STATIC STRATEGIC GAME APPROACH FOR MULTIPLE ATTRIBUTE DECISION MAKING PROBLEMS WITHOUT WEIGHT INFORMATION

In multiple attribute decision making (MADM) problems, it is usual that no single alternative works best for all performance attributes, so it is difficult to select the best from among multiple available alternatives, especially in the situation that the attribute weights are completely unknown. This research propose a game theory-based approach (GMADM) which incorporates static strategic game theory into MADM problems to derive the attribute weights, and then utilize the weight arithmetic average (WAA) operator to aggregate the attribute values corresponding to each alternative and rank alternatives by means of aggregated information. In GMADM, each attribute is regarded as a player taking part in the game, and the player's strategy is to select a value from interval [0, 1] to assign corresponding attribute weight, and the player's utility is defined as the agreement between the ranking of alternatives determined by the aggregated information and the one determined by the attribute values. When the game is in equilibrium status, the strategy profile is the best attribute weights which make each player have good utilities. Moreover, the equilibrium solution of game and the resolution method for the MADM problem without weight information have also been developed. Finally, the result of proposed approach for a practical MADM problem and its comparisons with one of other methods are given.