Analysis of Similarity Measures for Atanassov's Intuitionistic Fuzzy Sets

We consider some existing similarity measures for Atanassov’s intuitionistic fuzzy sets (A-IFSs, for short). We show that neither similarity measures treating an A-IF as a simple interval values fuzzy set, nor straightforward generalizations of the similarity measures well-known for the classic fuzzy sets work under reasonable circumstances. Next, expanding upon our previous works, we consider a family of similarity measures constructed by taking into account both all the three functions (the membership, non-membership and hesitation) describing an A-IF, and the complements of the elements we compare to each other. That is, we use all kinds and fine shades of information available. We point out their proper behavior and an intuitive appeal. Keywords— Atanassov’s intuitionistic fuzzy sets, similarity measures.