Robustness to rank reversal in pairwise comparison matrices based on uncertainty bounds

• Published in: European journal of operational research Vol. 304; no. 2; pp. 676 - 688
• Main Authors: Faramondi, Luca, Oliva, Gabriele, Setola, Roberto, Bozóki, Sándor
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2023
• Subjects: Pairwise comparison matrices; Rank reversal; Uncertainty; Pairwise comparison matrices; Uncertainty; Rank reversal
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2022.04.010

•Quantification of the minimum degree of uncertainty able to cause rank reversal phenomena in Pairwise Comparison Matrices.•Methodology able to assess robustness to rank reversal also when decision makers do not specify the uncertainty associated to the provided pairwise comparisons.•Extension of the classical consistency-driven workflow by additionally checking that data uncertainty is sufficiently small. In the context of decision making, pairwise comparisons matrices (PCMs) based on a ratio scale are essential for deriving absolute preferences from relative comparisons. Such techniques are based on Subject Matter Experts (SMEs), which express their relative judgements on pairs of alternatives, providing pairwise comparison information, also in the case of incomplete or uncertain data, in order to obtain an absolute ranking about the alternatives. In this work, we propose a novel approach, complementary to measuring inconsistency, able to integrate and evaluate the concept of uncertainty in PCMs in order to verify the credibility of the final outcome. Such approach characterizes how SMEs’ uncertainty reflects into rank reversal. This is done via a novel optimization problem aiming to identify the smallest perturbations of the pairwise comparison values which result in an altered ranking of alternatives, e.g., reverting the ranking for at least a pair of alternatives.