A new similarity measure for Pythagorean fuzzy sets

Abstract

One of the methods of studying on two sets is to calculate the similarity of two sets. Triangular norms and conorms generalize the basic connectives between fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets. In this paper we used triangular conorms (S-norm). The advantage of using S-norm is that the similarity order does not change using different norms. In fact, we are looking for a new definition for calculating the similarity of two Pythagorean fuzzy sets. To achieve this goal, using an S-norm, we first present a formula for calculating the similarity of two Pythagorean fuzzy values, so that they are truthful in similarity properties. Following that, we generalize a formula for calculating the similarity of the two Pythagorean fuzzy sets which prove truthful in similarity conditions. Finally, we give some examples of this method.