Least Square Prenucleolus of Fuzzy Coalition Cooperative Games Based on Excesses of Players

doi:10.12005/orms.2021.0217

Operations Research and Management Science ›› 2021, Vol. 30 ›› Issue (7): 77-82.DOI: 10.12005/orms.2021.0217

• Theory Analysis and Methodology Study • Previous Articles Next Articles

Least Square Prenucleolus of Fuzzy Coalition Cooperative Games Based on Excesses of Players

NAN Jiang-xia¹, WEI Li-xiao², LI Deng-feng², ZHANG Mao-jun¹

1. School of Business, Suzhou University of Science and Technology, Suzhou 215009, China;
2. School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 611731, China

Received:2019-06-01 Online:2021-07-25

基于个人超出值的模糊联盟合作博弈最小二乘预核仁

南江霞¹, 魏骊晓², 李登峰², 张茂军¹

1.苏州科技大学商学院,江苏苏州 215009;
2.电子科技大学经济与管理学院,四川成都 611731

作者简介:南江霞(1978-), 女,山西运城人, 博士,教授, 硕士生导师, 研究方向为模糊非合作博弈和模糊合作博弈理论及其应用;魏骊晓(1994-), 女,河南安阳人,博士研究生,研究方向为模糊非合作博弈和模糊合作博弈理论及其应用;李登峰(1965-), 男, 广西博白人,博士,教授, 博士生导师,研究方向为经济管理决策与对策;张茂军(1977-),男,山西人,博士,教授,硕士生导师,研究方向为博弈论及其在金融的应用研究。
基金资助:
国家自然科学基金资助项目(72061007,71961004);广西科技基地和人才专项(AD19245100);桂林电子科技大学研究生教育创新计划资助项目(2019YCXS082)

Abstract

Abstract: In this paper, the least square prenucleolus based on excesses of players as a new solution concept is proposed in infinite fuzzy coalition cooperative games. A quadratic programming model of the least square prenucleolus based on excesses of players is constructed, and some important properties on the solution of this model are given. It is also shown that the least square prenucleolus of any infinite fuzzy coalition cooperative game based on excesses of players is equal to the equalizer solution and the lexicographical solution of the infinite fuzzy coalition cooperative game based on excesses of players. Furthermore, it is proved that the least square prenucleolus of any classical cooperative game based on excesses of players is equal to the least square prenucleolus of an infinite fuzzy coalition cooperative game with Owen’s multilinear extension based on excesses of players. Finally, a numerical example is given to show the applicability and validity of the proposed model.

Key words: infinite fuzzy coalition cooperative games, excesses of players, excesses of coalitions, the least square prenucleolus

摘要： 本文给出了基于个人超出值的无限模糊联盟合作博弈最小二乘预核仁的求解模型,得到该模型的显式解析解,并研究该解的若干重要性质。证明了:本文给出的无限模糊联盟合作博弈的最小二乘预核仁与基于个人超出值的相等解(The equalizer solution),基于个人超出值的字典序解三者相等。进一步证明了:基于Owen线性多维扩展的无限模糊联盟合作博弈的最小二乘预核仁与基于个人超出值的经典合作博弈最小二乘预核仁相等。最后,通过数值实例说明本文提出的无限模糊联盟合作博弈求解模型的实用性与有效性。

关键词: 无限模糊联盟合作博弈, 个人超出值, 联盟超出值, 最小二乘预核仁

CLC Number:

O225

NAN Jiang-xia, WEI Li-xiao, LI Deng-feng, ZHANG Mao-jun. Least Square Prenucleolus of Fuzzy Coalition Cooperative Games Based on Excesses of Players[J]. Operations Research and Management Science, 2021, 30(7): 77-82.

南江霞, 魏骊晓, 李登峰, 张茂军. 基于个人超出值的模糊联盟合作博弈最小二乘预核仁[J]. 运筹与管理, 2021, 30(7): 77-82.

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Least Square Prenucleolus of Fuzzy Coalition Cooperative Games Based on Excesses of Players

基于个人超出值的模糊联盟合作博弈最小二乘预核仁

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