Similarity Measures between Intuitionistic Fuzzy Sets

In this chapter we consider similarity measures between intuitionistic fuzzy sets starting fromreminding the axiomatic relation between distance and similarity measures.We show that this relation is not satisfied for the intuitionistic fuzzy sets. We also consider some similarity measures for the intuitionistic fuzzy sets, known from the literature. We show that neither similarity measures treating an intuitionistic fuzzy set as a simple interval-valued 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 work, we consider a family of similarity measures constructed by taking into account both all the three terms (membership values, non-membership values, and hesitation margins) describing an intuitionistic fuzzy set, and the complements of the elements we compare. That is, we use all kinds and fine shades of information available. We also point out the traps one should be aware of while examining similarity between intuitionistic fuzzy sets. Finally, we consider correlation of the intuitionistic fuzzy sets.