Efficient vectors for simple perturbed consistent matrices

• Type: Article in International Scientific Journal
• Date: 2021

Authors

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

Journal

Title: International Journal of Approximate Reasoning

Vol. 139

Pages: 54-68

ISSN: 0888-613X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 12 Citations

Scopus - 12 Citations

Other information

Authenticus ID: P-00V-HDV

DOI: 10.1016/j.ijar.2021.09.007

Abstract (EN): In the Analytic Hierarchy process, a method used in Decision Making, it may be important to approximate a pairwise comparison matrix (PC matrix) by a consistent one. In this context, the notion of efficient vector for a PC matrix arises. In this paper we describe all efficient vectors for an n x n comparison pairwise matrix obtained from a consistent one by perturbing one entry above the main diagonal, and the corresponding reciprocal entry. As a consequence, we give a simple proof of the result obtained by K. Abele-Nagy and S. Bozoki (2016) that states that the principal eigenvector of a simple perturbed consistent matrix is efficient. In addition, we consider a set of non-efficient vectors associated with the simple perturbed consistent matrix and describe all the efficient vectors that dominate each vector in that set.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15