Efficiency analysis for the Perron vector of a reciprocal matrix

• Tipo: Artigo em Revista Científica Internacional
• Data: 2024

Autores

Susana Borges Furtado (Autor) FEP; Johnson, CR (Autor) Outra

Revista

Título: Applied Mathematics and Computation

Vol. 480

ISSN: 0096-3003

Editora: Elsevier

Indexação

ISI Web of Knowledge - 5 Citações

Scopus - 5 Citações

Outras Informações

ID Authenticus: P-010-P39

DOI: 10.1016/j.amc.2024.128913

Abstract (EN): In prioritization schemes, based on pairwise comparisons, such as the Analytical Hierarchy Process, it is necessary to extract a cardinal ranking vector from a reciprocal matrix that is unlikely to be consistent. It is natural to choose such a vector only from efficient ones. One of the most used ranking methods employs the (right) Perron eigenvector of the reciprocal matrix as vector of weights. It is known that the Perron vector may not be efficient. Here, we focus extending arbitrary reciprocal matrices and show, constructively, that two different extensions any fixed size always exist for which the Perron vector is inefficient and for which it is efficient, with the following exception. If B is consistent, any reciprocal matrix obtained from B by adding one row and one column has efficient Perron vector. As a consequence of our results, we obtain families of reciprocal matrices for which the Perron vector is inefficient. These include known classes of such matrices and many more. We also characterize the 4-by-4 reciprocal matrices with inefficient Perron vector. Some prior results are generalized or completed.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 14