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.

Improving consistency classification: An innovative benchmark‐based approach for the AHP

“…For the other batch of PCMs we use a variant of the method suggested by Bose (2022) to generate PCMs that are reasonably consistent and more like PCMs that would be assigned by a rational decision maker. Such PCMs are simulated by randomly choosing for each element of a benchmark PCM one of the three nearest ratios from the Fundamental Scale.…”

“…In Section 2 we have outlined a mediation model for the proposed consistency with Priority Preference Range as a mediator. An examination of the preference range for (a) random PCMs, (b) random PCMs with improved consistency by three successive applications of Harker's technique and (c) intentional PCMs simulated as in Bose (2022) reveals significant difference in Priority Preference Ranges and as its partial consequence, the consistency measure.…”

“…For the other batch of PCMs we use a variant of the method suggested by Bose (2022) Ranges and as its partial consequence, the BCI consistency measure.…”

“…The reason for this choice though lies in its straight‐forwardness and simplicity which contrasts with the difficulty of simulating ‘non‐random, reasonably consistent’ PCMs. In this study such reasonably consistent PCMs representative of the judgements of a rational decision maker are simulated using a variant of a process proposed by Bose (2022). These PCMs are hereafter referred to as intentional PCMs.…”

“…The potency of our framework derives from two pivotal factors: the inherent Priority Preference Range within the principal eigenvector and the order of the PCM. Statistical thresholds for consistency are established using a technique based on simulated, logical PCMs, proposed by Bose [2022]. This rigorous method ensures an unbiased, objective and pragmatic evaluation of consistency, eliminating the subjectivity inherent in arbitrary thresholds based on random PCMs.…”