求解支付值为区间直觉模糊数的矩阵对策的线性规划方法

提出了支付值为区间直觉模糊集的矩阵对策定义及其解的概念, 将求解局中人的极大-极小与极小-极大策略问题转化为求解一对辅助的非线性多目标规划, 进而转化为一对易于求解的原始-对偶线性规划. 数值实例表明了所提方法的有效性和实用性. 所提出的区间直觉模糊集矩阵对策理论与方法既是对经典矩阵对策理论的发展, 又可为解决其他带有区间直觉模糊信息的对策问题提供新的途径.

The linear programming approach to matrix games with payoffs of interval-valued intuitionistic fuzzy numbers

The definition of a matrix game with payoffs of interval-valued intuitionistic fuzzy sets(IVIF-sets) and the concept
of its solutions are given. The maximin and minimax strategies of two players can be obtained by solving a pair of primaldual linear programming models derived from two auxiliary nonlinear multi-objective programming models. A numerical example shows that the proposed method is effective and practical. The concept and methodology of matrix games with payoffs of IVIF-sets are not only an extension of those of classical matrix games, but also provide a new route for solving matrix games with interval-valued intuitionistic fuzzy information.