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

The analytic hierarchy process (AHP) is a cornerstone of multi-criteria decision analysis, enabling well-informed choices across diverse contexts. This paper introduces an original benchmark-based framework designed to enhance the precision of consistency classification for pairwise comparison matrices (PCMs) within the AHP methodology. This innovative approach quantifies the discrepancy between a given PCM and its benchmark matrix, comprising comparison ratios that faithfully reflect the relative preferences encapsulated within principal eigenvector values, thereby capturing the true degree of coherence. To ensure benchmark alignment with human perception, elements of the benchmark PCM are further rounded to the nearest values on the Fundamental Scale. 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. Our approach rectifies the inconsistencies in the conventional CR method that yields false positives for PCMs of orders 3 and 4, and false negatives for higher orders. By harnessing customized benchmarks and eschewing random matrices, our framework systematically confronts the inherent consistency challenges within AHP, thus enhancing its decision-making capability. The practical utility of our approach is aptly demonstrated through AHPtools, an R-based library package designed to showcase our novel consistency evaluation method. The demonstration of the package in Appendix B will facilitate readers to easily apply our methodology to real-world PCM classification scenarios within the AHP. In conclusion, our benchmark-based framework heralds a transformative era in consistency classification within the AHP, empowering real-world multi-criteria decision-making with unprecedented precision and reliability, and ushering in a new paradigm of informed and astute outcomes.