基于个人超出值的区间值合作博弈新的求解模型  

New models of interval values cooperative games based on player excess

作　　者：南江霞[1,2] 李梦祺 张茂军 NAN Jiang-xia;LI Meng-qi;ZHANG Mao-jun(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China;Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Guilin University of Electronic Technology,Guilin 541004,China;School of Business,Suzhou University of Science and Technology,Suzhou 215009,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]桂林电子科学大学广西高校数据分析与计算重点实验室,广西桂林541004 [3]苏州科技大学商学院,江苏苏州215009

出　　处：《控制与决策》2020年第7期1681-1688,共8页Control and Decision

基　　金：国家自然科学基金项目(71231003,71561008,71461005,71801060);广西自然科学基金项目(2014GXNSFAA118010,2017GXNSFBA198182)。

摘　　要：从个人超出值的视角研究特征函数为区间值的合作博弈和联盟为模糊集的无限模糊联盟区间值合作博弈.首先,利用区间值距离公式定义个人超出值;然后,建立最小化所有局中人个人超出值的最优化模型,进一步得到两类区间值合作博弈的显式解析解,并证明该解的性质;最后,通过数值实例验证所提出区间值合作博弈求解模型的实用性与有效性,为区间值合作博弈提供一种新的求解思路.Based on player excess,this paper studies the cooperative games in which the characteristic functions are expressed with interval values,and also the cooperative game with infinite number of fuzzy coalitions and interval values characteristic functions.In order to avoid the interval subtraction,player excesses are defined by the distance between interval values.Then,the sum of all player excesses is minimized and the solutions of two types of interval values cooperative games are obtained by constructing a mathematical programming model.Moreover,some useful properties of the solutions are discussed.Finally,a numerical example is given to illustrate the applicability and effectiveness of the proposed model which provides a new method for solving interval values cooperative games.

关 键 词：区间值合作博弈 区间值距离 个人超出值 联盟超出值 

分 类 号：O225[理学—运筹学与控制论]