λ模糊测度及其Mbius变换和关联系数间关系的推导

λ模糊测度及其Mbius变换和关联系数间关系的推导

章玲,周德群

南京航空航天大学经济与管理学院, 江苏南京 210016

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 章玲

Research on the relationships among the λ fuzzy measures, Mbius representation and interaction representation

ZHANG Ling , ZHOU De-qun

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

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: ZHANG Ling

摘要/Abstract

摘要： λ模糊测度常用于基于关联的多属性决策(multiple attribute decision making, MADM)问题中的属性和属性集重要程度建模,为了能充分地利用决策者可能提供的各类信息辅助多属性决策分析行为,在Grabisch给出的一般有限离散集上模糊测度与其Mbius变换和关联系数间相互转换关系的基础上,定义了λ模糊测度的Mbius变换和关联系数并研究了三者间的相互转换关系,最后给出算例解释λ模糊测度及其Mbius变换和关联系数间转换关系在实际MADM问题中的应用.

关键词: 多属性决策分析, λ模糊测度, 关联系数 , Mbius变换

Abstract: λ fuzzy measures are often utilized to model the importance of the attributes and their coalitions for the multi-attribute decision making (MADM) problems with interaction. In order to make full use of the information provided by the decision maker to assist the decision making, the concepts of the Mbius representation and interaction representation of the λ fuzzy measures are given and the relationships among the λ fuzzy measures, their Mbius representation and interaction representation are deduced based on the research of Grabisch, and an example is proposed to illustrate the application of the transforms of the λ fuzzy measures and their Mbius representation and interaction representation in practice problems of MADM.

Key words: interaction representation , Mbius transform, λ fuzzy measures, multiple attributes decision making

中图分类号:

N945.25

章玲,周德群 . λ模糊测度及其Mbius变换和关联系数间关系的推导[J]. J4, 2007, 42(7): 33-37 .

ZHANG Ling ,ZHOU De-qun . Research on the relationships among the λ fuzzy measures, Mbius representation and interaction representation[J]. J4, 2007, 42(7): 33-37 .

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