Consistency re-evaluation in analytic hierarchy process based on simulated consistent matrices

Abstract

A new approach to re-evaluating consistency in the analytic hierarchy process (AHP) using simulated consistent matrices is presented. The proposed consistency evaluation method makes use of statistically significant deviations from the average consistency measure for the simulated matrices. This addresses most of the deficiencies of the conventional consistency ratio (CR) method. A pairwise comparison matrix (PCM) is adjudged inconsistent by the proposed method if its consistency measure exceeds the modeled consistency threshold. Comparison of the consistency evaluation for simulated nearly-consistent matrices using the proposed method shows a statistically significant reduction of the order-specific bias in comparison with the CR method. The proportion of nearly consistent matrices which are evaluated as ‘inconsistent’ increases more than three-folds when the evaluation is done using the CR method. Several examples are presented which illustrate the advantages of the proposed method and differences in classification with the CR approach. Evaluation of consistency using the proposed method of statistically derived thresholds from simulated, nearly consistent matrices is more nuanced and objective, as well as intuitive in its interpretability.