基于熵和双向投影的区间毕达哥拉斯模糊决策

丁旭艳; 江登英; 尹圆圆; 饶从军; 丁旭艳; 江登英; 尹圆圆; 饶从军

doi:10.13306/j.1672-3813.2025.01.012

复杂系统与复杂性科学 >

2025 , Vol. 22 >Issue 1: 88 - 96

DOI: https://doi.org/10.13306/j.1672-3813.2025.01.012

研究论文

基于熵和双向投影的区间毕达哥拉斯模糊决策

丁旭艳 ,
江登英 ,
尹圆圆 ,
饶从军 ,
丁旭艳 ,
江登英 ,
尹圆圆 ,
饶从军

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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

丁旭艳(1999-),女,山西运城人,硕士,主要研究方向为模糊决策。

收稿日期: 2023-11-03

修回日期: 2023-12-06

网络出版日期: 2025-04-27

基金资助

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)

收起

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

DING Xuyan ,
JIANG Dengying ,
YIN Yuanyuan ,
RAO Congjun ,
DING Xuyan ,
JIANG Dengying ,
YIN Yuanyuan ,
RAO Congjun

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1. School of Science, Wuhan University of Technology, Wuhan 430070, China;
2. School of Mathematics and Physics, North China Electric Power University,Beijing 102206, China

Received date: 2023-11-03

Revised date: 2023-12-06

Online published: 2025-04-27

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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。

关键词： 多属性决策; 区间毕达哥拉斯模糊集; 熵; 双向投影法

本文引用格式

丁旭艳 , 江登英 , 尹圆圆 , 饶从军 , 丁旭艳 , 江登英 , 尹圆圆 , 饶从军 . 基于熵和双向投影的区间毕达哥拉斯模糊决策[J]. 复杂系统与复杂性科学, 2025 , 22(1) : 88 -96 . DOI: 10.13306/j.1672-3813.2025.01.012

Abstract

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.

Key words： multi-attribute decision-making; interval-valued Pythagorean fuzzy set; entropy; bidirectional projection method

参考文献

[1] ATANASSOV K T. Intuitionisticfuzzy sets[J]. Fuzzy Sets and Systems, 1986, 200(1): 87-96.
[2] YAGER R R, ABBASOV A M. Pythagorean membership grades, complex numbers and decision making[J]. International Journal of Intelligent Systems, 2013, 28(5): 436-452.
[3] YAGER R R. Pythagorean membership grades in multicriteria decision making[J]. IEEE Transactions on Fuzzy Systems, 2014, 22(4): 958-965.
[4] PENG X, YANG Y. Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators[J]. International Journal of Intelligent Systems, 2016, 31(5): 444-487.
[5] ZADEH L A. Probability measures of fuzzy events[J]. Journal of Mathematical Analysis and Applications, 1968, 23(2): 421-427.
[6] SUO C, LI X, LI Y. Distance-based knowledge measure and entropy for interval-valued intuitionistic fuzzy sets[J]. Mathematics, 2023, 11(16): 3468.
[7] PENG X, YUAN H, YANG Y. Pythagorean fuzzy information measures and their applications[J]. International Journal of Intelligent Systems, 2017, 32(10): 991-1029.
[8] 吴英晗, 李明达, 胡枫. 基于熵的多属性决策超网络重要节点识别方法[J]. 复杂系统与复杂性科学, 2023, 20(4): 40-46.
WU Y H, LI M D, HU F. A multi-attribute decision-making method based on entropy to identify important nodes in hypernetworks [J]. Complex Systems and Complexity Science, 2023, 20(4): 40-46.
[9] 孙倩倩, 李小南. 区间毕达哥拉斯模糊集的信息度量及其应用[J]. 山东大学学报(理学版), 2019, 54(9): 43-53.
SUN Q Q, LI X N. Information measure of interval valued Pythagorean fuzzy sets and their applications[J]. Journal of Shandong University (Science Edition), 2019, 54(9): 43-53.
[10] 王应明. 一种多指标决策与评价的方法-投影法[J]. 统计研究, 1998, 15(4): 66-69.
WANG Y M.A method for multi-index decision-making and evaluation-projection method[J]. Statistical Research, 1998, 15(4): 66-69.
[11] XU Z S, HU H. Projection models for intuitionistic fuzzy multiple attribute decision making[J]. International Journal of Informa-tion Technology & Decision Making, 2010, 9(2): 267-280.
[12] 邵良杉, 赵琳琳. 区间直觉模糊信息下的双向投影决策模型[J]. 控制与决策, 2016, 31(3): 571-576.
SHAO L S, ZHAO L L. Bidirectional projection method with interval-valued intuitionistic fuzzy information[J]. Control and Decision, 2016, 31(3): 571-576.
[13] 刘小弟, 朱建军, 刘思峰. 犹豫模糊信息下的双向投影决策方法[J]. 系统工程理论与实践, 2014, 34(10): 2637-2644.
LIU X D, ZHU J J, LIU S F. Bidirectional projection decision-making method under hesitant fuzzy information[J]. Systems Engineering Theory & Practice, 2014, 34(10): 2637-2644.
[14] 胡悦, 江登英, 李贺. 基于双向投影法的概率语言多属性群决策[J]. 系统工程与电子技术, 2020, 42(9): 2052-2059.
HU Y, JIANG D Y, LI H. Probabilistic language multi-attribute group decision making based on bidirectional projection method[J]. Systems Engineering and Electronics, 2020, 42(9): 2052-2059.
[15] DING Q Y, WANG Y M, MARK G. An extended TODIM approach for group emergency decision making based on bidirectional projection with hesitant triangular fuzzy sets[J]. Computers & Industrial Engineering, 2021, 151: 106959.
[16] 罗静, 沈淑霞, 王贵君. 基于毕达哥拉斯模糊数双向投影的VIKOR决策方法[J]. 模糊系统与数学, 2022, 36(1): 1-10.
LUO J, SHEN S X, WANG G J. VIKORdecision making method based on bidirectional projection of Pythagorean fuzzy numbers[J]. Fuzzy Systems and Mathematical Sciences, 2022, 36(1): 1-10.
[17] GARG H. A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multi-criteria decision making problem[J]. Journal of Intelligent & Fuzzy Systems, 2016, 31(1): 529-540.
[18] YIN C F, JI F, WANG L, et al. Site selection framework of rail transit photovoltaic power station under interval-valued Pythagorean fuzzy environment[J]. Energy Reports, 2022, 8: 3156-3165.
[19] ZHANG X. Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking methods[J]. Information Sciences, 2016, 330: 104-124.
[20] PENG X, LI W. Algorithms for interval-valued Pythagorean fuzzy sets in emergency decision making based on multiparametric similarity measures and WDBA[J]. IEEE Access, 2019, 7: 7419-7441.
[21] PENG X. New operations for interval-valued Pythagorean fuzzy set[J]. Scientia Iranica, 2019, 26(2): 1049-1076.
[22] 尹东亮, 崔国恒, 黄晓颖, 等. 基于改进得分函数和前景理论的区间毕达哥拉斯模糊多属性决策[J]. 系统工程与电子技术, 2022, 44(11): 3463-3469.
YIN D L, CUI G H, HUANG X Y, et al. Intervalpythagoras fuzzy multi-attribute decision based on improved score function and prospect theory[J]. Systems Engineering and Electronics, 2022, 44(11): 3463-3469.
[23] 沈小雪, 郭嗣琮. 新的直觉模糊熵公式及其应用[J]. 计算机工程与应用, 2013, 49(24): 28-37.
SHEN X X, GUO S C. New intuitive fuzzy entropy formulas and their applications[J]. Computer Engineering and Applications, 2013, 49(24): 28-37.
[24] 柯丽华, 唐华倩, 王其虎, 等. 基于二元联系数可能度函数的区间数排序方法及应用[J]. 系统科学与数学, 2023, 43(2): 417-430.
KE L H, TANG H Q, WANG Q H, et al. Interval number ranking method based on binary connection number possibility function and its application[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(2): 417-430.
[25] 张毛银, 郑婷婷, 郑婉容. 基于指数加权的区间直觉模糊熵及其应用[J]. 计算机科学, 2019, 46(10): 229-235.
ZHANG M Y, ZHENG T T, ZHENG W R. Interval intuitionistic fuzzy entropy based on exponential weighting and its application[J]. Computer Science, 2019, 46(10): 229-235.
[26] LAI Y J, LIU T Y, HWANG C L. TOPSIS for MODM[J]. European Journal of Operational Research, 1994, 76(3): 486-500.
[27] 赵慧冬, 关世霞, 包玉娥. 基于组合赋权的区间型多属性决策方法[J]. 统计与决策, 2012(19): 98-101.
ZHAO H D, GUAN S X, BAO Y E. Interval-based multi-attribute decision-making method based on combinatorial weighting[J]. Statistics and Decision, 2012(19): 98-101.

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