R model for case-based reasoning

Knowledge-Based Systems 16 (2003) 59–65
www.elsevier.com/locate/knosys
R 5 model for case-based reasoning
Gavin Finnie, Zhaohao Sun*
School of Information Technology, Bond University, Gold Coast 4229, Australia
Received 13 June 2001; revised 4 April 2002; accepted 8 April 2002
Abstract
This paper reviews some existing models of case-based reasoning (CBR) such as the R 4 model of CBR and proposes a R 5 model, in which
repartition, retrieve, reuse, revise and retain are the main tasks for the CBR process. The original idea behind this model is that case base
building is an important part of CBR and the case base can be built based on partitioning of the possible world of problems and solutions. It
argues that the proposed R 5 model is a new approach to using similarity-based reasoning to unify case base building, case retrieval, and case
adaptation, and therefore facilitates the development of CBR with applications. q 2003 Elsevier Science B.V. All rights reserved.
Keywords: Case-based reasoning; Similarity; Partition; Case base building
1. Introduction
Case-based reasoning (CBR) systems are a particular
type of analogical reasoning system which have a diversity
of applications in many fields, such as in intelligent Webbased sales service and Web-based planning as well as in
multiagent systems [4,9,12,16,17]. The goal of CBR is to
infer a solution for a current problem description in a special
domain from solutions of a family of previously solved
problems, the case base1 or case memory [3,4]. The core
idea of CBR is that ‘similar problems have similar
solutions.’ There have been many models for CBR that
attempt to provide better understanding of CBR. For
example, Kolodner and Leake consider CBR as a process
of ‘remember and adapt’ and propose a CBR cycle in Ref.
[8]. Aamodt and Plaza [1] also introduce a process model of
the CBR cycle, often referred to as the R 4 model, which
constitutes the following four processes: retrieve, reuse,
revise, and retain. However, they all assume that the case
base is ready for the first process, case retrieval, although
they discuss the representation of cases and believe that a
case-based reasoner is heavily dependent on the structure
and content of its collection of cases. In fact, it seems that
* Corresponding author. Tel.: þ 61-7-55953369; fax: þ 61-7-55953320.
E-mail addresses: [email protected] (Z. Sun), [email protected]
(G. Finnie).
1
We like to use case base instead of case memory even in the structured
case.
everyone believes that the representation of cases is
important for CBR, but there are no unified ways to
integrate it into the models of CBR. Furthermore, it seems
that almost all existing models are application-oriented, and
it is difficult to extend these models to a theoretical CBR. It
is obvious that CBR cannot develop robustly further without
a firm theoretical foundation.
In order to resolve these drawbacks, this paper reviews
four existing models of CBR and proposes a R 5 model, in
which repartition, retrieve, reuse, revise and retain are the
main tasks for the CBR process. The original idea behind
this model is that case base building is an important task in
CBR and the case base can be built based on partitioning of
the possible world of problems and solutions. The
partitioning depends on certain similarity relations. Therefore the case base building is a form of similarity-based
reasoning and can be improved using repartitioning of the
possible world of problems and solutions. This paper also
argues that the proposed R 5 model is more reasonable for a
theoretical foundation of CBR than the existing models,
because it provides a clear perspective that case base
building, case retrieval, and case adaptation can be unified
into a form of similarity-based reasoning.
The paper is structured as follows: Section 2 reviews a
few existing models for CBR, Section 3 examines case base
building based on partitioning, Section 4 proposes the R 5
model for CBR and Section 5 ends the paper with
concluding remarks.
0950-7051/03/$ - see front matter q 2003 Elsevier Science B.V. All rights reserved.
PII: S 0 9 5 0 - 7 0 5 1 ( 0 2 ) 0 0 0 5 3 - 9
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G. Finnie, Z. Sun / Knowledge-Based Systems 16 (2003) 59–65
Fig. 1. Hunt’s model of CBR.
2. Models of CBR
There have been many models of CBR that attempt to
provide better understanding of CBR. In what follows, we
review four models proposed by Hunt [7], Allen [2],
Kolodner and Leake [8] and Aamodt and Plaza [1], which
are all process-oriented.
2.1. Hunt’s model of CBR
Hunt [7] proposed a basic structure for the CBR process
after reviewing many CBR systems, shown in Fig. 1. Once a
case base has been obtained, the first step performed by a
CBR system is to analyse the inputs to the system in order to
determine the important features to use in selecting past
cases in the case base. These features are then passed to the
retrieval step along with the initial inputs. The retrieval step
then uses the information provided to it to obtain a list of
past cases which match the current situation.
Once the best match has been retrieved, it is often the case
that it must be altered to match the current problem, which is
adaptation. Once the case has been adapted, it must be
evaluated to determine whether it does provide a solution to the
current problem. If the case is accepted by the evaluation step,
then it is presented as the solution to the problem and stored in
the case base for future use. If some aspect of the current
problem is not solved by the case, then the case must be repaired
such that all aspects of the problem are addressed. This is done
by first identifying why the case failed to solve the problem and
then using this information to guide the repair process.
2.2. Allen’s model of CBR
Allen believed [2] that CBR can be considered as a fivestep problem solving process.
† Presentation: A description of the current problem is
input to the system.
† Retrieval: The system retrieves the closest-matching
cases stored in a case base.
† Adaptation: The system uses the current problem and
closest-matching cases to generate a solution to the
current problem. It should be noted that the differences in
adaptation power depend on how well the domain is
understood [14].
Fig. 2. The CBR cycle proposed in Ref. [8].
† Validation: The solution is validated through feedback
from the user or the environment.
† Update: If appropriate, the validated solution is added to
the case for use in future problem solving.
2.3. Kolodner and Leake’s model of CBR process
Kolodner and Leake consider CBR as a process of
‘remember and adapt’ or ‘remember and compare’ and
propose a model for the CBR cycle [8], illustrated in Fig. 2.
First and foremost, partially matched cases must be
retrieved to facilitate reasoning. Thus, case retrieval is a
primary process. The retrieval process depends on choosing
appropriate indexes to guide search for relevant cases in the
case base. In order to make sure that poor solutions are not
repeated along with the good ones, a reasoner must criticize
candidate solutions to identify potential problems. In order
to become more proficient, the reasoner must be able to
evaluate its performance, based on external feedback. In
CBR, after feedback is analyzed, cases are updated and their
outcomes recorded, and cases that were used to solve the
problem are reindexed based on analysis of their usefulness.
The tasks of CBR are often divided into two classes:
interpretation and problem solving [8]. Interpretive CBR
uses prior cases as reference points for classifying or
characterizing new situations and forms a judgement about
or classification of a new situation; problem solving CBR
uses prior cases to suggest solutions that might apply to new
circumstances. Therefore, each of the two classes of CBR
requires that different reasoning be followed once cases are
retrieved. The interpretive CBR requires justification
(which is not considered further here), while the problem
solving CBR performs adaptation. Adaptation is a process
of revising an old solution to fit a new situation. Criticism of
the candidate solution often triggers further adaptation
before the solution is applied.
These steps are in some sense recursive. The criticize and
adapt steps, for example, often require new cases to be
retrieved. There are also several loops in the process, as
reflected in Fig. 2. For example, evaluation of a potential
solution may lead to additional adaptation to repair
problems, and when reasoning is not progressing well
using one case, the whole process may need to be restarted,
beginning by choosing a new case to start from.
G. Finnie, Z. Sun / Knowledge-Based Systems 16 (2003) 59–65
61
future reuse, and the case base is updated by a new learned
case, or by modification of some existing cases.
As indicated in the figure, general knowledge usually
plays a part in this cycle, by supporting the CBR processes
[1]. This support may range from very weak (or none) to
very strong, depending on the type of CBR method. By
general knowledge, we here mean general domain-dependent knowledge, as opposed to specific knowledge embodied
by cases. For example, in diagnosing a patient by retrieving
and reusing the case of a previous patient, a model of
anatomy together with causal relationships between pathological states may constitute the general knowledge used by
a CBR system.
2.5. Further remarks on the existing models of CBR
Fig. 3. The CBR cycle described in Ref. [1].
2.4. R 4 model of CBR
At the highest level of generality, Aamodt and Plaza [1]
introduced a process model of the CBR cycle. This model is
commonly called the R 4 model of CBR [5,9,11,15], because
the process involved this model can be represented by a
schematic cycle comprising the four Rs, shown in Fig. 3.
1.
2.
3.
4.
Retrieve the most similar cases
Reuse the cases to attempt to solve the problem
Revise the proposed solution
Retain the new solution as a part of a new case.
A new problem is solved by retrieving one or more
previously experienced cases in the case base, reusing the
case in one way or another, revising the solution based on
reusing a previous case, and retaining the new experience
by incorporating it into the existing case base [1]. The four
processes each involve a number of more specific steps, for
example, retrieve involves identify, search, initially match
and select [1].
An initial description of a problem (top of figure) defines
a new case [1,4,5]. This new case is used to RETRIEVE a
case from the collection of previous cases. The retrieved
case is combined with the new case—through REUSE—
into a solved case, i.e. a proposed solution to the initial
problem. Through the REVISE process this solution is
tested for success, e.g. by being applied to the real world
environment or evaluated by a teacher, and repaired if
failed. During RETAIN, useful experience is retained for
So far we have briefly introduced four models of CBR. In
our view, these models basically share the common idea that
the CBR process consists of case retrieval, case adaptation,
case evaluation and case update. In comparison to other
mentioned models, the R 4 model provides a better understanding of CBR, because it not only covers the essential
process description of the CBR cycle, but also provides a
nested task decomposition (subprocess description) and
related problem solving method descriptions.
However, one of the flaws in these models is that the
terms of case, problem, and solution have not been
separated, thus these do not satisfy the basic concept that
the case ¼ problem þ solution [4,9]. Another disadvantage
of these models is that they assume that the case and case
base are also ready for their first process, case retrieval, and
ignore the fact that case base building is also a major CBR
task. In this task, repartitioning is the basic method from a
viewpoint of similarity relations, although Aamodt and
Plaza as well as others discussed representation of cases,
and they admitted that a case-based reasoner is heavily
dependent on the structure and content of its collection of
cases, which is often referred to as the case memory. In fact,
it seems that everyone believes that case representation is
important for CBR, but there are no unified ways to
integrate it into the models of CBR. Furthermore, it seems
that all these models are application-oriented and it is
difficult to extend these models to a theoretical CBR. If we
believe that CBR cannot develop healthily further without a
firm theoretical foundation, we will attempt to lessen these
flaws in these models by providing a new model for CBR in
the following sections.
3. Case base building based on partitioning
In this section, we examine case base building with
partitioning, which depends on certain similarity relations.
Therefore, case base building is a form of similarity-based
reasoning.
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G. Finnie, Z. Sun / Knowledge-Based Systems 16 (2003) 59–65
representative element2 of [ p ]. The set of all similarity
classes of Wp is denoted by [Wp].
3.1. Possible world of problems and solutions
As is known, an intelligent system can only serve to solve
certain types of problems in a special domain [6,19]. Any
CBR system can thus only give the solutions to problems in
a possible world, which corresponds to a scenario in the real
world. Based on this idea, the possible world of problems,
Wp, and the possible world of solutions, Ws, are the whole
world of an agent [10] to use CBR to do everything that he
can. If an agent considers a CBR system as a function h from
Wp to Ws, it is meaningless to discuss the image of hðxÞ if
x Wp : Therefore, the agent can only know and play in the
possible world Wp £ Ws : For example, in a CBR e-sale
system, the possible world of problems Wp might consist of
As is known, there is a one-to-one correspondence
between a similarity relation on Wp and a partition of Wp
[13], namely: If S is a similarity relation on Wp, then ½Pw ¼
{½plp [ Wp } is a partition of Wp, denoted by Wp/S.
Conversely, if {Ai} is a partition of Wp, then the sets Ai
are the similarity classes corresponding to some similarity
relation on Wp. In other words, any partition of Wp depends
on a certain similarity relation on Wp. Thus, in terms of
reasoning, we can view partitioning of a set as similaritybased reasoning.
†
†
†
†
Example 1. Let f be a function with domain Wp and
codomain Ws, namely, f : Wp ! Ws ; and define pSq if
f ðpÞ ¼ f ðqÞ; where ¼ means identity between two
elements in Ws. Then S is a similarity relation on Wp and
the similarity classes are the non-empty sets f 21 ðsÞ; where
s [ W s.
properties of goods,
normalized queries of customers,
knowledge of customer behavior,
general knowledge of business (similar to K in Ref. [11]),
etc.
And the possible world of solutions Ws consists of
† price of goods,
† customized answers to the queries of customers,
† general strategies for attracting customers to buy the
goods, etc.
3.2. Similarity relations on the possible world
The concept of a similarity relation is essentially a
natural generalization of the concept of similarity between
two triangles and between matrices in mathematics [6,19].
More specifically
Definition 1. A relation S on Wp is called a similarity
relation provided it satisfies:
(R) ;p, pSp
(S) if pSq then qSp
(T) if pSq, qSr then pSr
The conditions (R), (S), and (T) are the reflexive,
symmetric and transitive laws. If pSq we say that p and q are
similar [13].
It is obvious that the concept of similarity relations is
identical to that of equivalence relations in discrete
mathematics [13]. However, we prefer to use similarity
relations rather than equivalence relations in the context of
CBR, because similarity plays an important role in CBR [6].
Definition 2. Let S be a similarity relation on Wp. For each
p [ Wp we define
½p ¼ {qlpSq; q [ Wp }
It is obvious that for any similarity class [ p ] with respect
to S, if p1, p2 [ [ p ] then p1 and p2 have the same solution,
that is, f ðp1 Þ ¼ f ðp2 Þ: This reflects that ‘similar problems
have the same solution’, at least in some cases. For example,
in a shoe shop, the seller may put many different pairs of
shoes together and sell for the same price, i.e. $68.00. In this
case, the seller views those mentioned shoes as ‘similar’.
Furthermore, as a relation, equality is a special similarity
relation. The above result also reflects that ‘similar
problems have a similar solution’.
3.3. Case base building
In this section, we investigate cases and case bases based
on similarity relations on the possible world of problems Wp
and similarity relations on the possible world of solutions
Ws, which differs from other studies, in which similarity
relations are mainly used to treat case retrieval [4,11].
In many studies [4,9,19], cases are denoted as n þ mtuples of completely, incompletely or fuzzily described
attribute values, this set of attributes being divided in two
non-empty disjoint subsets, the subset of problem description attributes (n-tuples) and the subset of solution or
outcome attributes (m-tuples), denoted by P and Q,
respectively. A case, c, can be denoted as an ordered pair
( p, s ), where p [ P and s [ Q. The case base C is the set of
known cases [4]. Unfortunately, such studies neglect the
relationship between C and Wp. We can imagine that the
seller agent in the selling process always classifies the
products and customers using his special ‘similarity
relation’ before he performs ‘a similar query of customers
has a similar answer’. This suggests that we should examine
ð1Þ
[ p ] is called a similarity class containing p and p a
2
In practice, one element from a similarity class is chosen as the
representative element.
G. Finnie, Z. Sun / Knowledge-Based Systems 16 (2003) 59–65
Fig. 4. From Wp and Ws to case base C.
the relationship between C and Wp. The classification
performed by the seller agent can be considered as a
partition of the possible world of problems Wp, which can be
realized based on the similarity relation. That is, let a
relation S on Wp be a similarity relation. Then ½Pw ¼
{½pjp [ Wp } is a partition of Wp with respect to S.
Furthermore, for any two problems p1, p2 [ [ p ], p1 is
similar to p2 with respect to similarity relation S on Wp, and
they can have similar, or in particular, the same solution in
the possible world of solutions Ws. In such a way, it is
sufficient to choose the representative element p [ [ p ] and
find its corresponding solution s [ Ws to constitute a case
c ¼ ðp; sÞ and store it in the case base C. Therefore, we
conclude that
† a case c in the case base of a CBR system consists of a
representative element p of a similarity class [ p ] in terms
of similarity relation S on Wp and its corresponding
solution s in the possible world of solutions Ws, denoted
as c ¼ ðp; sÞ:
† the case base is made up of the representative elements pi
of all disjoint similarity classes in the partition of Wp in
terms of S and their own corresponding solution3 si in the
possible world of solutions Ws, i.e.
n
C ¼ ðpi ; si Þl
n
[
½pi z ¼ Wp ; ½pi > ½pj ¼ B;
1
if i – j; i; j [ {1; …; n}
o
ð2Þ
where si [ Ws is a solution of pi. We define P ¼
{pi lðpi ; si Þ [ C}; Q ¼ {si lðpi ; si Þ [ C} and call them the
set of precedent problem descriptions and the set of solution
descriptions and C a case base with respect to the partition
½Pw ¼ {½plp [ Wp }:
This result is also based on the following idea. We
partition the similar problems into a class, then select a
representative problem from this class and solve it. If we
have the solution to the representative problem, then we can
use this solution to solve all other problems in that similarity
class including the mentioned representative problem. It
also argued that it is reasonable to define the similarity
3
If there are more than one solutions, we select one of them as si.
63
relation on Wp rather than on P, which is a part of the case
base.
It is worth noting that there is, in practice, a similarity
relation, T, on Ws, too, which is motivated by [4,19]. Thus a
representative of a similarity class in Wp, e.g. pi is mapped to
an adequate representative of a similarity class in Ws, e.g. si.
For case retrieval, given a problem or an enquiry p0 [ Wp,
we firstly decide if p0 belongs to a similarity class [ pi] and
then look up an appropriate solution si in [si]. For case base
building, we generalize from the concrete class of problems
(i.e. find the representative of a similarity class), then look
for all possible solutions in the possible world of solutions
and then generalize from the similarity class of solutions,
i.e. find a representative. From here we claim that the
similarity relation S on the possible world of problems Wp
has to be defined in advance. The similarity relation T on the
possible world of solutions Ws is decided by the similarity
classes in the possible world of problems Wp: From each
similarity class [ pi] we choose a representative pi. For each
pi we then find a set of possible solutions (similar solutions)
in the possible world of solutions, {sij lj [ J}: If these sets
are disjoint they give a partition of Ws, i.e. {sij lj [ J} ¼ ½si ;
which corresponds to a similarity relation, called T, on Ws.
Finally we choose a representative si from [si]. The pairs ( pi,
si) constitute the case base. Therefore, the above discussion
can be demonstrated in Fig. 4.
So far, we have investigated the relationship between
similarity relations in the possible world of problems on one
side and similarity relations in the possible world of solutions
on the other side. We have also discussed that case base
building can be a process of partitioning of Wp and Ws. In
Section 3.4 we will investigate the relation between the
refinement of the partition of Wp and building of the case base.
3.4. Refining case bases
It is obvious that many similarity relations can be defined
on Wp. Different similarity relations on Wp lead to different
partitions of Wp and then form different case bases. Now a
new problem arises, which one among these different
similarity relations or case bases is better? This is still
neglected in CBR, because there are no studies on the
comparison of similarity relations. We can discuss it here in
some detail.
Definition 3. Let {Ai} and {Bj} be two partitions of Wp.
Partition {Ai} is called finer than {Bj}, if for every Ak [
{Ai } there exists a set Bj such that Ak # Bj : is called coarser
than partition {Ai}, if {Ai} is finer than {Bj}.
According to this definition, it is obvious that the coarsest
partition of Wp is ½Wp ¼ {Wp }: In this case, P ¼ {p0 }; where
p0 is any given element in Wp. The case base will thus have
only one case. This is not a real case base in any existing CBR
system. Further, the finest partition of Wp is ½Wp ¼ {½pl½p ¼
{p}; p [ Wp }; this means that every single element in Wp
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G. Finnie, Z. Sun / Knowledge-Based Systems 16 (2003) 59–65
Fig. 5. Hasse diagram for finer relation in Definition 3, the lower the finer.
forms a similarity class. In this case, P ¼ Wp. Therefore, the
case base is the largest and provides a corresponding solution
to every problem in the possible world Wp. This is also not
feasible in any existing CBR system, because it would require
full understanding of all problems. Usually, any similarity
relation based partition involved in CBR research and
development lies between these two extreme cases. We can
examine if a partition of Wp is finer than another one based on
Definition 3. In practice, it is worth refining the partition of Wp
if the built case base is not satisfactory based on the experience
of case retrieval or if the current case base is to be updated. If
so, we propose two loop processes, an inner loop and an outer
loop, to perform the refinement of the partition [19]. In the
inner loop, we change the partition such that the result is
neither finer nor coarser than the original one, because it is
easily shown that “finer” as a binary relation is a partial order.
We will repeat this for a given number of iterations (if P and Q
are not satisfactory).4 When we have reached the maximum
number of loops, if P and Q are still not satisfactory then we
enter the outer loop where the partition is refined once. For
brevity, we call the inner loop microadjustment and the outer
loop refinement. For example, let A ¼ {a1 ; a2 ; a3 ; a4 ; a5 ; a6 };
and S0, S1, S2, S3, S4, S5, S6 be similarity relations on A, and
their corresponding partitions of A are:
†
†
†
†
†
†
†
A=S0
A=S1
A=S2
A=S3
A=S4
A=S5
A=S6
¼ {a1 ; a2 ; a3 ; a4 ; a5 ; a6 };
¼ {{a1 ; a2 ; a3 }; {a4 ; a5 ; a6 }}
¼ {{a1 ; a2 }; {a3 ; a4 }; {a5 ; a6 }}
¼ {{a1 }; {a2 ; a3 }; {a4 ; a5 }; {a6 }}
¼ {{a1 }; {a2 }; {a3 ; a4 }; {a5 }; {a6 }}
¼ {{a1 ; a2 }; {a3 }; {a4 }; {a5 ; a6 }}
¼ {{a1 }; {a2 }; {a3 }; {a4 }; {a5 }; {a6 }}
The partial order “finer” between the partitions is
illustrated by the Hasse diagram in Fig. 5. It is easy to see
that A/S0 is the coarsest partition of A, A/S6 is the finest
partition of A. However, there are neither finer or coarser
relationships between A/S1 and A/S2, nor among A/S3, A/S4
or A/S5. If we believe that in the inner iteration A/S1 (i.e. its
corresponding P ) is not satisfactory, then we can choose A/S2
as an alternative, carrying out the inner loop. If A/S2 is
4
Which is based on the statistics of case retrieval.
Fig. 6. The R 5 model of CBR.
still not satisfactory, then we can refine A/S1 or A/S2 and
obtain either A/S3, A/S4 or A/S5, carrying out the outer loop,
etc. The concrete order of microadjustment and refinement
is application dependent and has to be chosen in advance
[19].
There is still a question, namely, how do we deal with
adding a new case c~ ¼ ð~p; s~Þ to the existing case base? This
question is of practical significance, because it is a frequent
action for any running CBR system to add a new case to its
case base. In our view, it is involved in case retrieval,
because we perform case retrieval to know if the problem
description p~ belongs to a certain similarity class [ pi]. If
p~ [ ½pi then there are two possibilities: (1) s~ [ ½si —we do
not need to put ð~p; s~ Þ in the case base; (2) s~ ½si for any i—
we have to repartition Ws. If p~ ½pi for any i, we should
repartition Wp or choose a new similarity relation on Wp so
that the p~ belongs to a certain similarity class in terms of the
new partition of Wp. Then we can add p~ as the representative
of the mentioned similarity class and its corresponding
solution s~ ; as a new case, into the case base.
Based on previous discussion, we conclude that the
transition from the possible world of problems Wp and the
possible world of solutions Ws to the case base C is also a
refinement process of partition and repartition.
4. R 5 model for CBR
From an engineering viewpoint, a knowledge-based
system such as a rule-based expert system can be regarded
as a process of the following sequential phases: knowledge
acquisition, knowledge representation, knowledge reasoning,
knowledge interpretation and knowledge utilization [18]. In
comparison with this, it seems that there is not a stage in the
CBR models mentioned in Section 2 that corresponds to
knowledge acquisition. This means that there has not been
G. Finnie, Z. Sun / Knowledge-Based Systems 16 (2003) 59–65
much discussion about case acquisition, although case
representation has been much discussed in CBR.
As mentioned in Sections 2.4 and 2.5, the R 4 model of
Aamodt and Plaza [1] is a widely used process model of
CBR, which mainly comprises retrieve, reuse, revise and
retain. In this model, retrieval is the first step in the process
of CBR, which means that the case acquisition and the case
base is already ready for performing CBR. However, this is
not the case in many applications.
Therefore, it is of significance to extend the R 4 model to
the R 5 model, shown in Fig. 6. In this proposed R 5 model,
repartition, retrieve, reuse, revise and retain are the main
process steps in the CBR. While the other process steps are
the same as those in the R 4 model mentioned in Section 2 or
in Ref. [1], repartition here is used to form a satisfactory
case base C ¼ (P, Q ) based on partitioning on Wp, as
discussed in Section 3. Furthermore, repartition provides the
theoretical foundation for case retrieval, because of the oneto-one correspondence between the partition of Wp and the
similarity relations on Wp. Thus, case base building and case
retrieval can be treated as a similarity-based reasoning in a
unified way [19]. Therefore, the proposed model can
facilitate the use of similarity-based reasoning to unify
case base building, case retrieval, and case adaptation.
5. Concluding remarks
In this paper, we reviewed four existing models of CBR
and proposed a R 5 model; that is, repartition, retrieve, reuse,
revise and retain. The central idea behind this model is that
case base building is an important task of CBR and the case
base can be built based on partitioning of the possible world
of problems and solutions. Because a partition corresponds
to a certain similarity relation, case base building is a form
of similarity-based reasoning. The core idea different from
other studies is that similarity relations are not only used to
case retrieval but also used to create the case base, although
it might be used in different stages in a different way. It is
obvious that almost all theoretical studies and practical
work start with case retrieval. Therefore, what we have done
provides a new attempt towards using similarity-based
reasoning to unify case base building, case retrieval, and
case adaptation, and thus facilitate the development of CBR
theory with applications. Furthermore, because fuzzy
similarity relations are an extension of similarity relations,
the above proposed model can be extended in a fuzzy
environment, which we will do in the future work.
Acknowledgments
This work was supported by an Australian Research
Council Small Grant and OPRS of the Australian government. The authors thank the anonymous reviewers for their
useful comments. The special thanks of the authors go to
Klaus Weber, for his valuable comments and revision.
65
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