Relationship between similarity measure and entropy of interval valued fuzzy sets

In this paper, we introduce concepts of entropy of interval valued fuzzy set which is different from Bustince and Burillo [Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems 78 (1996) 305–316] and similarity measure of interval valued fuzzy sets, discuss their relationship between similarity measure and entropy of interval valued fuzzy sets in detail, prove three theorems that similarity measure and entropy of interval valued fuzzy sets can be transformed by each other based on their axiomatic definitions and put forward some formulas to calculate entropy and similarity measure of interval valued fuzzy sets.