Affiliations: [a] Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Kende utca 13-17, 1111 Budapest, Hungary | [b] Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, Fővám tér 8, 1093 Budapest, Hungary. abele-nagy.kristof@sztaki.mta.hu; bozoki.sandor@sztaki.mta.hu
Correspondence:
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Address for correspondence: Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Kende utca 13-17, 1111 Budapest, Hungary
Abstract: Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the latter’s components is at least as close to the corresponding element of the pairwise comparison matrix as the one of the former’s components is, and the latter’s approximation is strictly better in at least one position. A pairwise comparison matrix is called simple perturbed if it differs from a consistent pairwise comparison matrix in one element and its reciprocal. One of the classical weighting methods, the eigenvector method is analyzed. It is shown in the paper that the principal right eigenvector of a simple perturbed pairwise comparison matrix is efficient. An open problem is exposed: the search for a necessary and sufficient condition of that the principal right eigenvector is efficient.
