加权的概率犹豫模糊集的三维向量测度法与决策应用  

Three dimensional vector measures for weighted probabilistic hesitant fuzzy sets and its decision applications

作　　者：朱国成[1] 赵瑞华 陈煜 ZHU Guocheng;ZHAO Ruihua;CHEN Yu(School of General Education,Guangdong Innovative Technical College,523960,Dongguan;Yun An Middle School,527500,Yunfu,Guangdong;School of Economics,Zhengzhou University of Aeronautics,450018,Zhengzhou,Henan,PRC)

机构地区：[1]广东创新科技职业学院通识教育学院,东莞市523960 [2]广东省云浮市云安中学,广东省云浮市527500 [3]郑州航空工业管理学院经济学院,河南省郑州市450018

出　　处：《曲阜师范大学学报（自然科学版）》2023年第4期24-32,共9页Journal of Qufu Normal University(Natural Science)

基　　金：广东创新科技职业学院特色创新类重点项目(2023TSZD05);广东省普通高校特色创新类项目(2023KTSCX414)。

摘　　要：为了更加精细化地描述概率犹豫模糊集,将概率犹豫模糊元中的隶属度添加相应的决策专家权重,并由此提出了加权的概率犹豫模糊集概念.用三维向量表示加权的概率犹豫模糊数,在此基础上建立了加权的概率犹豫模糊元的三维向量得分函数模型、三维向量离差函数模型、2个加权的概率犹豫模糊元的大小比较规则与距离测度模型.分别给出了属性的外部权重、内部权重以及综合权重的计算方法.在属性的3种权重条件下,运用方案的整体得分值与内部决策专家评价差异值2个因素计算方案的综合属性值,进而对各个方案排序.决策结果表明,在利用三维向量刻画加权的概率犹豫模糊集的基础上建立的决策算法不但有效可行,而且提供了一种多元化的决策方法.In order to describe the probabilistic hesitant fuzzy set in a more refined mamer,the weighted probabilistic hesitant fuzzy set was proposed by adding the corresponding decision expert weight to the membership degree of the probabilistic hesitant fuzzy element.The weighted probabilistic hesitant fuzzy numbers are represented by three dimensional vectors,and the three dimensional vector score function model,the three dimensional vector deviation function model,the size comparison rules of two weighted probabilistic hesitant fuzzy elements and the distance measure model are established to calculate weighted probabilistic hesitant fuzzy elements.The calculation methods of external weight,internal weight and comprehensive weight of attributes are set up respectively.Under the three weights of attributes,the overall score value of the scheme and the difference value of internal expert evaluation were considered to calculate the comprehensive attribute value of the scheme,and then the schemes were ranked.The decision results show that the decision algorithm based on describing weighted probabilistic hesitant fuzzy sets with three-dimensional vectors is effective and feasible,and also provides a diversified decision method.

关 键 词：加权的概率犹豫模糊集 三维向量 属性的外部权重 属性的内部权重 属性的综合权重 

分 类 号：O159[理学—数学]