模糊合作对策在凸几何上的Shapley函数  

The Shapley function for cooperative fuzzy games on convex geometries

作　　者：孟凡永[1] 张强[1] 

机构地区：[1]北京理工大学管理与经济学院,北京100081

出　　处：《系统工程与电子技术》2011年第6期1305-1309,共5页Systems Engineering and Electronics

基　　金：国家自然科学基金(70771010;70801064;71071018)资助课题

摘　　要：首先给出了模糊合作对策在凸几何上的定义。通过相应的公理体系,论述了模糊合作对策在凸几何上的Shapley函数。为了更好了解此类模糊合作对策,研究了两类特殊模糊合作对策在凸几何上的Shapley函数,并证明了其存在性和唯一性,拓展了模糊合作对策的研究范围。最后通过算例分析来具体说明局中人在此类模糊合作对策上的收益值。The definition for cooperative fuzzy games on convex geometries is given.The Shapley function for cooperative fuzzy games on convex geometries is studied by corresponding axiomatic system.Meantime,in order to better understand the cooperative fuzzy games on convex geometries,the Shapley functions for two special kinds of cooperative fuzzy games on convex geometries are studied,and their existence and uniqueness are also proved,which extend the studying scope of cooperative fuzzy games.Finally,numerical examples are offered to explain the players＇ payoffs on these kinds of cooperative fuzzy games.

关 键 词：模糊合作对策 凸几何 Shapley函数 多线性扩展 CHOQUET积分 

分 类 号：O225[理学—运筹学与控制论] O159[理学—数学]