Similarity measure between Pythagorean fuzzy sets based on lower, upper and middle fuzzy sets with applications to pattern recognition and multicriteria decision making with PF-TODIM

The choice of similarity measure (SM) plays an important role in distinguishing between objects. Similarity measure of Pythagorean fuzzy sets (PFSs) is very useful and effective in discriminating between different Pythagorean fuzzy sets. Therefore, in this paper, we suggest a new similarity measure for PFSs based on converting the PFSs into their lower, upper and middle fuzzy sets (FSs) to calculate their degree of similarity. We construct an axiomatic definition for a new SM of PFSs. Furthermore, we put forward a new way to express the similarity measure of PFSs to show its competency, reliability and applicability. For establishing reasonability and usefulness of the proposed methods, we present several practical examples related to pattern recognition and multicriteria decision making problems. Finally, we construct an algorithm for Portuguese of interactive and multiple attributes decision making (TODIM) method based on the proposed similarity measures, for handling complex multicriteria decision making problems related to day to day life. Our final results show that the suggested method is reasonable, reliable and useful in managing different complex decision making problems in the context of Pythagorean fuzzy sets as the domain.