EURO 2025 Leeds
Abstract Submission

450. Size independence of the consistency index for pairwise comparison matrices in AHP

Invited abstract in session TC-10: Pairwise comparisons and preference relations 1, stream Multiple Criteria Decision Aiding.

Tuesday, 12:30-14:00
Room: Clarendon SR 1.06

Authors (first author is the speaker)

1. Tsuneshi Obata
Faculty of Science and Engineering, Otemon Gakuin University
2. Shunsuke Shiraishi
Faculty of Applied Information Science, Hiroshima Institute of Technology

Abstract

In the Analytic Hierarchy Process (AHP), pairwise comparisons play a crucial role. Various consistency indices have been proposed to assess inconsistency in these comparisons. Among these, the Consistency Index (CI) proposed by Saaty is defined using the principal eigenvalue of the pairwise comparison matrix. In our previous research, we introduced an alternative index based on the relationship between a coefficient of the characteristic polynomial and the consistency of comparisons.
Saaty proposed a fixed threshold of 0.1 for CI as a guideline for an acceptable level of consistency, regardless of matrix size. However, whether this threshold represents an equivalent level of consistency across different matrix sizes, i.e., different numbers of evaluation criteria, remains unclear. In this study, we analyze the relationship between consistency and matrix size by examining pairwise comparison matrices constructed from a subset of evaluation criteria. Based on this analysis, we propose a fundamental property that a size-independent consistency index should satisfy.
Furthermore, we refine our previously proposed index to ensure that it satisfies this property and demonstrate that it coincides with an existing consistency index. Finally, we visualize the relationship between matrix size and consistency index values using randomly generated pairwise comparison matrices, providing insights into the impact of matrix size on consistency evaluation.

Keywords

Status: accepted

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