Inverse sensitive analysis of pairwise comparison matrices

In the analytic hierarchy process (AHP), the consistency of pairwise comparison is measured by the consistency index (CI) value of pairwise comparison matrices. The CI value is defined by the size and the principal eigenvalue of comparison matrix, and the larger the CI value is, the less consistent pairwise comparison is. In this paper, we propose the estimation method of consistency intervals, in which the pairwise comparison value can move without exceeding given CI threshold. The proposed method is based on the eigenvalue method but does not calculate the principal eigenvalue and eigenvector at all, and hence, the method enables quick estimation. The method also enables us to detect which pairwise comparison leads to inconsistency of pairwise comparison and what extent the consistency can be improved, if the CI value of an original comparison matrix is large. Several numerical examples show that the proposed method is practically efficient.