基于后悔理论的概率不确定语言中智决策方法  

Method for probabilistic uncertain linguistic neutrosophic decision making based on regret theory

作　　者：朱丽 陈春芳[2] 熊啟捷 ZHU Li;CHEN Chunfang;XIONG Qijie(School of Computer and Information Engineering,Jiangxi Agricultural University,Nanchang 330045,China;School of Mathematics and Computer Sciences,Nanchang University,Nanchang 330031,China;Ji Luan Academy,Nanchang University,Nanchang 330031,China)

机构地区：[1]江西农业大学计算机与信息工程学院,江西南昌330045 [2]南昌大学数学与计算机学院,江西南昌330031 [3]南昌大学际銮书院,江西南昌330031

出　　处：《南昌大学学报(理科版)》2025年第1期1-11,共11页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(12361095);江西省自然科学基金资助项目(20232BAB201028);江西省财政科技专项“包干制”试点示范项目(ZBG20230418001,ZBG20230418014);江西省市场监督管理局科技项目(GSJK202305)。

摘　　要：为研究语言环境下的概率中智决策问题,提出了概率不确定语言中智集和概率不确定语言中智元的概念,建立了一种基于后悔理论的概率不确定语言中智多属性决策方法。首先,通过定义得分函数和标准差,给出了概率不确定语言中智元的比较方法,同时也讨论了概率不确定语言中智元的距离度量及其性质。其次,针对属性值为概率不确定语言中智元的多属性决策问题,根据与理想点的灰色关联系数得到决策属性的期望效用值。然后,基于后悔理论,利用成对比较的后悔-欣喜值获得方案的综合感知效用值,实现方案的优选。最后,通过算例分析表明了该方法的有效性。In order to study the probabilistic neutrosophic decision making problem under linguistic environments,the concepts of the probabilistic uncertain linguistic neutrosophic sets and probabilistic uncertain linguistic neutrosophic numbers were proposed,and a method for probabilistic uncertain linguistic neutrosophic multi-attribute decision making based regret theory was established.First,by defining the score function and standard deviation,the comparison method of probabilistic uncertain linguistic neutrosophic numbers was presented,meanwhile,the concept and properties of the distance measure for probabilistic uncertain linguistic neutrosophic numbers were discussed.Next,the expected utility values of the decision attributes were obtained according to the grey relational coefficient from the ideal solution,in which the attribute values were in the form of probabilistic uncertain linguistic neutrosophic numbers.Then,based on regret theory,the comprehensive perceived utility value determined by regret-rejoice value through paired comparison was displayed to rank all the alternatives.Finally,an example was given to illustrate the effectiveness of the proposed method.

关 键 词：多属性决策 概率不确定语言中智集 后悔理论 灰色关联系数 

分 类 号：C934[经济管理—管理学]