基于几何平均犹豫度的概率犹豫模糊多属性决策方法

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中图分类号：TP391；0159 文献标志码：A 文章编号：1671-6841（2025）03-0049-08

DOI：10.13705/j. issn.1671-6841.2023187

Probabilistic Hesitant Fuzzy Multi-attribute Decision-making Method Based on Geometric Mean Hesitant Degree

ZHANG Yanna'， ZHANG Lixia1，²，WANG Yongbing1，2 （1. School of Mathematics and Physics， Anqing Normal University， Anqing ， China; 2. Key Laboratory of Modeling，Simulation and Control of Complex Ecosystem in Dabie Mountains of Anhui Province，Anqing ，China）

Abstract：A probabilistic hesitant fuzzy multi-tribute decision making method based on geometric mean hesitancy degree was proposed，， which could solve the problem of probabilistic hesitant fuzzy multi-attribute decision making with completely unknown atribute weights.Firstly，in response to the differences in membership degrees between elements and the varying number of elements in probabilistic hesitant fuzzy element，the geometric mean hesitant degree of probabilistic hesitant fuzzy element was defined. Secondly，based on the traditional distance measure of probabilistic hesitant fuzzy elements，the distance measure of probabilistic hesitant fuzzy elements based on geometric mean hesitant degree was proposed. Further，the probabilistic hesitant fuzzy element entropy measure was constructed based on the distance measure proposed，and the entropy weight method was combined to determine the attribute weight.Finally，the corresponding multi-attribute decision model was given in combination with TOPSIS method.The feasibility and practicability of the proposed method were verified by a specific case and sensitivity analysis of the corresponding parameters.

Key words： probabilistic hesitant fuzzy element； multi-tribute decision making；distance measure; hesitant degree;attribute weight

0 引言

由于实际问题的复杂性和人类自身知识的模糊性，在多属性决策问题中，存在很多不确定性。（剩余11760字）