2 Jorma K. Mattila, Text Book of Fuzzy Logic, Art House, Helsinki, [ISBN 951-884-152-7], 1998.
A32-c1 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
[A33] Robert Fullér and Tibor Keresztfalvi, On generalization of Nguyen’s theorem, FUZZY SETS AND SYSTEMS, 41(1991) 371-374. [MR 92g:04009] [Zbl.755.04004]. doi 10.1016/0165-0114(91)90139-H
in journals
2016
A33-c70 Dug Hun Hong, Blackwell type theorem for general T-related and identically distributed fuzzy variables, FUZZY OPTIMIZATION AND DECISION MAKING (to appear). 2016
http://dx.doi.org/10.1007/s10700-016-9234-z
2015
A33-c69 Dug Hun Hong, The Existence of T-iid Random Fuzzy Variables and its Law of Large Numbers,
INTERNATIONAL JOURNAL OF MATHEMATICAL ANALYSIS, 9: (49) pp. 2407-2418. 2015
http://dx.doi.org/10.12988/ijma.2015.58192
A33-c68 Hung T Nguyen, Statistics of Fuzzy Data: A Research Direction for Applied Statistics, Thailand
Statistician, 13(2015), number 1, pp. 1-31. 2015
It is sometimes convenient to work with level sets of membership functions. The following result,
known in the literature as Nguyen’s theorem (Nguyen [15]; Fuller and Keresztfalvi [A33]; Fuller
[K1]), is useful. (page 15)
A33-c67 Hung T Nguyen, Songsak Sriboonchitta, Berlin Wu, A Statistical Basis for Fuzzy Engineering Economics, International Journal of Fuzzy Systems, 17(2015), issue 1, pp. 1-11. 2015
http://dx.doi.org/10.1007/s40815-015-0010-y
A33-c66 Chun Yong Wang, Bao Qing Hu, Generalized extended fuzzy implications, Fuzzy Sets and Systems,
268(2015), pp. 93-109. 2015
http://dx.doi.org/10.1016/j.fss.2014.05.010
2014
A33-c65 Salicone S, The mathematical theory of evidence and measurement uncertainty - Expression and combination of measurement results via the random-fuzzy variables, IEEE INSTRUMENTATION AND MEASUREMENT MAGAZINE, 17(014), number 5, pp. 36-44. 2014
http://dx.doi.org/10.1109/MIM.2014.6912200
A33-c64 Scheerlinck K, Vernieuwe H, Verhoest NEC, Baets B De, Practical computing with interactive fuzzy
variables, Applied Soft Computing, 22(2014), pp. 518-527. 2014
Fullér and Keresztfalvi [A33] generalized Nguyen’s theorem for interactive fuzzy input variables.
Based on this generalization, the current paper presents a modified Fuzzy Calculator that allows
to take interactivity into account. It is therefore referred to as the ’generalized Fuzzy Calculator’. Firstly, the generalized Fuzzy Calculator is applied to the same test functions as described
in Scheerlinck et al. [44]. Some basic triangular norms will be used to describe the interactivity between the fuzzy input variables of these test functions. In this way, we can evaluate the
performance of the generalized Fuzzy Calculator. (page 519)
295
A33-c63 Dug Hun Hong, Renewal reward process for T-related fuzzy random variables on (Rp , Rq ), Fuzzy
Optimization and Decision Making, 13(2014), number 4, pp. 415-434. 2014
http://dx.doi.org/10.1007/s10700-014-9185-1
2013
A33-c62 Dug Hun Hong, Strong laws of large numbers for t-norm-based addition of fuzzy set-valued random
variables, FUZZY SETS AND SYSTEMS, 223(2013), pp. 26-38. 2013
http://dx.doi.org/10.1016/j.fss.2013.01.011
A33-c61 Dug Hun Hong, The law of large numbers and renewal process for T-related weighted fuzzy numbers
on Rq , INFORMATION SCIENCES, 228(2013), pp. 45-60. 2013
http://dx.doi.org/10.1016/j.ins.2012.12.016
A33-c60 Adam Bzowski and MichałK. Urbanski, A note on Nguyen-Fullér-Keresztfalvi theorem and Zadeh’s
extension principle, FUZZY SETS AND SYSTEMS, 213(2013), pp. 91-101. 2013
http://dx.doi.org/10.1016/j.fss.2012.09.004
This paper is devoted to the analysis of the generalised form of the Nguyen-Fullér-Keresztfalvi
theorem (NFK theorem). The classical NFK theorem expresses the Zadeh extension principle
in terms of α-cuts of fuzzy sets, but it is subjected to some constraining assumptions. These
assumptions concern all data in the problem: shape of fuzzy sets, topology of underlying spaces,
and regularity of functions and t-norms. In this paper we analyse consequences of dropping these
assumptions. (page 91)
In this final section we will return to the classical setting of the NFK formula (5). The aim is
to prove Theorem 10 which extends the applicability of the classical NFK formula to the class
of fuzzy sets with unbounded supports. This last part of the paper is only remotely connected
to the general analysis of the previous chapters. In particular we will not use level sets and the
generalised formulation of the NFK theorem here. In our approach the classical NFK formula (5)
as in [5] can be stated as follows. (page 100)
We should point out that in the original paper of Fullér and Keresztfalvi [5] the essential assumption on the topology of Z in Theorem 10 is omitted. The proof requires the assumption that every
one-point set in Z is closed (Z is T1 ). To see its necessity take any example where Theorem 10
does not work due to discontinuity of f only, and then change the topology on Z such that f regains
continuity. (page 101)
2010
A33-c59 Hsien-Chung Wu, Generalized Extension Principle, FUZZY OPTIMIZATION AND DECISION MAKING , 9(2010), issue 1, pp. 31-68. 2010
http://dx.doi.org/10.1007/s10700-010-9075-0
Fullér and Keresztfalvi (1990) generalized the result of Nguyen by considering t-norm operator in
the definition of extension principle without considering the 0-level set. When U1 = U2 = V = R,
Nguyen also obtained an equality that can be used in the arithmetics of fuzzy numbers. Fullér and
Keresztfalvi also generalized this equality when U1 , U2 and V are locally compact topological
spaces instead of assuming them as R. As a matter of fact, the definitions of 0-level set of Nguyen
(1978) and Fullér and Keresztfalvi (1990) are different. The zero-level set defined by Nguyen will
become the whole universal set and the zero-level set defined by Fullér and Keresztfalvi is based
on the closure of the support of a fuzzy set, which is not necessarily the whole universal set. In
this paper, we are going to show that those equalities still hold true for the 0-level set under some
suitable conditions. The t-norm operator adopted in Fullér and Keresztfalvi (1990) is defined on
the product space of two unit intervals. Based on the associativity of t-norm, it can be generalized
as a Tn operator that is defined on the product space of n unit intervals. The generalized extension
principle proposed in this paper is established on the Hausdorff space and defined by considering
an operator Wn that is more general than the t-norm operator Tn . (pages 31-32)
296
In Sect. 4, we define the generalized extension principle that will adopt an operator Wn that is
more general than Tn . Some useful results are will be derived based on this generalized extension
principle. In Sect. 5, the main results will be obtained, which will extend the results obtained by
Nguyen (1978) and Fullér and Keresztfalvi (1990). Under this generalized extension principle,
many useful and interesting equalities regarding the α-level sets for α ∈ [0, 1] are obtained in
which the 0-level set is taken into account. Of course, those results will reduce to the conventional results when the infinite-dimensional Hausdorff space is reduced as the finite-dimensional
Euclidean space and the operator Wn is reduced as the minimum or t-norm operator. (page 32)
A33-c58 A Mencattini, S Salicone, How to Process the Random Part of RFVs: Comparison of Available Methods and New Proposal, IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT,
59(2010), issue 1, pp. 15-26. 2010
http://dx.doi.org/10.1109/TIM.2009.2025685
Definition (2) is given in terms of MFs. Moreover, from considerations in Section II, the t-norm
has to be inserted in the EP given by (1). To reduce the complexity of a direct implementation
of the EP, we use the Nguyen theorem [A33]. It allows us to define each t-norm in terms of the
α-cuts of the two initial FVs A and B as follows:
2009
A33-c57 M.T. Mizukoshi, L.C. Barros, R.C. Bassanezi, Stability of fuzzy dynamic systems, INTERNATIONAL
JOURNAL OF UNCERTAINTY, FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 17(2009), pp.
69-83. 2009
http://dx.doi.org/10.1142/S0218488509005747
2008
A33-c56 Y. Chalco-Cano, Jiménez-Gamero, H. Román-Flores and M.A. Rojas-Medar, An approximation to the
extension principle using decomposition of fuzzy intervals, FUZZY SETS AND SYSTEMS, 159(2008),
pp. 3245-3258. 2008
http://dx.doi.org/10.1016/j.fss.2008.06.011
A33-c55 Z. Gera, J. Dombi, Exact calculations of extended logical operations on fuzzy truth values, FUZZY
SETS AND SYSTEMS, 159(2008), pp. 1309-1326. 2008
http://dx.doi.org/10.1016/j.fss.2007.09.020
In this setting the arguments are interactive, and this interactivity is represented by the Łukasiewicz
t-norm. Here we do not discuss the non-interactive case, for references, see Nguyen’s theorem in
[10]. Fullér and Keresztfalvi [A33] generalized the Nguyen theorem to non-interactive arguments,
but did not provide explicit formulas for computations. Here, we provide pointwise, easy-tocompute formulas for the above operations on linear fuzzy truth values. (page 1321)
2001
A33-c54 Heriberto Román-Flores, Laécio C. Barros and Rodney C. Bassanezi, A note on Zadeh’s extensions,
FUZZY SETS AND SYSTEMS, 117(2001) 327-331. 2001
http://dx.doi.org/10.1016/S0165-0114(98)00408-4
On the other hand, we know that f can verify Eq. (4) without being necessarily continuous. For
example [A33]: (page 329)
A33-c53 Michael Wagenknecht, Rainer Hampel and Veit Schneider, Computational aspects of fuzzy arithmetics
based on Archimedean t-norms, FUZZY SETS AND SYSTEMS, 123(2001) 49-62. 2001
http://dx.doi.org/10.1016/S0165-0114(00)00096-8
We have the following important result [A33].
Theorem 1. Let F and Ai be as in Defnition 2. Additionally, suppose F to be continuous over
297
the Cartesian product of cl suppAi whereby the Ai are fuzzy numbers. Moreover, let T be an usc.
Then
[
Bα = [F (A1 , . . . , An )]α =
F (A1α1 , . . . , Anαn )
T (α1 ,...,αn )≥α
for all α ∈ (0, 1]. (page 51)
1999
A33-c52 J J Buckley, Aimin Yan, Fuzzy topological vector spaces over R̄, FUZZY SETS AND SYSTEMS,
105(1999), pp. 259-275. 1999
http://dx.doi.org/10.1016/S0165-0114(98)00325-X
Proof. It is the consequence of Theorem 2 of [A33]. (page 264)
1997
A33-c51 H.T. Nguyen, V. Kreinovich, V. Nesterov and M. Nakamura, On hardware support for interval computations and for soft computing: theorems, IEEE TRANSACTIONS ON FUZZY SYSTEMS, Vol 5, No 1,
1997 108-127. 1997
http://ieeexplore.ieee.org/iel4/91/12077/00554456.pdf
A33-c50 R.Mesiar, Shape preserving additions of fuzzy intervals, FUZZY SETS AND SYSTEMS, 86(1997)
73-78. 1997
http://dx.doi.org/10.1016/0165-0114(95)00401-7
1996
A33-c49 B.Bouchon-Meunier, V.Kreinovich, A.Lokshin and H.T.Nguyen, On the formulation of optimization
under elastic constraints (with control in mind), FUZZY SETS AND SYSTEMS, 81(1996) 5-29. 1996
http://dx.doi.org/10.1016/0165-0114(96)88181-4
1994
A33-c48 Phil Diamond and A. Pokrovskii, Chaos, entropy and a generalized extension principle, FUZZY SETS
AND SYSTEMS , 61(1994) 277-283. 1994
http://dx.doi.org/10.1016/0165-0114(94)90170-8
Apparently, the usual fuzzification and sup-min composition are inadequate to describe complexities which may arise in fuzzy control. This is not completely unexpected since other tnorm/conorm operations are being used in [12] and more general extension principles have been
developed [A33]. (page 277)
A33-c47 M.F.Kawaguchi and T.Da-te, Some algebraic properties of weakly non-interactive fuzzy numbers,
FUZZY SETS AND SYSTEMS, 68(1994) 281-291. 1994
http://dx.doi.org/10.1016/0165-0114(94)90184-8
On the other hand, in the case of sup-(t-norm) convolution, the generalized Nguyen’s Theorem,
introduced by Fullér et al. [A33], illustrated the complicated relation between the α-level sets of
operand fuzzy numbers and those of the results of operation. (page 290)
1993
A33-c46 M.F.Kawaguchi and T.Da-te, Properties of fuzzy arithmetic based on triangular norms, Journal of
Japan Society for Fuzzy Theory and Systems, 5(1993) 1113-1121 (in Japanese). Japanese Journal of Fuzzy
Theory and Systems, 5(1993) 677-687 (English Translation version). 1993
in proceedings and edited volumes
2015
298
A33-c30 Marina T Mizukoshi, Moiseis dos Santos Cecconello, Bifurcations of fuzzy solutions, In: Fuzzy
Information Processing Society (NAFIPS) held jointly with 2015 5th World Conference on Soft Computing
(WConSC), 2015 Annual Conference of the North American. IEEE, 2015. (ISBN 978-1-4673-7247-3), pp.
1-6. 2015
http://dx.doi.org/10.1109/NAFIPS-WConSC.2015.7284175
A33-c29 Estevao Esmi, Gustavo Barroso, Laecio C Barros, Peter Sussner, A Family of Joint Possibility Distributions for Adding Interactive Fuzzy Numbers Inspired by Biomathematical Models, In: Proceedings of
the 16th World Congress of the International Fuzzy Systems Association (IFSA) and the 9th Conference of
the European Society for Fuzzy Logic and Technology (EUSFLAT), Atlantis Press, (ISBN 978-94-6252077-6), pp. 1318-1323. 2015
http://dx.doi.org/10.2991/ifsa-eusflat-15.2015.186
2013
A33-c28 Janusz T Starczewski, Algebraic Operations on Fuzzy Valued Fuzzy Sets, in: Advanced Concepts in
Fuzzy Logic and Systems with Membership Uncertainty, Studies in Fuzziness and Soft Computing, vol.
284/2013, Springer, [ISBN 978-3-642-29520-1], pp. 33-76. 2013
http://dx.doi.org/10.1007/978-3-642-29520-1_2
2009
A33-c27 Mayuka F. Kawaguchi, Masaaki Miyakoshi, Generalized Extended t-Norms as t-Norms of Type 2,
39th International Symposium on Multiple-Valued Logic, May 21-May 23, 2009, Naha, Okinawa, Japan,
pp. 292-297. 2009
http://dx.doi.org/10.1109/ISMVL.2009.63
2008
A33-c26 A Mencattini, S Salicone, A comparison between different methods for processing the random part
of Random-Fuzzy Variables representing measurement results, IEEE International Workshop on Advanced
Methods for Uncertainty Estimation in Measurement, July 21-22, 2008, Sardagna, Italy, [ISBN: 978-14244-2236-4], pp. 72-77. 2008
http://dx.doi.org/10.1109/AMUEM.2008.4589938
A33-c25 Michal K Urbanski, Adam Bzowski, Error Analysis Using Fuzzy Arithmetic Based on t-norm, 12th
IMEKO TC1-TC7 joint Symposium on Man, Science and Measurement, September 3-5, 2008, Annecy,
France, pp. 109-115. 2008
http://www.imeko.org/publications/tc1-tc7-2008/IMEKO-TC1-TC7-2008-013.pdf
Using Fuller’s theorem it is easy to estimate the error of fuzzy sets addition by means of the
discretization procedure. In case of symmetric triangular fuzzy numbers with support equals to [0,
1] a number N > 2/ of α-cuts assures that the error in the sense of (13) is less than . In case of
the fuzzy number coming from normal distribution for Yager t-norm with p = 2 and 20 averaging,
a number of α-cuts which guarantees that the error of 0.05-cut is biased with the error less than
0.01 is about 100. (page 113)
2007
A33-c24 Mencattini A, Salmeri M, Lojacono R., On a generalized T-norm for the representation of uncertainty
propagation in statistically correlated measurements by means of fuzzy variables, In: 2007 IEEE International Workshop on Advanced Methods for Uncertainty Estimation in Measurement, Trento; Italy, pp.
10-15. 2007
http://dx.doi.org/10.1109/AMUEM.2007.4362562
299
What we expect, according to the T-norm used, is that the final result could emulate or not the
result obtained by a Monte Carlo simulation. It is well know that the Extension Principle (EP) by
L. Zadeh [11], is the natural way of combining fuzzy variables into a nonfuzzy function f . Also, it
is well known that implementation of EP is quite complex. So, recently, the equivalence between
applying EP and operating directly on α-cuts have been proved (Nguyen’s Theorem [12]), when
T-norm is implemented by the minimum operator (Tmin in the following). In this way, calculus is
strongly simplified, but this result does not hold for different types of T-norms. However, another
result (Fullér’s Theorem [A33, A32]) generalizes that equivalence to the case of a general T-norm.
(page 10)
2002
A33-c23 Dug Hun Hong, Distributivity of fuzzy numbers, in: Proceedings of the Korea Fuzzy and Intelligent
Systems Research Institute 2002 Fall Convention and Meeting, pp. 22-24. 2002
A33-c22 Makó Zoltán, The Opposite of Quasi-triangular Fuzzy Number, In: Third International Symposium of
Hungarian Researchers on Computational Intelligence, pp. 229-238. 2002
http://www.bmf.hu/conferences/HUCI2002/MakoZ.pdf
2000
A33-c21 Michael Wagenknecht, Rainer Hampel and Veit Schneider, On the Approximate Solution of Fuzzy
Equation Systems in: Hampel, Rainer; Wagenknecht, Michael; Chaker, Nasredin (Eds.) Fuzzy Control
Theory and Practice, Series: Advances in Soft Computing , Vol. 6, Springer, [ISBN: 978-3-7908-1327-2]
2000, pp. 132-141. 2000
A33-c20 D.Dubois, E.Kerre, R.Mesiar and H.Prade, Fuzzy interval analysis, in: Didier Dubois and Henri Prade
eds., Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, Volume 7, Kluwer Academic
Publishers, [ISBN 0-7923-7732-X], 2000, 483-581. 2000
Fullér and Keresztfalvi (1991) have generalised Nguyen’s reduction of the extension principle
(10.19) to a set-valued calculation to the case of weakly interactive variables in the sense of a
t-norm. Namely, they proved that (page 529)
1998
A33-c19 Phil Diamond, Chaos and Fuzzy Systems, in: H. T.Nguyen and M. Sugeno eds., Fuzzy Systems Modeling and Control, The Handbooks of Fuzzy Sets Series, (series editors: Didier Dubois and Henri
Prade), Vol. 2, Kluwer, Boston, [ISBN 0-7923-8064-9], 1998 489-515. 1998
1997
A33-c18 L.C. de Barros, R.C.Bassanezi and P.A.Tonelli, On the continuity of the Zadeh’s extension principle,
in: M.Mareš et al, eds., Proceedings of the Seventh IFSA World Congress, June 25-29, 1997, Academia,
Prague, Vol. II, [ISBN 8020006338], 1997 3-8. 1997
1996
A33-c17 H.T. Nguyen, V. Kreinovich., Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and
Applications, in: Kearfott, R. Baker; Kreinovich, V. eds., Applications of Interval Computations, Series:
Applied Optimization , Vol. 3, Springer, [ISBN: 978-0-7923-3847-5], pp. 245-290. 1996.
Instead of describing a function with finitely many values, it is often more convenient to approximate it by a continuous function. In other words, we can generalize it to the case of infinite set A.
Generalization of Proposition 4 to infinite A and related problems are described in Nguyen [53]
and Fuller et al [A33].
1995
300
A33-c16 H.T. Nguyen and Y. Maeda, On Fuzzy Inference Based on α-Level Sets, in: Y. Yam, K. S. Leung
eds., Future Directions of Fuzzy Theory and Systems, World Scientific, [ISBN 978-9810219192], 1995,
pp. 142-150. 1995
http://ebooks.worldscinet.com/ISBN/9789812831590/9789812831590_0011.html
1994
A33-c15 M.F.Kawaguchi, T.Da-te and H.Nonaka, A necessary condition for solvability of fuzzy arithmetic
equations with triangular norms, in: Proceedings of Third IEEE International Conference on Fuzzy Systems,
1994, pp. 1148-1152. 1994
http://dx.doi.org/10.1109/FUZZY.1994.343896
in books
A33-c6 Adrian I Ban, Lucian Coroianu, Przemyslaw Grzegorzewski, FUZZY NUMBERS: APPROXIMATIONS, RANKING AND APPLICATIONS, Institute of Computer Science, Polish Academy of Sciences,
2015. Information technologies: research and their interdisciplinary applications, vol. 9, (ISBN 978-8363159-21-4). 2015
A33-c5 B. Bede, Mathematics of Fuzzy Sets and Fuzzy Logic, Studies in Fuzziness and Soft Computing, vol.
295/2013, Springer Verlag, [ ISBN 978-3-642-35220-1]. 2013
http://dx.doi.org/10.1007/978-3-642-35221-8
A33-c4 E. P. Klement, Radko Mesiar, Endre Pap, Triangular Norms, Springer, [ISBN 0792364163], 2000.
A33-c3 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
A33-c2 M. Grabisch, H. T. Nguyen and E. A. Walker, Fundamentals of uncertainty calculi with applications to
fuzzy inference, (Kluwer, Dordrecht, 1995). 1995
A33-c1 H. Rommelfanger, Fuzzy Decision Support-Systeme, Springer-Verlag, Heidelberg, 1994 [ISBN 3-54057793-9] (Second Edition). 1994
in Ph.D. dissertations
• Karolien Scheerlinck, Metaheuristic versus tailor-made approaches to optimization problems in the biosciences, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Belgium. 2012
However, the application of the extension principle to compute with fuzzy quantities is a complex
matter. Luckily, a more practical approach operating directly on α-cuts was established by Nguyen
[121] and is applicable to continuous functions and upper semi-continuous fuzzy quantities with
compact support describing non-interactive variables as inputs. It effectively turns computing
with fuzzy intervals into interval analysis [122] on α-cuts. Fullér and Keresztfalvi (1991) [123]
generalized Nguyens theorem for interactive variables, described by triangular norms, as input.
In general, however, the result is approximative merely, since only a finite number of α-cuts can
be considered. For the common arithmetic operations, such as addition and multiplication, this
approach leads to a kind of layered interval arithmetic. (page 171)
• Zsolt Gera, Fuzzy reasoning models and fuzzy truth value based inference, Department of Computer Algorithms and Artificial Intelligence, University of Szeged, Szeged, Hungary. 2009
http://www.sci.u-szeged.hu/fokozatok/PDF/Gera_Zsolt/phd.pdf
• Joe Halliwell, Linguistic Probability Theory, School of Informatics University of Edinburgh, United Kingdom.
2007
A theorem first presented by Nguyen (1978) for classical fuzzy truth operators and extended to
arbitrary sup t-norm convolutions by Fullér and Keresztfalvi (1990) connects alpha cuts and extended functions. In plain language it states that the alphacuts of the image of a fuzzy set (under
an extended operator) are just the images of the alphacuts of that set. (page 16)
301
http://www.joehalliwell.com/thesis.pdf
• Barnabás Bede, Numerical Methods in Fuzzy Mathematics, BABES-BOLYAI UNIVERSITY CLUJ-NAPOCA,
FACULTY OF MATHEMATICS AND INFORMATICS, 2004.
[A34] Robert Fullér, On stability in possibilistic linear equality systems with Lipschitzian fuzzy numbers, FUZZY
SETS AND SYSTEMS, 34(1990) 347-353. [MR 91a:15029] [Zbl.696.15003].
doi 10.1016/0165-0114(90)90219-V
in journals
A34-c13 da Silva Wilson Ricardo Leal, Smilauer Vit, Fuzzy affinity hydration model, JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 28: (1) pp. 127-139. 2015
http://dx.doi.org/10.3233/IFS-141282
A34-c12 R Ghanbari, N Mahdavi-Amiri, R Yousefpour, EXACT AND APPROXIMATE SOLUTIONS OF
FUZZY LR LINEAR SYSTEMS: NEW ALGORITHMS USING A LEAST SQUARES MODEL AND
THE ABS APPROACH, IRANIAN JOURNAL OF FUZZY SYSTEMS, 7(2010), number 2, pp. 1-18.
2010
A34-c11 Vroman A, Deschrijver G, Kerre EE, Using Parametric Functions to Solve Systems of Linear Fuzzy
Equations with a Symmetric Matrix, INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 1(2008), Number 3, pp. 248-261. 2008
http://dx.doi.org/10.2991/ijcis.2008.1.3.5
A34-c10 Vroman A, Deschrijver G, Kerre EE Solving systems of linear fuzzy equations by parametric functions
- An improved algorithm FUZZY SETS AND SYSTEMS, 158 (14): 1515-1534 JUL 16 2007
http://dx.doi.org/10.1016/j.fss.2006.12.017
Consequently, the exact solution does not exist and therefore the search for an alternative solution
has a solid ground. There are already some alternative approaches known in literature. Fuller
[A34] considers a system of linear fuzzy equations with Lipschitzian fuzzy numbers. He assigns a
degree of satisfaction to each equation in the system and then calculates a measure of consistency
for the whole system. Abramovich et al. [1] try to minimize the deviation of the left-hand side
from the right-hand side of the system with LR-type fuzzy numbers. Both methods try to approximate the exact solution, i.e. they try to minimize the error when one reenters the solution into the
system. (page 1516)
A34-c9 Rybkin VA, Yazenin AV On the problem of stability in possibilistic optimization, NTERNATIONAL
JOURNAL OF GENERAL SYSTEMS, 30 (1): 3-22. 2001
http://dx.doi.org/10.1080/03081070108960695
A34-c8 E.B. Ammar and M.A.El-Hady Kassem, On stability analysis of multicriteria LP problems with fuzzy
parameters, FUZZY SETS AND SYSTEMS, 82(1996) 331-334. 1996
http://dx.doi.org/10.1016/0165-0114(95)00266-9
Hamacher et al. in [4] introduced a sensitivity analysis of FLP problems with crisp parameters
and soft constraints, where a functional relationship between change parameters on the righthand side and those of the optimal value of the primal objective function was derived for almost
all conceivable cases. Fullér in [A34] introduced the stability of the FLP problems with fuzzy
parameters. In the present paper we investigate the stability of the solution in fuzzy multiobjective
linear programming (FMLP) problems with symmetrical triangular fuzzy numbers and extended
operations and inequalities with respect to change of fuzzy parameters. We show that the solutions
of this problem is stable (in the matrix m) under small variations in the membership function of
the fuzzy numbers. (page 331)
A34-c7 S.Jenei, Continuity in approximate reasoning, Annales Univ. Sci. Budapest, Sect. Comp., 15(1995)
233-242. 1995
302
A34-c6 M.Kovács, Stable embeddings of linear equality and inequality systems into fuzzified systems, FUZZY
SETS AND SYSTEMS, 45(1992) 305-312. 1992
http://dx.doi.org/10.1016/0165-0114(92)90148-W
The obtained stability results are the generalizations of the stability properties of the fuzzified
linear systems proved in [A35, A34, 3,5]. (page 311)
in proceedings and edited volumes
A34-c5 D.Dubois, E.Kerre, R.Mesiar and H.Prade, Fuzzy interval analysis, in: Didier Dubois and Henri Prade
eds., Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, Volume 7, Kluwer Academic
Publishers, [ISBN 0-7923-7732-X], 2000, 483-581. 2000
Another type of fuzzy intervals is considered hy Fullér (l990): Lipschitzian fuzzy intervals M
such that there is positive constant k such that |M (a) − M (a0 )| ≤ k|a − a0 |. He proves that
the class of Lipschitzian fuzzy intervals is closed under fuzzy addition and scalar multiplication.
(page 507)
A34-c4 V.A.Rybkin and A.V.Yazenin, Regularization and stability of possibilistic linear programming problems, in: Proceedings of the Sixth European Congress on Intelligent Techniques and Soft Computing (EUFIT’98), Aachen, September 7-10, 1998, Verlag Mainz, Aachen, Vol. I, 1998 37-41. 1998
in books
A34-c3 R. Lowen, Fuzzy Set Theory, Kluwer Academic Publishers, [ISBN: 0-7923-4057-4], 1996.
A34-c2 Y.J.Lai and C.L.Hwang, Fuzzy Multiple Objective Decision Making, Lecture Notes in Economics and
Mathematical Systems, No. 404, Springer Verlag, [ISBN: 978-3-540-57595-5], Berlin 1994.
A34-c1 Y.J.Lai and C.L.Hwang, Fuzzy Mathematical Programming, Methods and Applications, Lecture Notes
in Economics and Mathematical Systems, No. 394, Springer Verlag, [ISBN 3-540-56098-X], Berlin 1992.
[A35] Robert Fullér, On stability in fuzzy linear programming problems, FUZZY SETS AND SYSTEMS, 30(1989)
339-344. [MR 90c:90143] [Zbl.704.90101]. doi 10.1016/0165-0114(89)90026-2
in journals
2016
A35-c41 M Ghaznavi, F Soleimani, N Hoseinpoor, Parametric Analysis in Fuzzy Number Linear Programming
Problems, INTERNATIONAL JOURNAL OF FUZZY SYSTEMS (to appear). 2016
http://dx.doi.org/10.1007/s40815-015-0123-3
2014
A35-c41 D A Molodtsov, D V Kovkov, Stability and Approximation of Maximin Problems, AUTOMATION
AND REMOTE CONTROL, 75: (3) pp. 447-457. (2014)
http://dx.doi.org/10.1134/S0005117914030035
A35-c40 B. Farhadinia, Sensitivity Analysis in Interval-Valued Trapezoidal Fuzzy Number Linear Programming
Problems, APPLIED MATHEMATICAL MODELLING, 38(2014), pp. 50-62. 2014
http://dx.doi.org/10.1016/j.apm.2013.05.033
Nowadays, sensitivity analysis is one of the interesting researches in fuzzy linear programming.
The first attempt to study sensitivity analysis for fuzzy linear programming problems is due to
Hamacher et al. [9] and later followed by others [A35, 8, 14]. (page 52)
2013
303
A35-c39 H A Hashem, Sensitivity Analysis for Fuzzy Linear Programming with its Applications in the Transportation Problem, Middle East Journal of Applied Sciences, 3(2013), number 4, pp. 150-155. 2013
http://curresweb.com/pages/mejas/2013/150-155.pdf
Fuller (1989) proposed that the solution of FLP problems with symmetrical triangular fuzzy numbers is stable with respect to small changes in centers of fuzzy numbers. (page 150)
A35-c38 Behrouz Kheirfam, José-Luis Verdegay, The dual simplex method and sensitivity analysis for fuzzy
linear programming with symmetric trapezoidal numbers, FUZZY OPTIMIZATION AND DECISION
MAKING, 12(2013), number 2, pp. 171-189. 2013
http://dx.doi.org/10.1007/s10700-012-9152-7
Sensitivity analysis is a basic tool for studying perturbations in optimization problems, and is considered to be one of the most interesting research areas in the field of FLP problems. Sensitivity
analysis in FLP was first considered by Hamacher et al. (1978), who derived a functional relationship between changes of parameter on the right-hand-side and those of the optimal value of
the primal objective function, for almost all conceivable cases. Fuller (1989) showed that the solution to FLP problems with symmetrical triangular fuzzy numbers is stable with respect to small
changes to the centers of fuzzy numbers. Perturbations occur due to calculation errors or simply when answering ”What if é?” management questions. In this paper, we first extend the dual
simplex method to a type of fuzzy linear programming problem involving symmetric trapezoidal
fuzzy numbers, without converting them to crisp linear programming problems.We then study
sensitivity analysis for these problems and derive bounds for the values of the parameters when
the data are perturbed, while the fuzzy optimal solution remains invariant. (page 172)
2012
A35-c37 Saati Saber, Adel Hatami-Marbini, Madjid Tavana, Elham Hajiahkondi, A Two-Fold Linear Programming Model with Fuzzy Data, INTERNATIONAL JOURNAL OF FUZZY SYSTEMS APPLICATIONS,
2(2012), number 3, pp. 1-12. 2012
http://dx.doi.org/10.4018/ijfsa.2012070101
A35-c36 Amit Kumar, Neha Bhtia, Strict Sensitivity Analysis for Fuzzy Linear Programming Problem, Journal
of Fuzzy Set Valued Analysis, 2012(2012), Article ID jfsva-00107. 2012
http://dx.doi.org/10.5899/2012/jfsva-00107
A35-c35 Neha Bhatia, Amit Kuma, Mehar’s method for solving fuzzy sensitivity analysis problems with LR flat
fuzzy numbers, APPLIED MATHEMATICAL MODELLING, 36(2012), number 9, pp. 4087-4095. 2012
http://dx.doi.org/10.1016/j.apm.2011.11.038
2011
A35-c34 Amit Kumar, Neha Bhatia, A new Method for Solving Sensitivity Analysis for Fuzzy Linear Programming Problems, INTERNATIONAL JOURNAL OF APPLIED SCIENCE AND ENGINEERING, 9(2011),
number 3, pp. 169-176. 2011
http://www.cyut.edu.tw/˜ijase/2011/9(3)/3_021007.pdf
A35-c33 Amit Kumar, Neha Bhatia, A New Method for Solving Fuzzy Sensitivity Analysis Problems, INTERNATIONAL JOURNAL OF APPLIED SCIENCE AND ENGINEERING, 9(2011), number 2, pp. 49-64.
2011
http://www.cyut.edu.tw/˜ijase/2011/9(2)/1_020010.pdf
Fuller [A35] proposed that the solution to FLP problems with symmetrical triangular fuzzy numbers is stable with respect to small changes of centers of fuzzy numbers. (page 50)
A35-c32 A. Ebrahimnejad, Sensitivity analysis in fuzzy number linear programming problems, MATHEMATICAL AND COMPUTER MODELLING, 53(2011), number 9-10, pp. 1878-1888. 2011
http://dx.doi.org/10.1016/j.mcm.2011.01.013
304
Fullér [A35] investigated the stability of the solution of FLP problems with respect to changes
of centers of fuzzy parameters. He showed that the solution to these problems is stable under
variations in the membership function of the fuzzy coefficients. In this paper, we generalize the
concept of sensitivity analysis on the parameters of the crisp linear programming [27] to the fuzzy
number linear programming and show that the fuzzy primal simplex algorithm stated in [11] and
the fuzzy dual simplex algorithm presented in [19] would be useful for post optimality analysis on
linear programming problems with fuzzy numbers. (page 1879)
2010
A35-c31 Takashi Hasuike, Hideki Katagiri, Sensitivity Analysis for Random Fuzzy Portfolio Selection Model
with Investor’s Subjectivity, IAENG INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS 40(2010),
issue 3. 2010
http://www.iaeng.org/IJAM/issues_v40/issue_3/IJAM_40_3_09.pdf
Furthermore, we consider the sensitivity analysis in order to deal with investor’s subjectivity.
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