🤖 AI Summary
To address the limitations of the conventional Consistency Ratio (CR) in the Analytic Hierarchy Process (AHP)—including low discriminative accuracy, rigid thresholding, sensitivity to matrix order, and poor interpretability—this paper proposes a novel consistency classification method based on triplet Preference Reversal (PR). The method explicitly models local–global inconsistency by detecting directional conflicts between local 3×3 submatrices and the global priority vector, yielding an interpretable consistency metric centered on the preference reversal ratio and maximum reversal magnitude. Implemented within the R package *AHPtools*, the approach integrates k-means clustering and logistic regression for robust classification. Experimental evaluation on synthetic pairwise comparison matrices demonstrates a classification accuracy of 97%, substantially outperforming the CR-based method (50%); the false rejection rate is reduced to 2.6%, significantly enhancing the robustness and credibility of AHP-based decision-making.
📝 Abstract
Assessing consistency in Pairwise Comparison Matrices (PCMs) within the Analytical Hierarchy Process (AHP) poses significant challenges when using the traditional Consistency Ratio (CR) method. This study introduces a novel alternative that leverages triadic preference reversals (PR) to provide a more robust and interpretable assessment of consistency. Triadic preference reversals capture inconsistencies between a pair of elements by comparing the direction of preference derived from the global eigenvector with that from a 3x3 submatrix (triad) containing the same pair, highlighting local-global preference conflicts. This method detects a reversal when one eigen ratio exceeds one while another falls below one, signaling inconsistency. We identify two key features: the proportion of preference reversals and the maximum reversal, which mediate the impact of a PCM's order on its consistency. Using these features simulated PCMs are clustered into consistent and inconsistent classes through k-means clustering, followed by training a logistic classifier for consistency evaluation. The PR method achieves 97% accuracy, significantly surpassing the Consistency Ratio (CR) method's 50%, with a false negative rate of only 2.6% compared to 5.5%. These findings demonstrate the PR method's superior accuracy in assessing AHP consistency, thereby enabling more reliable decision-making. The proposed triadic preference reversal (PR) approach is implemented in the R package AHPtools publicly available on the Comprehensive R Archive Network (CRAN).