基于风险偏好得分函数和Choquet积分算子的毕达哥拉斯模糊决策方法  

Pythagorean Fuzzy Decision Making Method Based on the Risk Preference Score Function and Choquet Integral Operator

作　　者：罗静 孙刚 王贵君[3] LUO Jing;SUN Gang;WANG Gui-jun(Mathematics Group,No.2 Junior High School of Zhumadian,Zhumadian 463000,China;School of Science,Hunan Institute of Technology,Hengyang 421002,China;School of Mathematical Sciences,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]驻马店第二初级中学数学组,河南驻马店463000 [2]湖南工学院理学院,湖南衡阳421002 [3]天津师范大学数学科学学院,天津300387

出　　处：《模糊系统与数学》2022年第4期70-79,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61463019);湖南省自然科学基金资助项目(2019JJ40062)。

摘　　要：毕达哥拉斯(Pythagorean)模糊集(PFS)不仅是传统直觉模糊集的一种拓展,而且也是准确反映专家赋予初始决策信息的有效工具,尤其它能在更广泛区域上处理多属性模糊信息的决策问题。本文首先介绍Pythagorea模糊数(PFN)的基本定义和相关运算,并指出传统得分函数的某些缺陷,进而通过引入风险偏好因子提出新的得分函数、精确函数和排序准则。其次,在毕达哥拉斯模糊环境下介绍离散型模糊Choquet积分平均(几何)集成算子,并通过初始评价矩阵和熵公式给出决策专家的权重向量。最后,依据离散型模糊Choquet积分平均算子和风险偏好得分函数的排序准则提出一种新的毕达哥拉斯模糊决策方法,并通过实例验证该决策方法的有效性。Pythagorean fuzzy set(PFS)is not only an extension of the traditional intuitionistic fuzzy set,but also an effective tool to accurately reflect the initial decision information given by experts.In particular,it can deal with decision-making problems with multi-attribute fuzzy information in a wider area.In this paper,some definitions and related operations for Pythagorean fuzzy number(PFN)are first introduced,and points out the defects of its traditional scoring function,then,the new scoring function,accurate function and ranking criterion are proposed by introducing risk preference factor.Secondly,in Pythagorean fuzzy environment,the discrete fuzzy Choquet integral average(or geometric)integration operator is introduced,and the weight vector of decision experts is given through the initial evaluation matrix and entropy formula.Finally,based on the discrete fuzzy Choquet integral averaging operator and the ranking criteria of risk preference score function,a new Pythagorean fuzzy decision-making method is proposed,and its effectiveness is verified by an example.

关 键 词：毕达哥拉斯模糊数(PFN) 风险偏好得分函数 模糊Choquet积分 毕达哥拉斯模糊决策方法 

分 类 号：O159[理学—数学]