Elsevier

Applied Soft Computing

Volume 13, Issue 4, April 2013, Pages 2057-2064
Applied Soft Computing

Fuzzy rule-based similarity model enables learning from small case bases

https://doi.org/10.1016/j.asoc.2012.11.009Get rights and content

Abstract

The concept of similarity plays a fundamental role in case-based reasoning. However, the meaning of “similarity” can vary in situations and is largely domain dependent. This paper proposes a novel similarity model consisting of linguistic fuzzy rules as the knowledge container. We believe that fuzzy rules representation offers a more flexible means to express the knowledge and criteria for similarity assessment than traditional similarity metrics. The learning of fuzzy similarity rules is performed by exploiting the case base, which is utilized as a valuable resource with hidden knowledge for similarity learning. A sample of similarity is created from a pair of known cases in which the vicinity of case solutions reveals the similarity of case problems. We do pair-wise comparisons of cases in the case base to derive adequate training examples for learning fuzzy similarity rules. The empirical studies have demonstrated that the proposed approach is capable of discovering fuzzy similarity knowledge from a rather low number of cases, giving rise to the competence of CBR systems to work on a small case library.

Highlights

► A fuzzy similarity model is proposed for case-based reasoning. ► Similarity degrees between cases are evaluated via fuzzy rule based reasoning. ► Fuzzy similarity rules can be learned from rather small case bases. ► The proposed method presents a new paradigm for relation-oriented learning.

Introduction

Case-based reasoning (CBR) presents an important cognitive methodology in Artificial Intelligence, which advocates the use of previous experiences to solve new problems [1]. A fundamental principle that underlies CBR is the hypothesis that similar problems have similar solutions. Hence a CBR system first retrieves cases in the case base that are similar to a query problem and then refines the solutions of the retrieved cases to tackle the new situation at hand.

Similarity assessment plays a key role in CBR in that it decides the quality of retrieved cases. A competent similarity model has to reflect the real utility/relevance of cases for solving new problems [2]. So far a wealth of similarity measures has been established for successful applications of CBR in various real-world scenarios. Cunningham [3] proposed a coherent taxonomy which organized the broad range of similarity mechanisms into the four categories (direct, information-based, transformation-based and emergent measures). The work of this paper belongs to the first category and aims to develop direct similarity models for cases with feature-value representation.

Our objective is to build the similarity model as a knowledge container to guide the CBR process [4]. Fuzzy if–then rules are adopted in this paper as the form of knowledge representation due to the following two reasons. First, fuzzy rules provide a flexible means to express the knowledge and criteria for similarity assessment. Second, fuzzy rule based systems are proved universal approximators [5], able to produce accurate reasoning results for similarity evaluation. The learning of fuzzy similarity rules is implemented by exploiting the case base. We consider the case base a valuable resource with hidden knowledge for similarity learning. A sample of similarity is created from a pair of known cases in which the vicinity of case solutions reflects the similarity of case problems. We do pair-wise comparisons of cases in the case base to derive adequate training examples for learning fuzzy similarity rules. The empirical studies have demonstrated that the proposed approach is capable of discovering fuzzy similarity knowledge from a very limited number of cases, giving rise to the competence of CBR systems to work on a small case library.

The paper is organized as follows. Section 2 discusses related works. Section 3 outlines a general CBR paradigm used in the paper. The fuzzy similarity model for case matching is addressed in Section 4. Then, in Section 5, we discuss the issue of how to learn these fuzzy similarity rules from the case base. In Section 6, we present experimental results for evaluation of the proposed method. Finally, concluding remarks are given in Section 7.

Section snippets

Related works

The issue of similarity has received much research attention from the CBR community. Plaza et al. [6] discussed the ways to exploit similarity information for explaining CBR results in classification tasks. They indicated that suitable explanation can be derived from building symbolic descriptions of similar aspects among cases. They also illustrated that symbolic descriptions of similarity can be utilized to support various steps (including retrieve, reuse, revise and retain) within a CBR

Case-based reasoning: a general paradigm

The general idea of the case-based approach is exploitation of information in the previous cases to solve a new problem. A general CBR paradigm used in this paper is shown in Fig. 1. It starts with similarity matching between a query problem and known cases in the case library. A properly defined similarity function has to be employed in this stage. As the evaluated similarity values reflect the utility or appropriateness of solutions of the known cases, they offer important information to be

Fuzzy rules based similarity model

This section explains how similarity matching between cases can be implemented by fuzzy rules based reasoning. We will start with discussing the benefits of fuzzy rules as similarity model in Section 4.1. Then we explain the general rule structure and fuzzy reasoning procedure employed for similarity assessment in Section 4.2.

Learning fuzzy rules from case bases

Supervised learning is performed in this paper to generate fuzzy rules for the similarity model. We need a “teacher” to specify samples of desired similarity values for various pairs of cases as training examples. The task of learning is to revise fuzzy similarity rules to reduce the discrepancy between the desired similarity scores as given by the “teacher” and the estimated similarity values produced by the (similarity) model. The general learning paradigm is shown in Fig. 3 in which a

Experimental evaluations

To evaluate the capability of the proposed method, we show in this section the experimental results on six well-known data sets from the UCI Machine Learning Repository [27]. All these data sets contain cases characterized by numerical features and discrete classes, with the numbers of features ranging from 4 to 13 and the numbers of classes between 2 and 6, as illustrated in Table 1. We used the classification accuracy based on small case bases as the criterion to evaluate the learning ability

Conclusion

This paper puts forward a new method of employing fuzzy rules as the representation of similarity models in CBR research. Fuzzy rules are considered a more powerful vehicle to accommodate rich domain knowledge than conventional similarity metrics. Fuzzy rule-based reasoning is conducted to estimate the degrees of similarity between cases in the case library and a new problem. Further we explain that fuzzy similarity rules can be generated by exploiting the information from a rather small case

Acknowledgement

The author would like to sincerely thank the anonymous referees for their valuable comments and suggestions for improvement of the paper.

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