Multi-attribute decision making model based on optimal membership and relative entropy

To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete,a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy.Firstly,the definitions of the optimal membership and the relative entropy are given.Secondly,for all alternatives,a set of preference weight vectors are obtained by solving a set of linear programming models whose goals are all to maximize the optimal membership.Thirdly,a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined.Based on this optimal weight vector,the algorithm of deviation degree minimization is proposed to rank all the alternatives.Finally,a decision making example is given to demonstrate the feasibility and rationality of this new model.