Two computational formulae for similarity measures on intuitionistic fuzzy sets based on intuitionistic fuzzy equivalencies

The measure of the similarity between intuitionistic fuzzy sets (IFSs) is an important topic in IFSs theory. In this paper, we propose two computational formulae for similarity measures on IFSs based on a quaternary function called intuitionistic fuzzy equivalence. We first propose the concept of intuitionistic fuzzy equivalence. Then we give a computational formula for intuitionistic fuzzy equivalencies (i.e., Eq. (1)), which is obtained from combining dissimilarity functions and fuzzy equivalencies. Based on Eq. (1), we obtain two computational formulae for similarity measures on IFS s. The first one is obtained by aggregating Eq. (1). The second one is obtained by respectively aggregating the numerator and the denominator of Eq. (1). We also examine some properties of the proposed similarity measures on IFSs. Finally, we make a comparison between the proposed similarity measures on IFSs and those existing ones in the literature through several counter-intuitive cases.