Combination Generalized Grey Target Decision Method for Mixed Attributes Based on Zero-Sum Game Theory

Generalized grey target decision method (GGTDM) for mixed attributes has different decision-making bases (DMBs) owing to different mechanisms. A combination GGTDM based on zero-sum game theory is proposed to obtain the desirable decision-making effect by fully using the characteristics and information of different DMB based GGTDMs. First, two players are set to compete in the zero-sum game. One player takes different DMB based GGTDMs as the set of his strategies, while the other player adopts the alternatives as the other player’s set of strategies. Then, the ranking values of all alternatives decided by different GGTDMs are converted into scores by equivalent way, and the scores are regarded as the payoffs of the two players. Next, the zero-sum game based linear programming model is built to obtain the solutions when reaching the Nash equilibrium. Finally, the combination decision-making values of all alternatives can be calculated based on the strategy solutions for all GGTDMs. And the decision making is based on the value with which the smaller the better. The application analysis verifies that the proposed method has its feasible and can make full use of the advantages of different DMB based GGTDMs and avoid their shortcomings.