Pairwise comparison matrices with uniformly ordered efficient vectors

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Susana Borges Furtado (Author) FEP; Johnson, CR (Author) Other

Journal

Title: International Journal of Approximate Reasoning

Vol. 173

ISSN: 0888-613X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 1 Citation

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16