Abstract: There is few research on properties of interval number complementary judgment matrix in literatures at home and abroad,so the priority approach research is short of the base of corresponding theory.For the reason that the flaws are given above,this paper conducts the research on properties and priority of interval number complementary judgment matrix.On the grounds of the definition of interval number complementary judgment matrix,this paper proposes concepts of complete consistency,restricted max-max transitivity and weak transitivity for interval number complementary judgment matrix,studies their relations which show that these concepts of consistency for interval number complementary judgment matrix are in accord with the consistency of human thinking.Based on the consistent propriety,nonlinear programming methods for priorities of interval number complementary judgment matrix which is illustrated by a numerical number are set up.

Key words: interval number complementary judgment matrix, complete consistency, restricted max-max transitivity, priority