直觉模糊联盟合作博弈的非线性规划模型  

Quadratic Programming Models of the Intuitionistic Fuzzy Coalition Cooperative Games

作　　者：南江霞 卜红 李登峰 

机构地区：[1]桂林电子科技大学数学与计算科学学院广西高校数据分析与计算重点实验室 [2]福州大学管理学院

出　　处：《运筹与管理》2018年第1期43-48,共6页Operations Research and Management Science

基　　金：国家自然科学基金(71231003;71561008;71461005);广西自然科学基金(2014GXNSFAA118010);桂林电子科技大学研究生教育创新计划资助项目(2016YJCX0)

摘　　要：本文研究联盟是直觉模糊集的合作博弈。首先,给出直觉模糊联盟的定义,并根据Choquet积分的直觉模糊形式,得到直觉模糊联盟合作博弈的区间值特征函数,进一步证明直觉模糊联盟合作博弈的区间值特征函数具有超可加性、凸性、弱超可加性.其次根据区间数的闵可夫斯基距离、区间数的排序及损失函数的定义,建立直觉模糊联盟合作博弈的非线性规划模型,并对其求解得到最优分配.最后给出一个具体的事例说明本文所建立的模型的合理性和有效性。The aim of this paper is to study the cooperative game： the coalition is the intuitionistic fuzzy set. Firstly, intuitionistic fuzzy coalition is defined and the interval characteristic function of the intuitionistic fuzzy coalition cooperative games is deduced based on the intuitionistic fuzzy choquet integral form. Furthermore, the supperadditivity, convexity and weakly supperadditivity of the interval characteristic function are proved. Secondly, the nonlinear programming model for solving the intuitionistic fuzzy coalition cooperative games is con- structed based on the Minkowski distance of interval numbers and the definition of the loss function, and the optimal allocation of the solution is obtained. Finally, a numerical example is examined to demonstrate the validity, superority and applicability of methodology proposed in this methodology.

关 键 词：直觉模糊联盟合作博弈 非线性规划 CHOQUET积分 

分 类 号：O225[理学—运筹学与控制论]