基于个人超出值的模糊联盟合作博弈最小二乘预核仁

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。

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

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.