概率对偶犹豫模糊交互融合算子及其在多属性决策中的应用  

Probabilistic Dual Hesitant Fuzzy Interaction Aggregation Operators and Their Application to Multi-attribute Decision-making

作　　者：杨彦坡 张丽芝 宁宝权[1] 陈跃 张华伟[1] Yang Yanpo;Zhang Lizhi;Ning Baoquan;Chen Yue;Zhang Huawei(School of Mathematics and Statistics,Liupanshui Normal University,Liupanshui 553004,China;NO.10 middle school of Liupanshui,Liupanshui 553004,China)

机构地区：[1]六盘水师范学院数学与统计学院,贵州六盘水553004 [2]六盘水市第十中学,贵州六盘水553004

出　　处：《六盘水师范学院学报》2024年第3期75-91,共17页Journal of Liupanshui Normal University

基　　金：六盘水师范学院科学研究(培育)项目“基于概率对偶犹豫模糊集的多属性群决策方法及其应用研究”(LPSSY2023KJZDPY08);六盘水师范学院学科(培育)团队项目“学科教学(数学)”(LPSSY2023XKPYTD04);六盘水师范学院教育教学研究与改革项目“大学数学教学改革研究”(2022-17-004)。

摘　　要：生产生活实践中的多属性决策问题往往充满了不确定性与模糊性,概率对偶犹豫模糊集作为模糊集的推广能够更全面准确地表达决策者提供的信息。另外,基于融合算子的多属性决策方法是常用的一种模糊决策方法。首先,在融合多个属性下的概率对偶犹豫模糊信息时隶属度与非隶属度会产生相互影响,提出概率对偶犹豫模糊交互运算法则并研究相关性质;其次,给出概率对偶犹豫模糊加权交互平均算子、加权交互几何算子及其性质;然后,建立基于概率对偶犹豫模糊交互融合算子的多属性决策方法;最后,通过一个实例验证提出的决策方法的有效性。The multi-attribute decision-making problems in production and life are often full of uncertainty and fuzziness.Probabilistic dual hesitant fuzzy set,as an extension of fuzzy set,can express the information provided by decision makers more comprehensively and accurately.In addition,multi-attribute decision-making method based on aggregation operator is a commonly used fuzzy decision-making method.Therefore,considering the interaction between membership degree and non-membership degree when aggregating probabilistic dual hesitancy fuzzy information with multiple attributes,the probabilistic dual hesitancy fuzzy interaction operational rules are proposed and the related properties are studied.Secondly,the probabilistic dual hesitation fuzzy weighted interactive average operator,weighted interactive geometric operator and their properties are given.Then,a multi-attribute decision-making method based on probabilistic dual hesitating fuzzy interactive aggregation operator is established.Finally,an example is given to verify the effectiveness of the proposed decision-making method.

关 键 词：多属性决策 概率对偶犹豫模糊交互运算法则 概率对偶犹豫模糊交互融合算子 

分 类 号：O225[理学—运筹学与控制论]