Similarity in fuzzy systems

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.