Design of Similarity and Dissimilarity Measures for Fuzzy Sets on the Basis of Distance Measure

Abstract 1 In this paper, we survey the relationship between the similarity measure and dissimilarity measure for fuzzy sets. First, we design a similarity measure using a distance measure for fuzzy sets and prove its usefulness. From this result, we assert that the similarity between two complementary fuzzy sets satisfies the fuzzy entropy definition. We also show that the summation of the similarity and dissimilarity measures between two membership functions of fuzzy sets constitute all the information of the fuzzy set itself. We then extend our results to two data group fuzzy sets. Data similarity and dissimilarity measures between two fuzzy membership functions satisfy complementary. We also verify and discuss the characteristics of the relation between the similarity measure and dissimilarity measure with illustrative example.