A new method for priorities in the analytic hierarchy process

The eigenvector method (EM) proposed by T.L. Saaty has been popularly used at each branching of the Analytic Hierarchy Process. It is an especially effective tool for analysing hierarchical problems. In this paper, we present a least perturbations method (LPM) to derive the priority vectors of judgement matrices and give a simple convergent iterative algorithm and some numerical examples. The LPM is preferable to the EM in several important respects. Theoretical analysis and the numerical results all show that the LPM is feasible and effective.