Transitive matrices and their applications
In Section 2, transitive matrices and symmetrically reciprocal (SR) matrices are defined and the spectral properties of these matrices are described. In most of the applied problems, certain pairs of elements of a transitive matrix are perturbed, such that its transitivity is lost, but it remains in SR. In Section 3, the quite simple spectral properties of a perturbed transitive matrix are presented. In Section 4, a controversial aspect of analytic hierarchy process (AHP), the phenomenon of rank reversal is considered. It is proven that a rank reversal is inherent in the AHP, if its input transitive matrix is subjected to certain arbitrarily small perturbations.
scientific article; zbMATH DE number 1419879