The Analysis of the Principal Eigenvector of Pairwise Comparison Matrices
نویسنده
چکیده
This paper develops the spectral properties of pairwise comparison matrices (PCM) used in the multicriteria decision making method called analytic hierarchy process (AHP). Perturbed PCMs are introduced which may result in a reversal of the rank order of the decision alternatives. The analysis utilizes matrix theory to derive the principal eigenvector components of perturbed PCMs in explicit form. Proofs are presented for the existence of rank reversals. Intervals over which such rank reversals occur are also established as function of a continuous perturbation parameter. It is proven that this phenomenon is inherent in AHP even in the case of the slightest departure from consistency. The results are demonstrated through a sample illustration.
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