Entropy of interval-valued fuzzy sets and intuitionistic fuzzy sets

Fuzzy entropy is a non-probabilistic quantity which investigate measure of fuzziness and vagueness of system. In this research, we introduce entropy of fuzzy sets as a criterion for uncertainty. After that, we introduce σ-entropy on fuzzy sets and distance measure for a fuzzy set and we investigate relationship between distance measure and fuzzy entropy. The distance measure is a measure that describes the difference between fuzzy sets. Using the concept of σ-distance measure, we have studied some properties of fuzzy entropy. Then, we will study fuzzy relative entropy based on relative entropy. Next, we introduce inclusion measure of interval-valued fuzzy set and relationship among the normalized distance, the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets is investigated in detail. ​