Relationships Among Several Fuzzy Measures

Abstract

In fuzzy set theory, similarity measure, divergence measure, subsethood measure and fuzzy entropy are four basic concepts. They surface in many fields, such as image processing, fuzzy neural networks, fuzzy reasoning, fuzzy control, and so on. The similarity measure describes the degree of similarity of fuzzy sets A and B. The divergence measure describes the degree of difference of fuzzy sets A and B. The subsethood measure (also called inclusion measure) is a relation between fuzzy sets A and B, which indicates the degree to which A is contained in B. The entropy of a fuzzy set is the fuzziness of that set.