Study on optimum value of Grey Matrix Game Based on Token of Grey Interval Number

Profit and loss matrix in the matrix game is made up of grey interval number because of that there are unsymmetrical information, finite knowledge and rational. This kind of game is called grey matrix game. Using thoughts of grey systems and theories of systems engineering, the paper studies pure strategy optimum grey game value and its solution, defines the concept of grey pure strategy solution, proves the sufficient and necessary condition of profit and loss relation and grey pure strategy solution. And based on this, studies the problems of optimum grey game value and it's solution under mixed strategy condition, sets up concepts of the most optimism and pessimism profit and loss matrix, and the concept of the optimization grey game value, studies the solution algorithm of max (min) grey game value. In the end, taking the decision-making of coal stores for winter warm as an example, the results show that it acquires well effect with the theories above.