基于模糊等价的毕达哥拉斯模糊集相似度构造方法

毕达哥拉斯模糊集是Zadeh模糊集的一种推广形式,其相似度刻画方法是毕达哥拉斯模糊集理论的重要研究内容。现有的毕达哥拉斯模糊集相似度大多针对具体问题而提出。为推广毕达哥拉斯模糊集理论的应用范围,文中基于模糊等价研究毕达哥拉斯模糊集相似度的一般构造方法。将模糊等价概念推广至毕达哥拉斯模糊数,提出了PFN(Pythagorean Fuzzy Number)模糊等价的概念,并给出了PFN模糊等价的构造方法。进一步,通过聚合算子给出了基于PFN模糊等价的毕达哥拉斯模糊集相似度的一般构造方法。通过实例说明了现有的一些相似度是文中构造的相似度的特例。

Similarity Construction Method for Pythagorean Fuzzy Set Based on Fuzzy Equivalence

The notion of Pythagorean fuzzy set is a generalization of Zadeh’s fuzzy sets.The study of similarity measures between Pythagorean fuzzy sets is an important topic of Pythagorean fuzzy set theory.Most of the existing similarity measures are presented based on specific practical problems.This paper focuses on general constructing methods of similarity measures between Pythagorean fuzzy sets by using fuzzy equivalences.The notion of fuzzy equivalence is extended to Pythagorean fuzzy numbers and the notion of PFN fuzzy equivalence is proposed.The constructing methods of PFN fuzzy equivalences are presented.Furthermore,by using aggregation operators,some general methods for constructing similarity measures between Pythagorean fuzzy sets are proposed.It is shown that some of the existing similarity measures are special cases of the similarity measures proposed in this study.