A new method for priorities of fuzzy complementary judgment matrix

The aim of this paper is to propose a method for priorities from fuzzy complementary judgment matrix, which can be either consistent or inconsistent. In the method, firstly, based on property of fuzzy complementary consistent judgment matrix, the deviation term is introduced and deviation function is constructed. Then, in order to minimize the inconsistency of fuzzy complementary matrix, mathematical programming model is constructed. The formula of computing priorities is deduced by applying Lagrangepsilas method of multipliers to the mathematic programming model and an algorithm for priority of fuzzy complementary judgment matrix is given. Finally, a numerical example is given to demonstrate proposed method is feasible and practical.