Method of hybrid multi-attribute decision making based on relative entropy weight and projection algorithm

The problem of hybrid multi-attribute decision making, which integrates with interval numbers and linguistic fuzzy numbers, and incomplete information on attribute weights, is studied. Based on the relative entropy weight and projection algorithm, a new method of hybrid multi-attribute decision making is presented. First of all, the definitions of closeness degree and relative entropy are given, and the method of transforming the interval numbers and linguistic fuzzy numbers into triangular fuzzy numbers is presented. Secondly, by solving a set of linear programming models whose goals are to maximize the closeness degree, a series of preference weight vectors which are partial for each alternative are obtained, and then the optimal weight vector is got by aggregating the preference weight vectors through establishing a relative entropy weight model. Thirdly, based on this optimal weight vector, the projection algorithm is presented to rank order for all alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new method.