2021/02/28 by Kolos Csaba Ágoston, Łászló Csató, László Csató · 4 citations
Computer Science · Decision Sciences · #Data Management and Algorithms #Multi-Criteria Decision Making #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.1016/j.omega.2021.102576
openalex publication_date 2021/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.