基于交叉熵和Shapley值的犹豫模糊多属性决策方法

doi:10.12005/orms.2019.0249

运筹与管理 ›› 2019, Vol. 28 ›› Issue (11): 60-67.DOI: 10.12005/orms.2019.0249

基于交叉熵和Shapley值的犹豫模糊多属性决策方法

于倩¹, 侯福均², 曹俊¹, 廖娅¹

1.重庆科技学院工商管理学院,重庆 401331;
2.北京理工大学管理与经济学院,北京 100081

收稿日期:2017-03-26 出版日期:2019-11-25
作者简介:于倩(1984-),女,河北衡水,讲师,博士,研究方向:多属性决策,最优化分析;侯福均(1967-),男,副教授,博士生导师,研究方向:决策理论与方法,运筹与优化,不确定理论及应用。
基金资助:
重庆市教委科技项目(KJQN201901505);重庆市教委重点项目(19SKGH181)

ethod for Multiple Attribute Decision Making Based On Shapley Value and Cross-entropy with Hesitant Fuzzy Set

YU Qian¹, HOU Fu-jun², CAO Jun¹, LIAO Ya¹

1. School of Business and Administration, Chongqing University of Science&Technology, Chongqing 401331, China;
2. School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China

Received:2017-03-26 Online:2019-11-25

摘要/Abstract

摘要： 针对属性值以犹豫模糊集形式给出的多属性决策问题,将Shapley理论和模糊测度进行结合,提出了两种更加能全面融合信息的诱导型广义犹豫模糊混合Shapley平均(I-GHFHSA)算子和诱导型广义犹豫模糊混合Shapley几何(I-GHFHSG)算子,同时详细研究了它们的相关特性。这两种算子综合考虑了数据不同组合的重要性、数据间的关联性,以及数据位置之间的相互依赖性。考虑到有时会存在属性权重以及数据位置权重未知的多属性决策问题,将交叉熵理论和Shapley函数进行结合,建立了最优模糊测度确定模型。最后提出了一种基于I-GHFHSA算子和I-GHFHSG算子的犹豫模糊多属性决策方法,并通过实际案例验证了其可行性和合理性。

关键词: 多属性决策, Shapley函数, 模糊测度, 犹豫模糊集, 交叉熵

Abstract: Based on the combination of Shapley theory and fuzzy measures, an induced generalized hesitant fuzzy hybrid Shapley average(I-GHFHSA)operator and an induced generalized hesitant fuzzy hybrid Shapley geometric(I-GHFHSG)operator are proposed for hesitant fuzzy multi-attribute decision making to utilize information more completely. And some related properties of these operators are studied in detail. The proposed operators can not only globally reflect the interactive characteristics among the hesitant fuzzy arguments themselves and their ordered positions,but also consider the importance of the arguments and their ordered positions. Moreover, considering the existence of the situations where the fuzzy measures of attributes and ordered set are incompletely known,a series of programming models based on cross-entropy and Shapley function are constructed to determine the optimal fuzzy measures. Furthermore, a multi-attribute decision making approach in the form of hesitant fuzzy information based on the proposed operators is presented. Finally, an illustrative example is used to verify the feasibility and rationality of the method.

Key words: multi-attribute decision making(MADM), Shapley function, fuzzy measures, hesitant fuzzy set, cross-entropy

中图分类号:

C934

于倩, 侯福均, 曹俊, 廖娅. 基于交叉熵和Shapley值的犹豫模糊多属性决策方法[J]. 运筹与管理, 2019, 28(11): 60-67.

YU Qian, HOU Fu-jun, CAO Jun, LIAO Ya. ethod for Multiple Attribute Decision Making Based On Shapley Value and Cross-entropy with Hesitant Fuzzy Set[J]. Operations Research and Management Science, 2019, 28(11): 60-67.

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基于交叉熵和Shapley值的犹豫模糊多属性决策方法

ethod for Multiple Attribute Decision Making Based On Shapley Value and Cross-entropy with Hesitant Fuzzy Set

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