Using Inconsistency Reduction Algorithms in Comparison Matrices to Improve the Performance of Generating Random Comparison Matrices with a Given Inconsistency Coefficient Range

The aim of this paper is to present a new method for generating random pairwise comparison matrices with a given inconsistency ratio (CR) interval using inconsistency reduction algorithms. Pairwise comparison (PC) is a popular technique for multi-criteria decision-making, its purpose is to assign weights to the compared entities, thus ranking them from best to worst. The presented method combines the traditional random generation of comparison matrices supported by inconsistency reduction algorithms: the “Xu and Wei” algorithm and the “Szybowski” algorithm. This paper presents research that shows an increase in performance when generating such matrices relative to the standard random comparison matrix generation procedure using the “Szybowski” algorithm. The other algorithms also improve the process, but to a lesser extent, making the “Szybowski” supporting algorithm the preferred solution for the new process. As a result of the research, a free online tool “PC MATRICES GENERATOR” has also been made available to efficiently generate a large number of comparison matrices with a given CR factor range, any matrix size, and any number of matrices, enabling much more efficient and less time-consuming research in many fields that use comparison matrices, as the analytic hierarchy/network process (AHP/ANP), ELECTREE, PAPRIKA, PROMETHE, VIKOR or the Best-Worst method (BWM).