Relationship between similarity measure and entropy of interval type-2 fuzzy sets

The similarity measure and entropy of fuzzy sets are two important fuzzy measures in fuzzy logic theory and it is significant to research their relationship. In this paper, we mainly discuss the relationship between the similarity measure and entropy of interval type-2 fuzzy sets (IT2 FSs) proposed by Zheng et al., and give two Theorems and a Corollary that can reflect the mutual conversion relationship between two indexes. These conclusions have extensive practicability in many fields.