基于累积前景理论的概率犹豫模糊多属性决策方法  

Probabilistic Hesitant Fuzzy Multi-criteria Decision-making Method Based on Cumulative Prospect Theory

作　　者：高建伟[1,2] 黄鑫[1,2] 郭奉佳 李响珍[1,2] GAO Jian-wei;HUANG Xin;GUO Feng-jia;LI Xiang-zhen(School of Economics and Management,North China Electric Power University,Beijing 102206,China;Beijing Key Laboratory of New Energy and Low-Carbon Development North China Electric Power Univer sity,Beijing 102206,China)

机构地区：[1]华北电力大学经济与管理学院,北京102206 [2]华北电力大学新能源电力与低碳发展研究北京市重点实验室,北京102206

出　　处：《数学的实践与认识》2021年第10期45-58,共14页Mathematics in Practice and Theory

基　　金：国家自然科学基金(72071076);北京市自然科学基金(9202017)。

摘　　要：针对属性权重信息未知的概率犹豫模糊多属性决策问题,提出基于累积前景理论的多属性决策方法.首先,考虑概率犹豫元素之间的关系,定义概率犹豫模糊熵,分析其性质,并在此基础上提出新的得分函数.其次,鉴于决策者主观风险态度,引入累积前景理论构建前景决策矩阵.进而利用模糊熵最小化和综合效用最大化构建优化模型计算属性权重.最后,结合累积前景理论和准则权重建立多属性决策模型,以综合前景值大小排序得最优方案,并通过算例证明该模型的合理性.This paper provides a multi-criteria decision-making method based on cumulative prospect theory in which the criteria are probabilistic hesitant fuzzy elements and the attribute weights are completely unknown.Firstly,considering the relationship between the elements of probability hesitation,the fuzzy entropy is defined,analyze its properties and on this basis,propose a new scoring function.Secondly,in view of the subjective risk attitude of decision makers,the cumulative prospect theory is introduced to construct the prospect decision matrix.Then using fuzzy entropy minimization and comprehensive utility maximization to construct an optimization model to calculate attribute weights.Finally,a multi-attribute decision-making model is established based on the cumulative prospect theory and criterion weights,and the optimal scheme is obtained by sorting the comprehensive prospect values,and the rationality of the model is proved by calculation examples.

关 键 词：多属性决策 概率犹豫模糊元 模糊熵 得分函数 累积前景理论 

分 类 号：O225[理学—运筹学与控制论] O159[理学—数学]