On the Convergence of the Pairwise Comparisons Inconsistency Reduction Process
Abstract
This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into a consistent PC matrix which is generated by the geometric means of rows of a given inconsistent PC matrix. The distance-based inconsistency indicator was defined in 1993 for pairwise comparisons. Its convergence was analyzed in 1996 (regretfully, with an incomplete proof; finally completed in 2010). However, there was no clear interpretation of the convergence limit which is of considerable importance for applications and this study does so.
Keywords
Cite
@article{arxiv.1505.01325,
title = {On the Convergence of the Pairwise Comparisons Inconsistency Reduction Process},
author = {Waldemar W. Koczkodaj and Jacek Szybowski},
journal= {arXiv preprint arXiv:1505.01325},
year = {2015}
}
Comments
16 page, 1 figure. For pairwise comparisons, the normalized vector o geometric means (GM) is equal to the normalized principal eigenvector (EV) for consistent matrices. For inconsistent matrices, the limit is "make it consistent" process is GM (specifically, not EV). This contribution finally concludes the discussion "GM or EV" originated in 1980s