Abstract
This paper proposes to study the concept of similarity and its use in the design of fuzzy system. The concept of similarity relation is effectively used in fuzzification of crisp values. Similarity index is used in measuring approximate (graded) equality of fuzzy sets over a given universe of discourse. It is proposed to use such an index in modifying a fuzzy relation. Different similarity measures in the literature are elucidated, and a comparative study between different pairs of fuzzy sets is presented. One of these similarity measures has been used successfully in rule selection and modification of a fuzzy relation. In the process, a number of modification schemes based on different logic have been extensively studied for different reasoning mechanisms based on the same data and results are tabulated. A specificity-based approach to defuzzification is also presented, which is found to be suitable for similarity-based fuzzy systems. The results are illustrated with the behaviour of a direct current (DC) shunt motor.
Highlights
A system is defined as an integrated set of interacting elements/objects/components that accomplish a defined objective
We have developed a mechanism to compute the matching degree of two fuzzy sets - representation of imprecise concepts
It has been shown that the concept of similarity is inherent in approximate reasoning methodology
Summary
A system is defined as an integrated set of interacting elements/objects/components that accomplish a defined objective. All the existing methods [18,20,21,27] use the similarity measure for a direct computation of inference without considering the induced relation, i.e. how the underlying relation (a condition) is modified in the presence of the given fact This is important in deriving a consequence of the fact from the rule. We may recall here that the authors computed the conclusion B = min(1, B/s), where s is the measure of similarity between fuzzy sets A and A without considering the information suggested by the conditional rule. We believe that in a similarity-based reasoning methodology, a scheme for computation of the induced relation, when a fact and a conditional statement is given, should satisfy the following axioms: A1.
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