山西大学学报（自然科学版）2025，Vol.48Issue(1)：101-119,19.DOI:10.13451/j.sxu.ns.2024153
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
摘要
Abstract
Probabilistic hesitant fuzzy sets play an important role in decision analysis because they can accurately describe the proba-bility distribution of the hesitancy of alternatives with respect to the attributes.In multi-attribute group decision-making,the alterna-tives can be effectively ranked according to their representativeness by using the similarity and distance function between the alterna-tives.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 hesi-tant 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 similari-ty 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Key words
comprehensive similarity/distance function based on logarithmic/weight/group consensus/technique for order prefer-ence by similarity to ideal solution分类
数理科学引用本文复制引用
宁帅康,冯涛,李艳,米据生..基于改进距离函数的概率犹豫模糊多属性群决策[J].山西大学学报（自然科学版）,2025,48(1):101-119,19.基金项目
国家自然科学基金(62076088) （62076088）
河北省自然科学基金(A2020208004 （）
A2021210027) （）
