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基于k-可加模糊测度的变权多属性决策分析

章 玲1,周德群1,张佳春2   

  1. 1. 南京航空航天大学 经济与管理学院,江苏 南京 210016；

    2. 上海大学 教务处,上海 200444

  • 收稿日期:2006-08-16 修回日期:2007-03-05 出版日期:2007-07-30 发布日期:2007-07-30

Multi-criteria Decision Making Based on Variable Weights and k-Additive Fuzzy Measures

ZHANG Ling1, ZHOU De-qun1, ZHANG Jia-chun2   

  1. 1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;

    2. Academic Administration Office, Shanghai University, Shanghai 200444, China

  • Received:2006-08-16 Revised:2007-03-05 Online:2007-07-30 Published:2007-07-30

被引次数

28

摘要： k-可加模糊测度具有很好的柔性,本文采用k-可加模糊测度对基于关联的变权多属性决策(Multi-Criteria Decision Making, MCDM)中属性和属性集的重要程度建模；依据模糊测度理论和属性间独立情形下的变权理论定义基于k-可加模糊测度的变权和状态变权的公理体系；依据Marichal熵理论讨论基于关联的变权MCDM问题的k-可加模糊测度的求解,依据模糊积分计算决策方案的综合评价值,以此对方案进行排序并选择最优方案；最后以某煤炭企业选择接替资源为例验证了理论和模型的合理性和可行性.

关键词: 基于关联的多属性决策分析, k-可加模糊测度, Marichal熵, 模糊积分, 变权向量, 状态变权向量

Abstract: As k-additive fuzzy measures are flexible, the importance of decision-making criteria and their coalitions are modelled by k-additive fuzzy measures for the multi-criteria decision-making (MCDM) problems with interaction. The axiomatic system of variable weight and local state variable weight are introduced based on the k-additive fuzzy measures and the existing theories of variable weight. Determination of k-additive fuzzy measures for criteria and their coalitions are discussed based on Marichal entropy. Synthetical values of alternatives are calculated by fuzzy integrals. Finally, an example of selecting the succeed resource for coal enterprice is given to show that the theory and the method are reasonable and feasible.

Key words: multi-criteria decision making with interaction, k-additive fuzzy measures, local state variable weight vector
, Marichal entropy, fuzzy integrals, variable weight vector