Similarity-based multi-criteria decision making technique of pythagorean fuzzy sets

Pythagorean fuzzy set (PFS) is a more flexible and effective way than intuitionistic fuzzy set (IFS) to seize indeterminacy. In this context, the main aim is to develop a number of new diverse types of PFS similarity measures which not only satisfy the well-known axioms, but also conquer the division-by-zero problem successfully. Moreover, the developed measures are based on two concepts of t-norm and s-norm together with the distance measure between PFSs. In order for further clarifying the role of proposed PFS similarity measures, we assess here two aspects of comparison: the microscopy aspect and the macroscopy aspect. The latter aspect allows us to know how the results are actually obtained on the basis of structural form of similarity measures, and the former aspect enables us to judge about the results of similarity measures without considering how they have been concluded. We then investigate a number of desirable properties of proposed PFS similarity measures, and show their effectiveness compared to the existing ones by encountering both of existing and newly constructed measures in some case studies concerning pattern recognition and medical diagnosis.