Transitive matrices and their applications Original Research Article

Transitive matrices and symmetrically reciprocal (SR) matrices are defined and spectral properties of certain SR perturbations of transitive matrices are studied. The results are applied to a multicriteria decision making method, the analytic hierarchy process (AHP), which uses an SR matrix with positive entries. A proof is given that rank reversal is inherent in this method, if its input matrix is perturbed.