Data perturbations of matrices of pairwise comparisons

Data perturbations of matrices of pairwise comparisons

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Article ID: iaor20021371
Country: Netherlands
Volume: 101
Issue: 1
Start Page Number: 401
End Page Number: 425
Publication Date: Jan 2001
Journal: Annals of Operations Research
Authors: ,
Abstract:

This paper deals with data perturbations of pairwise comparison matrices (PCM). Transitive and symmetrically reciprocal (SR) matrices are defined. Characteristic 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 PCMs occurring in various fields of interest, such as in the analytic hierarchy process (AHP) to the paired comparison matrix entries of which are positive numbers, in the dynamic input–output analysis to the matrix of economic growth elements of which might become both positive and negative and in vehicle system dynamics to the input spectral density matrix whose entries are complex numbers.

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