基于改进距离函数的概率犹豫模糊多属性群决策  

Probabilistic Hesitant Fuzzy Multi-attribute Group Decision Based on Improved Distance Function

作　　者：宁帅康 冯涛[1] 李艳[1] 米据生[2] NING Shuaikang;FENG Tao;LI Yan;MI Jusheng(School of Sciences,Hebei University of Science and Technology,Shijiazhuang 050018,China;School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北科技大学理学院,河北石家庄050018 [2]河北师范大学数学科学学院,河北石家庄050024

出　　处：《山西大学学报(自然科学版)》2025年第1期101-119,共19页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(62076088);河北省自然科学基金(A2020208004,A2021210027)。

摘　　要：概率犹豫模糊集能精准地描述方案相对于属性取值的犹豫性概率分布,因而在决策分析中占有重要地位。在多属性群体决策中,利用方案间的相似性和距离函数,可以依据方案的代表性的强弱进行有效排序。若结合现有的排序结果,还可改进最优方案。为此,本文探讨概率犹豫模糊系统中基于代表性强弱的多属性群决策问题。本文首先提出了基于对数的距离函数,并利用余弦相似度与杰卡德相似系数构建了综合相似度。然后,利用基于对数的距离函数改进专家的客观权重,并与主观相结合计算专家的综合权重。同时在群共识的基础上,针对代表性提出了基于相似度均值的综合决策矩阵的正、负理想解。并结合基于对数的距离函数计算属性权重。最后,利用贴进度法给出群共识下基于代表性强弱的备选方案的排序方法。在实例验证环节,与传统多属性群决策模型进行对比分析,验证了本文所提出模型的可行性和有效性。同时本模型的结果与传统排序相结合可以得到最优方案选择。Probabilistic hesitant fuzzy sets play an important role in decision analysis because they can accurately describe the probability distribution of the hesitancy of alternatives with respect to the attributes.In multi-attribute group decision-making,the alternatives can be effectively ranked according to their representativeness by using the similarity and distance function between the alternatives.If combined with the existing ranking results,the more suitable optimal alternative can also be acquired.This paper discusses the multi-attribute group decision-making problem based on the representativeness strength of every alternative in probabilistic hesitant fuzzy systems.The distance function based on logarithm is proposed,and the comprehensive similarity is constructed by using cosine similarity and Jaccard similarity coefficient.Then,the objective weight of experts is improved by using the distance function based on logarithm,and the comprehensive weight of experts is calculated by combining with the subjective weight.Meanwhile,based on the group consensus,the positive and negative ideal solutions for the comprehensive decision matrix based on the similarity mean are proposed for the representativeness.And the attribute weight can be calculated by combining the distance function based on the logarithm.Finally,the ranking method of alternatives based on the strength of representativeness under group consensus is given by using the closeness degree method.In the part of example verification,the feasibility and effectiveness of the proposed model are verified by comparing with the traditional multi-attribute group decision-making model.At the same time,the results of this model can be combined with the traditional ranking to get the optimal alternative selection.

关 键 词：综合相似度 基于对数的距离函数 权重 群共识 逼近理想解法 

分 类 号：O225[理学—运筹学与控制论] O159[理学—数学]