Relative entropy aggregation method in group decision making based on different types of preference information

The problem of group decision making based on different types of preference information is studied. Experts usually provide four forms of preference information to the set of alternatives by their personalities during group decision making, which includes preference ordering and utility value giving the orders of alternatives directly, reciprocal judgement matrix and fuzzy complementary judgement matrix obtained by pair comparison between two alternatives. First the computational formulae are given to uniform three types of preference information, i.e. preference ordering, reciprocal judgement matrix and fuzzy complementary judgement matrix, into the form of utility value. Then a relative entropy aggregation optimal model is proposed from the concept of relative entropy, and the solution of this model is also given. Finally two examples are analyzed to show the effectiveness of this model.