Pairwise comparison matrices with uniformly ordered efficient vectors

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

Autores

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

Revista

Título: International Journal of Approximate Reasoning

Vol. 173

ISSN: 0888-613X

Editora: Elsevier

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 1 Citação

Outras Informações

ID Authenticus: P-013-XQK

DOI: 10.1016/j.ijar.2024.109265

Abstract (EN): Our primary interest is understanding reciprocal matrices all of whose efficient vectors are ordinally the same, i.e., there is only one efficient order (we call these matrices uniformly ordered, UO). These are reciprocal matrices for which no efficient vector produces strict order reversals. A reciprocal matrix is called column ordered (CO) if each column is ordinally the same. Efficient vectors for a CO matrix with the same order of the columns always exist. For example, the entry- wise geometric mean of some or all columns of a reciprocal matrix is efficient and, if the matrix is CO, has the same order of the columns. A necessary, but not sufficient, condition for UO is that the matrix be CO and then the only efficient order should be satisfied by the columns (possibly weakly). In the case n = 3, CO is necessary and sufficient for UO, but not for n > 3 . We characterize the 4-by-4 4 UO matrices and identify the three possible alternate orders when the matrix is CO (and give entry-wise conditions for their occurrence). We also describe the simple perturbed consistent matrices that are UO. Some of the technology developed for this purpose is of independent interest.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 16