基于风险偏好的区间毕达哥拉斯犹豫模糊得分函数及其多属性决策  

Interval-valued Pythagorean Hesitancy Fuzzy Score Function Based on Risk Preference and Its Multi-attribute Decision

作　　者：王鸿均 张贤勇 WANG Hongjun;ZHANG Xianyong(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066;Laurent Mathematical Center,Sichuan Normal University,Chengdu 610066;Institute of Intelligent Information and Quantum Information,Sichuan Normal University,Chengdu 610066)

机构地区：[1]四川师范大学数学科学学院,四川成都610066 [2]四川师范大学Laurent数学中心,四川成都610066 [3]四川师范大学智能信息与量子信息研究所,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2025年第1期114-121,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(61673258);四川省自然科学基金(2022NSFSC0929);四川省科技计划(2022ZYD0001和2021YJ0085)。

摘　　要：针对属性权重已知、评价信息为区间毕达哥拉斯犹豫模糊数的多属性决策问题,对区间毕达哥拉斯犹豫模糊集的得分函数进行深入分析,考虑决策者的主观态度对决策结果的影响,提出一种基于风险偏好因子的新得分函数.首先,介绍区间毕达哥拉斯犹豫模糊数的基本定义和相关运算,考虑决策者在面临风险时的不同主观价值感受,进而通过引入风险偏好因子提出新的得分函数和排序准则.其次,给出新得分函数的取值范围、最值和单调性等性质并进行证明.最后,基于该得分函数给出一种全新的TOPSIS多属性决策方法,并通过解决实际问题检验该方法的可行性、实用性和有效性.区间毕达哥拉斯犹豫模糊数得分函数的改进丰富了多属性决策理论.Aiming at the problem of multi-attribute decision making with known attribute weights and interval Pythagorean hesitancy fuzzy number,the score function of interval Pythagorean hesitancy fuzzy set is deeply analyzed,and a new score function based on risk preference factor is proposed considering the influence of decision maker’s subjective attitude on the decision result.Firstly,the basic definition and related operation of interval Pythagorean hesitation fuzzy number are introduced.Considering different subjective value feelings of decision makers when facing risks,a new scoring function and ranking criteria are proposed by introducing risk preference factor.Secondly,the value range,maximum value and monotonicity of the new score function are given and proved.Finally,a new TOPSIS multi-attribute decision-making method is proposed based on the scoring function,and the feasibility,practicability and effectiveness of the method are tested by solving practical problems.The improvement of the interval Pythagorean hesitancy fuzzy score function enriches the theory of multi-attribute decision making.

关 键 词：区间毕达哥拉斯犹豫模糊集 风险偏好 得分函数 多属性决策 

分 类 号：O159[理学—数学]