AHP INCONSISTENCY REDUCTION THROUGH TWO GREEDY ALGORITHMS APPLICATION

Abstract

The purpose of this paper is to present two greedy algorithms that can improve the consistency of an AHP Matrix adjusting the original comparisons with discrete values. The first one aims to preserve the original pairwise comparisons as much as possible and the second one improves the consistency ratio as much as possible. Both algorithms were compared with other 11 methods, from the past and recent literature, through three numerical examples: one inconsistent matrix with 9 criteria, one with 8 criteria and the last one, a highly inconsistent matrix with 7 criteria. Our method performed better than all the other ones. The proposed method can be used independently from the techniques to derive the eigenvector, eigenvalue or the consistent ratio, and naturally, in order to make a sensible comparison, all methods were compared using the same techniques. The Conservative Algorithm solution, gains in quality because it can preserve most of the original information, however the consistent ratio value stays just below the consistency threshold, in the other hand, the Progressive Algorithm gains in quantity, because it aims to reduce the consistent ratio to zero or near zero. Our approach offers two types of solutions, that are fast and near optimal.