A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition

Unlike an ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a non-membership degree, is a more flexible way to capture the uncertainty. One of the important topics in IFS is the measure of the similarity between IFSs for which several studies have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity, and provide counter-intuitive cases. In this paper, a new general type of similarity measure for IFS with two parameters is proposed along with its proofs. A comparison between the existing similarity measures and the proposed similarity measure is also performed in terms of counter-intuitive cases. The findings indicate that the proposed similarity measure does not provide any counter-intuitive cases.