Uncertain number reciprocal fuzzy preference relations and uncertain number complementary judgment matrix

The consistency of the uncertain number (interval number, triangular fuzzy number and trapezoidal fuzzy number) complementary judgment matrix is studied. The concept of the describing matrix is introduced which associates the uncertain number complementary judgment matrix with the preference information given by experts. The describing matrix is usually named complementary judgment matrix. After giving the properties of consistently describing matrix, the paper proposes methods for obtaining consistently describing matrix of uncertain number complementary judgment matrix which can be consistently described. These concepts and methods keep practicable when it is to crisp number complementary judgment matrix. Finally, an illustrative example is given.