Efficient vectors in priority setting methodology

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

Authors

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

Journal

Title: Annals of Operations Research

Vol. 332 No. 3

Pages: 743-764

ISSN: 0254-5330

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00Z-QF0

DOI: 10.1007/s10479-023-05771-y

Abstract (EN): The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of pair-wise comparisons. It has been shown that the entry-wise geometric mean of all columns is efficient for any reciprocal matrix. Here, by combining some new basic observations with some known theory, we (1) give a method for inductively generating large collections of efficient vectors, and (2) show that the entry-wise geometric mean of any collection of distinct columns of a reciprocal matrix is efficient. We study numerically, using different measures, the performance of these geometric means in approximating the reciprocal matrix by a consistent matrix. We conclude that, as a general method to be chosen, independent of the data, the geometric mean of all columns performs well when compared with the geometric mean of proper subsets of columns.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 22