犹豫模糊语言环境下基于Shapley值和三支决策的多属性群决策方法研究
Multi-Attribute Group Decision Making Method Based on Shapley Values and Three-Way Decisions under Hesitant Fuzzy Linguistic Environment
DOI: 10.12677/ORF.2021.111007, PDF,    国家科技经费支持
作者: 王芹芹：对外经济贸易大学，信息学院，北京；刘巧英：惠民县孙武镇中学，山东 滨州；鞠大伟：邮政科学研究规划院，中国邮政集团有限公司邮政研究中心，北京
关键词: 犹豫模糊语言术语集；Shapley值；多属性群决策；三支决策；Hesitant Fuzzy Linguistic Term Set； Shapley Values； Multi-Attribute Group Decision Making； Three-Way Decisions
摘要: 针对属性值为犹豫模糊语言术语集且属性间相互关联的多属性群决策问题，本文提出了基于Shapley值的犹豫模糊语言三支决策模型，在给出每个方案行动策略的同时确定方案的排序。首先，基于决策矩阵和方案的两两比较偏好关系，考虑属性间的关联关系，利用Shapley值构建以群体非一致性最小化为目标的优化模型，求得属性权重和正负理想解；然后，基于求得的属性权重和正负理想解，构建每位决策者对每个方案的综合损失矩阵，以TOPSIS思想中的相对贴近度作为条件概率确定个体三支决策，并建立以个体和群体三支决策偏差最小化为目标的优化模型，求得群体三支决策，给出每个方案应采取的最佳行动策略；最后，运用相对贴近度对方案进行排序，给出行动策略为“接受”的方案集中方案的排序。
Abstract: In order to solve multi-attribute group decision making (MAGDM) problems in which the assessment values of alternatives are expressed by hesitant fuzzy linguistic term set (HFLTS) and the attributes are interrelated, this paper proposes a three-way decisions method based on Shapley val-ues for MAGDM under hesitant fuzzy linguistic environment. Firstly, based on decision matrices and preference relations between alternatives, considering the interdependent or interactive phenomena among attributes, the Shapley values are used to construct the programming model by minimizing group inconsistency index to determine the attribute weights and positive (negative) ideal solutions. Then, based on the obtained attribute weights and positive (negative) ideal solutions, the comprehensive loss matrix of each alternative is constructed for each decision maker, and taking the relative closeness degree in TOPSIS method as conditional probability, the individual three-way decisions are obtained. Furthermore, to determine the group three-way decisions, a programming model is established by minimizing the deviations between individual and group three-way decisions. Finally, the relative closeness degrees of alternatives are calculated to obtain the ranking order of alternatives whose actions are acceptable.
文章引用：王芹芹, 刘巧英, 鞠大伟. 犹豫模糊语言环境下基于Shapley值和三支决策的多属性群决策方法研究[J]. 运筹与模糊学, 2021, 11(1): 47-62. https://doi.org/10.12677/ORF.2021.111007

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