Computationally efficient orthogonalization for pairwise comparisons method
Julio Benitez, Waldemar W. Koczkodaj, Adam Kowalczyk
TL;DR
This paper introduces a computationally efficient orthogonalization method for pairwise comparison matrices, enhancing consistency and approximation accuracy using a generalized Frobenius inner product.
Contribution
It presents a novel orthogonalization technique tailored for pairwise comparison matrices, improving computational efficiency and consistency measures.
Findings
The method effectively improves matrix consistency.
Numerical examples demonstrate enhanced approximation quality.
Visualizations support theoretical claims.
Abstract
Orthogonalization is one of few mathematical methods conforming to mathematical standards for approximation. Finding a consistent PC matrix of a given an inconsistent PC matrix is the main goal of a pairwise comparisons method. We introduce an orthogonalization for pairwise comparisons matrix based on a generalized Frobenius inner matrix product. The proposed theory is supported by numerous examples and visualizations.
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