Abstract:The inconsistency of pairwise comparisons remains difficult to interpret in the absence of acceptability thresholds. The popular 10% cut-off rule proposed by Saaty has recently been applied to incomplete pairwise comparison matrices, which contain some unknown comparisons. This paper refines these inconsistency thresholds: we uncover that they depend not only on the size of the matrix and the number of missing entries, but also on the undirected graph whose edges represent the known pairwise comparisons. Therefore, using our exact thresholds is especially important if the filling in patterns coincide for a large number of matrices, as has been recommended in the literature. The strong association between the new threshold values and the spectral radius of the representing graph is also demonstrated. Our results can be integrated into software to continuously monitor inconsistency during the collection of pairwise comparisons and immediately detect potential errors.
From: László Csató [view email]
[v1]
Thu, 30 Oct 2025 21:24:34 UTC (21 KB)
[v2]
Wed, 28 Jan 2026 14:39:50 UTC (22 KB)
[v3]
Mon, 13 Apr 2026 14:40:05 UTC (26 KB)
[v4]
Fri, 22 May 2026 12:40:46 UTC (26 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。