Vague linguistic matrix game approach for multi-criteria decision making with uncertain weights

Vague linguistic numbers are especially adaptive to describe the evaluations of alternatives in multi-criteria decision making. Such description reveals the DM's preference and hesitant degree simultaneously. For handling the uncertainty in setting the weights of criteria, a fuzzy matrix game related with the initial decision matrix is established. This fuzzy game model is then transformed to a linear programming. By solving this programming, the weights of criteria are obtained. The weighted arithmetic average operator of vague linguistic numbers yields the aggregated ranking values of alternatives. An example illustrates the procedure of the proposed method.