| λ模糊测度及其Mbius变换和关联系数间关系的推导 |
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| 引用本文： | 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].山东大学学报(理学版),2007,42(7):33-37. |
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| 作者姓名： | 章 玲 周德群 |
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| 作者单位： | 南京航空航天大学经济与管理学院,江苏南京210016 |
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| 基金项目： | 基金项目：国家自然科学基金资助项目（90510010）;教育部博士点基金资助项目（20050287026）;国家软科学研究计划资助项日（2006GXQ38184） |
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| 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.
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| 关 键 词： | 多属性决策分析 λ模糊测度 Mbius变换 关联系数 |
| 文章编号： | 1671-9352（2007）07-0033-05 |
| 修稿时间： | 2006-10-10 |
Research on the
relationships among the |
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| ZHANG Ling and ZHOU De-qun.Research on the
relationships among the[J].Journal of Shandong University,2007,42(7):33-37. |
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| Authors: | ZHANG Ling and ZHOU De-qun |
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| Institution: | College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China |
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| 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. |
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| Keywords: | multiple attributes decision making λ fuzzy measures Mbius transform interaction representation |
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