A novel approach for detecting and adjusting inconsistencies in AHP models

In the Analytic Hierarchy Process (AHP), addressing inconsistencies in pairwise comparison matrices (PCMs) is vital for ensuring the accuracy of decision-making. This study introduces a novel consistency indicator, the Consistent Ratio and Cycles (CRC), which simultaneously identifies and corrects both cardinal and ordinal inconsistencies. An optimisation algorithm based on CRC is developed to modify PCMs with minimal changes, effectively reducing inconsistencies. To enhance ordinal consistency, the optimal non-one-element equivalent PCM (ONE-PCM) is proposed, ensuring precise calculation of three-way cycles. Two optimisation models are constructed for discrete and continuous entries, aiming to make minimal adjustments to the original PCM. Additionally, to tackle over-correction, a model that integrates decision-maker suggestions is presented. The proposed algorithm demonstrates superior performance in achieving better consistency, higher accuracy, and ease of implementation compared to existing methods, as evidenced by comprehensive comparisons and analyses.