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Inconsistency thresholds for incomplete pairwise comparison matrices

Ágoston, Kolos Csaba and Csató, László ORCID: https://orcid.org/0000-0001-8705-5036 (2022) Inconsistency thresholds for incomplete pairwise comparison matrices. Omega International Journal of Management Science, 108 . DOI 10.1016/j.omega.2021.102576

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Official URL: https://doi.org/10.1016/j.omega.2021.102576


Abstract

Pairwise comparison matrices are increasingly used in settings where some pairs are missing. However, there exist few inconsistency indices for similar incomplete data sets and no reasonable measure has an associated threshold. This paper generalises the famous rule of thumb for the acceptable level of inconsistency, proposed by Saaty, to incomplete pairwise comparison matrices. The extension is based on choosing the missing elements such that the maximal eigenvalue of the incomplete matrix is minimised. Consequently, the well-established values of the random index cannot be adopted: the inconsistency of random matrices is found to be the function of matrix size and the number of missing elements, with a nearly linear dependence in the case of the latter variable. Our results can be directly built into decision-making software and used by practitioners as a statistical criterion for accepting or rejecting an incomplete pairwise comparison matrix.

Item Type:Article
Uncontrolled Keywords:Analytic hierarchy process (AHP), Decision analysis, Inconsistency threshold, Incomplete pairwise comparisons, Multi-criteria decision-making
Subjects:Mathematics, Econometrics
DOI:10.1016/j.omega.2021.102576
ID Code:7058
Deposited By: MTMT SWORD
Deposited On:08 Dec 2021 15:26
Last Modified:23 Mar 2022 14:49

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