Efficient vectors for double perturbed consistent matrices

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Susana Borges Furtado (Author) FEP

Journal

Title: Optimization

Vol. 72 No. 11

Pages: 2679-2701

ISSN: 0233-1934

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 2 Citations

Scopus

Other information

Authenticus ID: P-00W-M6G

DOI: 10.1080/02331934.2022.2070067

Abstract (EN): Efficiency, also called Pareto optimality, is a fundamental concept in multi-criteria decision making. In this paper we describe all the efficient vectors for an n x n double perturbed consistent matrix A, that is, a pairwise comparison matrix obtained from a consistent one by perturbing two entries above the main diagonal and the corresponding reciprocal entries. We also give conditions under which, when deleting a certain entry of an efficient vector for A, we obtain an efficient vector for the corresponding (n - 1) x (n - 1) principal submatrix of A. As a simple consequence of our work, we obtain the result by Abele-Nagy et al. (2018) which states that the principal eigenvector of a double perturbed consistent matrix is efficient. This paper extends the recent paper by Cruz et al. (2021) in which the description of the efficient vectors for simple perturbed consistent matrices is given.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 23