Efficiency of any weighted geometric mean of the columns of a reciprocal matrix

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

Authors

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

Journal

Title: Linear Algebra and Its Applications

Vol. 680

Pages: 83-92

ISSN: 0024-3795

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00Z-5FR

DOI: 10.1016/j.laa.2023.10.001

Abstract (EN): We focus upon the reciprocal matrix component of the often discussed Analytic Hierarchy Process and its approximation by a consistent matrix formed from an efficient vector. It is known that a vector is efficient for a reciprocal matrix A if and only if a certain digraph is strongly connected. Here, we give a transparent and relatively simple matricial proof of this important result. Then we show that any Hadamard weighted geometric mean of the columns of a reciprocal matrix is efficient. This is a major generalization of the known result that the Hadamard geometric mean of all columns is efficient, and of the recent result that the geometric mean of any subset of the columns is efficient.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10