基于熵和双向投影的区间毕达哥拉斯模糊决策  

Interval-valued Pythagorean Fuzzy Decision-making Based on the Entropy and Bidirectional Projection

作　　者：丁旭艳 江登英 尹圆圆 饶从军[1] DING Xuyan;JIANG Dengying;YIN Yuanyuan;RAO Congjun(School of Science,Wuhan University of Technology,Wuhan 430070,China;School of Mathematics and Physics,North China Electric Power University,Beijing 102206,China)

机构地区：[1]武汉理工大学理学院,武汉430070 [2]华北电力大学数理学院,北京102206

出　　处：《复杂系统与复杂性科学》2025年第1期88-96,共9页Complex Systems and Complexity Science

基　　金：教育部人文社会科学研究一般项目(13YJCZH060);国家自然科学基金(72071150)。

摘　　要：针对区间毕达哥拉斯模糊集现有熵公式中犹豫度缺失及属性客观权重未知等问题,根据该模糊集的特点定义模糊度,基于模糊度和犹豫度给出区间毕达哥拉斯模糊集熵的新公理化定义,提出改进的熵公式计算属性客观权重,并将双向投影法拓展到区间毕达哥拉斯模糊环境下,构建基于改进熵和双向投影的多属性决策方法。通过理论证明和算例分析验证相关性质与所提方法的合理性、有效性,为解决此类客观权重未知的多属性决策问题提供了新思路。In response to the problems of unknown objective weights of attributes and missing hesitancy in the existing entropy formulas of interval-valued Pythagorean fuzzy sets,the fuzziness is defined according to the characteristics of the set.A new axiomatic definition of the entropy for interval-valued Pythagorean fuzzy set is given based on the fuzziness and hesitancy.An improved entropy formula is proposed to calculate objective weights of attributes,and the bidirectional projection method is extended to interval-valued Pythagorean fuzzy environments.A multi-attribute decision-making method based on the improved entropy and bidirectional projection is constructed.Through theoretical proofs and numerical analysis,the related properties,the rationality and effectiveness of the proposed method are verified,providing new ideas for solving multi-attribute decision-making problems with unknown objective weights.

关 键 词：多属性决策 区间毕达哥拉斯模糊集 熵 双向投影法 

分 类 号：C934[经济管理—管理学] O159[理学—数学]