Efficiency of the principal eigenvector of some triple perturbed consistent matrices

• Type: Article in International Scientific Journal
• Date: 2022-05

Authors

Fernandes, R (Author) Other; Susana Borges Furtado (Author) FEP

Journal

Title: European Journal of Operational Research

Vol. 298 No. 3, 1

Pages: 1007-1015

ISSN: 0377-2217

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 7 Citations

Other information

Authenticus ID: P-00V-BN1

DOI: 10.1016/j.ejor.2021.08.012

Abstract (EN): In this paper we study the efficiency of the principal eigenvector of a pairwise comparison matrix obtained from a consistent one by perturbing three entries above the main diagonal, and the corresponding reciprocal entries, in a way that there is a submatrix of size 2 containing three of the perturbed entries and not containing a diagonal entry. Our approach uses the characterization of vector efficiency based on the strongly connection of a certain digraph associated with the matrix. By imposing some conditions on the magnitudes of the perturbations, we identify a class of matrices for which the principal eigenvector is efficient. This class is the union of two subclasses such that the digraph of all the matrices in the same subclass contains a common cycle with all vertices. The matrices we analyse include the simple perturbed consistent matrices, as well as a subfamily of the double perturbed consistent matrices, whose principal eigenvector efficiency has been studied in the literature. For completeness, we also include some examples of triple perturbed matrices for which the principal eigenvector is not efficient. Explicit expressions for the characteristic polynomial and the principal eigenvector of the triple perturbed consistent matrices we consider are also given. © 2021 Elsevier B.V.

Language: English

Type (Professor's evaluation): Scientific