Issue: 2020/Vol.30/No.2, Pages 77-89
SATISFACTION OF THE CONDITION OF ORDER PRESERVATION. A SIMULATION STUDY
Jiří Mazurek
, Konrad Kułakowski
Cite as: J. Mazurek, K. Kulakowski. Satisfaction of the condition of order preservation. A simulation study. Operations Research and Decisions 2020: 30(2), 77-89. DOI 10.37190/ord200205
Abstract
We examine the satisfaction of the condition of order preservation (COP) concerning different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order from 3 to 9, where a priority vector is derived both by the eigenvalue (eigenvector) method (EV) and the geometric mean (GM) method. Our results suggest that the GM method and the EV method preserve the COP almost identically, both for the less inconsistent matrices (with Saaty’s consistency index below 0.10), and the more inconsistent matrices (Saaty’s consistency index equal to or greater than 0.10). Further, we find that the frequency of the COP violations grows (almost linearly) with the increasing inconsistency of MPCMs measured by Koczkodaj’s inconsistency index and Saaty’s consistency index, respectively, and we provide graphs to illustrate these relationships.
Keywords: pairwise comparisons, eigenvalue method, geometric mean method, condition of order preservation,numerical simulation
Received: 4 February 2019 Accepted: 20 July 2020