一类具有模糊支付的矩阵对策模型与分析

A Kind of Matrix Game Models with Fuzzy Payoff and An Analysis on it

本文考察营销中一个两人零和对策模型。由于市场的不确定性,其支付为区间数或模糊数。当每一支付的发生概率给定时,原对策模型转化为一特殊的决策模型,文中给出了这类模型的一个算法。对于原对策模型,文中作出了对策值的上界与下界估计,给出了优化策略的定义并证明了存在性。文中还给出了近似优化策略的一个目标规划模型,及其应用的简单示例。最后,讨论了进一步研究的问题。

In this paper we consider a two-person zero-sum game model with payoff to be an interval number or a fuzzy number due to the uncertainty of the market. When the probability of each payoff is given the original game model will become a special kind of decision making models. We give an algorithm of this model. As to original game model, we find out the upper and lower bound of such game value. In the paper we give a definition of an optimal strategy and show the existence of it. On the basis of the definition we give a goal programming model for the approximate optimal strategy. A simple example is included to show the application of model. At the end of the paper a question for further study is raised and discussed.