Issue: 2025/Vol.35/No.4, Pages 1-10
A NEW AND SIMPLE METHOD TO GET THE PRIORITY VECTOR FOR RECIPROCAL MATRICES
Julio Benítez
, Carlos Serra-Jiménez
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), 1-10. 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 uses QR decomposition, and the second approach performs 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 2025 Accepted: 13 May 2025
Published online: 22 May 2025