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.
Highlights
Atanassov [1] initiated the concept of intuitionistic fuzzy set (IFS), which is a generalization of Zadeh’s fuzzy sets
The motivation for writing this paper is that we introduced triangular conorms (S-norm) as a new similarity measure for Pythagorean fuzzy sets
In “S-similarity measure of Pythagorean fuzzy sets” section, we propose several new similarity measures for Pythagorean fuzzy based on norms
Summary
Atanassov [1] initiated the concept of intuitionistic fuzzy set (IFS), which is a generalization of Zadeh’s fuzzy sets. Peng and Yang [14] developed a Pythagorean fuzzy superiority and inferiority ranking method to solve uncertainty multiple attribute group decision-making problem. Zhang [31] developed a new decision method based on similarity measure to address multiple criteria group decision-making problems within Pythagorean fuzzy environment. Wei and Wei [33] presented similarity measures of Pythagorean fuzzy sets based on the cosine function for dealing with the decision-making problems. Our aim is to propose similarity measures based on norms for PFSs, and some of the basic properties of the new similarity measures were discussed. We propose a multi-criteria group decision-making method based on the new similarity measures.
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