Data perturbations of matrices of pairwise comparisons

This paper deals with data perturbations of pairwise comparison matrices (P CM). Transitive and symmetrically reciprocal (SR) matrices are defined. Cha racteristic polynomials and spectral properties of certain SR perturbations of transitive matrices are presented. The principal eigenvector components of some of these PCMs are given in explicit form. Results are applied to P CMs occurring in various fields of interest, such as in the analytic hierar chy process (AHP) to the paired comparison matrix entries of which are posi tive numbers, in the dynamic input-output analysis to the matrix of economi c growth elements of which might become both positive and negative and in v ehicle system dynamics to the input spectral density matrix whose entries a re complex numbers.