Multiobjective matrix game with vague payoffs

There are always uncertainty, incompleteness and imprecision existing in decision making information. These are why fuzzy set theory is commonly used in decision making. Vague set can indicate the decision makers' preference information in terms of favor against and neutral. When dealing with uncertain information, vague set indicates information more abundant than fuzzy set. According to the theories of multiobjective decision making and fuzzy game, the multiobjective two-person zero-sum matrix game, whose payoff values are vague values is researched. Firstly, the concept of vague set and the order function is introduced. Then the model of multiobjective two-person zero-sum matrix game based on vague set is described. Thirdly, two solutions of vague multiobjective two-person zero-sum matrix game are discussed: one is making the vague multiobjective game problem crisp through the order function of vague values, then turning it into single objective game; the other method is turning vague multiobjective game problem into vague single objective game problem first, then making it crisp through the order function of vague values. Finally, numerical examples are given to apply the proposed methods.