基于优势关系的毕达哥拉斯模糊集上的三支决策  

Three-way Decision on Pythagorean Fuzzy Set Based on Dominance Relationship

作　　者：赵蒙 张少谱 冯涛[2] ZHAO Meng;ZHANG Shao-pu;FENG Tao(Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;School of Sciences,Hebei University of Science and Technology,Shijiazhuang 050018,China)

机构地区：[1]石家庄铁道大学数理系,河北石家庄050043 [2]河北科技大学理学院,河北石家庄050018

出　　处：《模糊系统与数学》2020年第6期109-129,共21页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61573127);河北省自然科学基金资助项目(A2018210120,A2020208004);河北省人才工程培养项目(A2017002112,A201901049)。

摘　　要：在实际生活中,由于人们面对的信息大部分是不完整的或不确定的,因此在当下不能确定应该采取什么措施的时候,三支决策中的延迟措施便能发挥很好的作用。三支决策是当今的一个热点话题,它通常将论域划分为正域、负域和边界域三个互不相交的部分。现在已经在很多领域得到了很好的应用。毕达哥拉斯模糊集在决策过程中能更灵活地处理不确定信息,因此探究毕达哥拉斯模糊集上的三支决策是有意义的。在粗糙集中通常考虑将等价关系作为二元关系划分等价类,但实际生活中有很多情景需要满足"优于"、"劣于"的关系,即满足优势关系。因此本文将探究基于优势关系的毕达哥拉斯模糊集上的三支决策。在文章中列出了两种毕达哥拉斯模糊集中条件概率的定义方法,其中第二种条件概率将条件从经典集扩展到了毕达哥拉斯模糊集,并且给出了两种三支决策策略。分析对比了基于两种条件概率在两种策略下三支决策的结果。In actual life,since most of the information people faced with is incomplete or uncertain,it is not possible to determine what measures should be taken at the moment,then the delay measures in the three-way decision can play a good role.Three-way decision is a hot topic today.It usually divides the discourse domain into three disjoint parts:positive domain,negative domain and boundary domain.Now it has been well applied in many fields.Pythagorean fuzzy set can deal with uncertain information more flexibly in the decision-making process,so it is meaningful to explore three-way decision on Pythagorean fuzzy sets.In rough sets,the equivalent relationship is usually considered as a binary relationship to divide the equivalent class.However,there are many scenarios in real life that need to satisfy the"excellent"or"inferior"relationship.Therefore,we consider the dominance relationship as a binary relationship and make three-way decision.In this paper,two definitions of conditional probability in Pythagorean fuzzy sets are listed,the second one extends the conditional probability from classic sets to Pythagorean fuzzy sets,and two three-way decision strategies are given.The analysis compares the results of three-way decisions under two strategies based on two conditional probabilities.

关 键 词：条件概率 二元关系 等价关系 三支决策 毕达哥拉斯模糊集 不确定信息 等价类 决策过程 

分 类 号：O236[理学—运筹学与控制论]