计算机科学 ›› 2021, Vol. 48 ›› Issue (1): 152-156.doi: 10.11896/jsjkx.191100102

• 数据库&大数据&数据科学 • 上一篇    下一篇

基于模糊等价的毕达哥拉斯模糊集相似度构造方法

胡平, 秦克云   

  1. 西南交通大学数学学院 成都 611756
  • 收稿日期:2019-11-13 修回日期:2020-01-07 出版日期:2021-01-15 发布日期:2021-01-15
  • 通讯作者: 秦克云(keyunqin@263.net)
  • 作者简介:1125476515@qq.com
  • 基金资助:
    国家自然科学基金项目(61976130,61473239)

Similarity Construction Method for Pythagorean Fuzzy Set Based on Fuzzy Equivalence

HU Ping, QIN Ke-yun   

  1. College of Mathematics,Southwest Jiaotong University,Chengdu 611756,China
  • Received:2019-11-13 Revised:2020-01-07 Online:2021-01-15 Published:2021-01-15
  • About author:HU Ping,born in 1994,M.S.candidate.Her main research interests include rough set theory and so on.
    QIN Ke-yun,born in 1962,Ph.D,is a se-nior member of China Computer Federation.His main research interests include rough set theory,formal concept analysis and so on.
  • Supported by:
    National Natural Science Foundation of China(61976130,61473239).

摘要: 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。

关键词: 毕达哥拉斯模糊集, 毕达哥拉斯模糊数, 模糊等价, 相似度

Abstract: 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.

Key words: Fuzzy equivalence, Pythagorean fuzzy number, Pythagorean fuzzy set, Similarity measure

中图分类号: 

  • TP182
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