Pythagorean Fuzzy Rough Set Model And Its Applications

The similarity of fuzzy sets is an important uncertainty measure in fuzzy set theory.It is the hot topic of related theory and application research.In addition,fuzzy similarity is also the basic problem of fuzzy rough set model.Pythagorean fuzzy set is a kind of extension of Zadeh fuzzy set.The similarity of Pythagorean fuzzy sets has been extensively investigated.Based on specific application problems,a variety of Pythagorean fuzzy sets similarities have been constructed.In order to extent the application scope of Pythagorean fuzzy sets,this paper is devoted to the discussion of the general construction methods of similarity measures between Pythagorean fuzzy sets and its application in fuzzy rough set models.Based on fuzzy equivalences we propose the general construction methods of similarity measures between Pythagorean fuzzy sets.In addition,we present the similarity relation on objects in Pythagorean fuzzy information systems and construct the related fuzzy rough set models.The main research content includes:1.By using the concept of fuzzy equivalence,the notion of PFN fuzzy equivalence of Pythagorean Fuzzy Number is proposed,and the construction method of PFN fuzzy equivalence is presented.Based on the study of the properties of aggregation operators,a class of similarity measures of Pythagorean fuzzy sets are constructed by using PFN fuzzy equivalences.Some existing similarities are special cases of the general similarity constructed in the article.2.The similarity relation of objects in Pythagorean fuzzy information system is presented by using PFN fuzzy equivalences.The related fuzzy approximation space and fuzzy rough set model are further constructed.The basic properties of the upper and lower approximation operators are investigated.