On Eigenvalues and Eigenvectors of Perturbed Pairwise Comparison Matrices

Abstract

This work studied eigenvalues and eigenvectors of a class of perturbed pairwise comparison matrices (PCMs). This type of matrices arises from Analytical Hierarchical Process with inconsistency comparison. By employing some nice structures of the PCMs, we show that the object dimension of size n ≥ 3 can be reduced into a case of size 3, hence simplify the studies.