Issue: 2025/Vol.35/No.4, Pages
A NEW AND SIMPLE METHOD TO GET THE PRIORITY VECTOR FOR RECIPROCAL MATRICES
Julio Benítez
, Carlos Serra-Jiménez
This is not yet the definitive version of the paper. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article.
Cite as: J. Benítez, C. Serra-Jiménez. A new and simple method to get the priority vector for reciprocal matrices. Operations Research and Decisions 2025: 35(4). DOI 10.37190/ord/205080
Abstract
A new optimization method is proposed to find the priority vector of a non-consistent reciprocal matrix, which leads to the solution of a constrained least squares problem, specially suited for large matrices. Two different approaches are used to solve this problem, the first approach by using the QR decomposition and a second approach by performing the singular value decomposition leading to simple solutions. In addition, a comparison of the proposed method with other methods, used in the consulted bibliography, is made to obtain the priority vector and finally an illustrative example is shown.
Keywords: AHP, comparison matrices, priority vector, least squares method
Received: 25 January 2024 Accepted: 13 May 2025
Published online: 22 May 2025