Study on the model of grey matrix game based on grey mixed strategy—solution of grey linear program model on grey matrix game

Abstract

The key to grey matrix game lies in the solution of grey linear program model. On this paper, we have proved the necessary and sufficient condition of the existence of grey basic feasible solution in grey linear program problem. We have also certified that grey basic feasible solution corresponds to grey apex of grey feasible field. Then, having proved that any point of grey convex set can be linearly expressed by the grey apex of the grey convex set, we proved that grey optimal value of the objective function corresponds to the grey apex of the grey convex in the grey linear program problem of the grey matrix game. Therefore, grey optimal value of it certainly corresponds to some unity grey numbers of grey element in the grey game matrix Atilde(otimes).