Two methods for priorities of complementary judgement matrices weighted least-square method and eigenvector method

By using the transformation formulas of reciprocal judgement matrix and complementary judgement matrix, this paper defines the concepts of transformation matrices of complementary judgement matrices. A weighted least-square method for priorities of complementary judgement matrices is proposed and a strict theoretical proof is given. Further, based on the transformation matrices, an eigenvector method for priorities of complementary judgement matrices is proposed, and a corresponding iterative algorithm and a consistency checking approach are also presented. Finally, an example is given to illustrate the methods and approach.