引用本文:李胜利,魏翠萍,宋燕红.基于信任关系和互补判断矩阵的群决策方法[J].控制与决策,2020,35(5):1240-1246
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基于信任关系和互补判断矩阵的群决策方法
李胜利1,2, 魏翠萍1, 宋燕红3
(1. 扬州大学数学学院,江苏扬州225002;2. 太原师范学院数学系,山西晋中030619;3. 北京电子科技学院计算机科学与技术系,北京100070)
摘要:
随着信息和网络技术的不断发展,基于社会网络的群决策问题受到越来越多研究者的关注.针对社会网络环境下模糊互补判断矩阵的群决策问题,研究群体共识调整过程和方案选择方法.首先,融合决策者之间的社会关系、身份地位、知识能力3个方面信息来构建决策者两两之间的信任关系;其次,提出一种尽可能减少元素间共识补偿的共识度度量方法,在此基础上建立基于信任关系的共识调整模型,并从理论上证明该模型的有效性;最后通过信任关系矩阵的特征向量中心度分别求出专家的重要性权重,用以集结专家的偏好信息和对方案进行排序选择,算例分析表明了所提出方法的有效性.
关键词:  群决策  共识  一致性  社会网络  信任关系  模糊互补判断矩阵
DOI:10.13195/j.kzyjc.2018.1288
分类号:C934
基金项目:国家自然科学基金项目(71971190).
Group decision making method for fuzzy complementary judgement matrices based on trust relationships
LI Sheng-li1,2,WEI Cui-ping1,SONG Yan-hong3
(1. Department of Mathematics,Yangzhou University,Yangzhou225002,China;2. Department of Mathematics, Taiyuan Normal University,Jinzhong030619,China;3. Department of Computer Science and Technology, Beijing Electronic Science and Technology Institute, Beijing100070,China)
Abstract:
With the development of information and network technology, group decision making problems based on social network have attracted the attention of more and more researchers. This paper focuses on a consensus adjustment process and an alternative selection approach for the group decision making problems with fuzzy complementary judgement matrices under the social network environment. Firstly, we build a trust relationship among decision makers by fusing the information from three aspects: social relation among decision makers, the decision maker’ status, and his/her knowledge ability. Then a consensus index is proposed to minimize consensus compensation between elements as far as possible, a consensus model based on the trust relationship is established, and the feasibility of the model is proved theoretically. Finally, the eigenvector centrality of the trust matrix is used to calculate the weights of experts, which is incorporated into aggregating the individual preference values and ranking alternatives. The effectiveness of the proposed method is further verified by a numerical example.
Key words:  group decision making  consensus  consistency  social network  trust relationship  fuzzy complementary judgement matrices

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