The complete set of efficient vectors for a pairwise comparison matrix

• Tipo: Artigo em Revista Científica Internacional
• Data: 2025

Autores

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

Revista

Título: Computational and Applied Mathematics

Vol. 44

ISSN: 0101-8205

Editora: Birkhäuser Boston

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-017-TM7

DOI: 10.1007/s40314-024-03062-1

Abstract (EN): Efficient vectors are the natural set from which to choose a cardinal ranking vector for a pairwise comparison matrix. Such vectors are the key to certain business project selection models. Many ways to construct specific efficient vectors have been proposed. Yet, no previous method to produce all efficient vectors was known. Here, using some graph theoretic ideas, as well as a numerical extension technique, we show how to generate inductively all efficient vectors for any given pairwise comparison matrix. We apply this method to give a matricial proof of the fact that the set of efficient vectors, as well as some of its important subsets, are piecewise linearly connected. In addition, we determine explicitly all efficient vectors for a 4-by-4 pairwise comparison matrix. Several examples are provided.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 17