模糊联盟合作对策的平均树解

运筹学学报 ›› 2012, Vol. 16 ›› Issue (4): 77-85.

模糊联盟合作对策的平均树解

聂翠平^1,2 张强¹

1. 北京理工大学管理与经济学院 2. 石家庄学院数学与信息科学系

出版日期:2012-12-15 发布日期:2012-12-15
通讯作者: 聂翠平 E-mail:niecuiping7@163.com
基金资助:
国家自然科学基金(Nos. 71071018, 71201089), 高等学校博士学科点专项科研基金(No. 20111101110036)

The average tree solution in graph games with fuzzy coalitions

NIE Cuiping^1,2 ZHANG Qiang¹

1. School of Management and Economics, Beijing Institute of Technology 2. Department of Mathematics and Information Science, Shijiazhuang College

Online:2012-12-15 Published:2012-12-15
Contact: NIE Cuiping E-mail:niecuiping7@163.com

摘要/Abstract

摘要： 给出图对策中平均树解的拓展形式, 证明其是满足分支有效性和分支公平性的唯一解. 针对具有模糊联盟的图对策, 提出了一种模糊分配, 即模糊平均树解. 当模糊联盟图对策为完全图对策时, 模糊平均树解等于模糊Shapley值. 最后, 讨论了模糊平均树解与模糊联盟核心之间的关系, 并进行了实例论证.

关键词: 图对策, 模糊平均树解, 模糊Shapley值, 模糊联盟, 连凸性

Abstract: In this paper, the generalization of the average tree solution is considered. It is the unique solution satisfying component fairness and component efficiency when the crisp graph game is cycle-free. We propose the fuzzy average tree solution that is an imputation for the graph game with fuzzy coalitions. Moreover, on a complete graph game with fuzzy coalitions the fuzzy average tree solution coincides with the fuzzy Shapely value. Finally, we give the relationship between the fuzzy average tree solution and the fuzzy core.

Key words: graph game, fuzzy average tree solution, fuzzy Shapley value, fuzzy coalition, link-convex

中图分类号:

O225

聂翠平, 张强. 模糊联盟合作对策的平均树解[J]. 运筹学学报, 2012, 16(4): 77-85.

NIE Cuiping, ZHANG Qiang. The average tree solution in graph games with fuzzy coalitions[J]. Operations Research Transactions, 2012, 16(4): 77-85.

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