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运筹学学报 >

2015 , Vol. 19 >Issue 2: 61 - 71

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2015.02.007

运筹学

基于多维线性扩展的模糊联盟合作对策tau值性质与计算方法

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  • 1. 福州大学经济与管理学院, 福州 350108

收稿日期: 2014-12-11

  网络出版日期: 2015-06-15

基金资助

国家自然科学基金(Nos. 71231003, 71171055), 国家教育部新世纪优秀人才支持计划(No. NCET-10-0020), 福建省社会科学规划项目(No. 2012C022), 高等学校博士学科点专项科研基金 (No. 20113514110009)

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Properties and solving method of  tau-value for fuzzy cooperative games with multilinear extension form

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  • 1. School of Economics and Management, Fuzhou University, Fuzhou 350108, China

Received date: 2014-12-11

  Online published: 2015-06-15

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摘要

研究模糊联盟合作对策tau值的计算方法及其性质. 利用多维线性扩展方法定义了模糊联盟合作对策的tau值, 证明了其存在性、唯一性等性质, 并推导出基于多维线性扩展凸模糊联盟合作对策tau值的计算公式. 研究结果发现, 基于多维线性扩展的模糊联盟合作对策tau值是对清晰联盟合作对策tau值的扩展, 而清晰联盟合作对策tau值仅是其特例. 特别地, 对于凸模糊联盟合作对策, 利用其tau值计算公式, 可进一步简化求解过程.

关键词： 模糊联盟合作对策; 多维线性扩展; tau值; 对策论; 模糊集

本文引用格式

杨靛青, 李登峰 . 基于多维线性扩展的模糊联盟合作对策tau值性质与计算方法[J]. 运筹学学报, 2015 , 19(2) : 61 -71 . DOI: 10.15960/j.cnki.issn.1007-6093.2015.02.007

Abstract

In this paper, we research the solving method and properties of  tau-value for fuzzy cooperative games. Using the multilinear extensive method, we define the tau-value for fuzzy cooperative games, prove its existence, uniqueness and other properties, and deduce the computational formulae of the  tau-value for convex fuzzy cooperative games. The research result shows that the  tau-value for the fuzzy cooperative games with multilinear extension form is an extension of the  tau-value for crisp cooperative games. Especially, for the convex fuzzy cooperative games, the computational process of the  tau-value can be simplified.

Key words： fuzzy cooperative game; multilinear extension; tau-value; game theory; fuzzy set

参考文献

Tijs S. Bounds for the core and the \tau-value [M]//Game Theory and Mathematical Economics. North-Holland: Amsterdam, 1981, 123-132.
 
Driessen T.  Cooperation Games, Solutions and Application [M]. Netherlands: Kluwer Academic Publisher, 1988.


Casas-mendez B, Garcia-jurado I, Nouweland A, et al. An extension of the \tau-value to games with coalition structures [J].  European Journal of Operational Research, 2003, 148: 494-513.
 
王文文, 孙浩, 韩卫彬. 图限制下合作对策的 \tau 值 [J]. 运筹学学报, 2011, 15: 75-84.

 吴美容, 孙浩, 陈辉. 双准均衡合作对策 \tau 值的公理化 [J].  运筹学学报, 2014, 18: 119-125.

 Owen G. Multilinear extensions of games [J].  Management Sciences, 1972, 18: 64-79.

 Meng F, Zhang Q. The Shapley function for fuzzy cooperative games with multilinear extension form [J].  Applied Mathematics Letters, 2010, 23: 644-650.

 孟凡永, 张强, 孙红霞. 模糊合作对策上的Banzhaf函数 [J].  系统工程学报, 2012, 27: 1-8.

 Meng F, Zhang Q. The symmetric Banzhaf value for fuzzy games with a coalition structure [J].  International Journal of Automation and Computing, 2012, 9: 600-608.

 Borkotokey S, Hazarika P, Mesiar R. Fuzzy bi-cooperative games in multilinear extension form [J].  Fuzzy Sets and Systems, 2015, 259: 44-55.

 Tijs S. An axiomatization of the  \tau-value [J].  Mathematical Social Sciences, 1987, 13: 177-181.

 Branzei R, Dimitrov D, Tijs S.  Models in Cooperative Game Theory [M]. Berlin: Springer, 2008.

 Shapley L. Cores of convex games [J].  International Journal of Game Theory, 1971, 1: 11-26.

 
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