Inconsistency Adjustment in the AHP Using the Complete Transitivity Convergence Algorithm

In the analytic hierarchy process (AHP), the pairwise comparisons are generally applied to determine the weights of multiple criteria at the same level or the ranks of alternatives under a specific criterion. However, when one must rate the importance of multiple criteria and each criterion uses different measurement units, or when one must determine the ranks of alternatives under a qualitative criterion, there is always an inconsistency problem. This research, based on complete transitivity of preference, develops a single stage recursive algorithm to find out outliers, and enables the pairwise comparison matrix to approximate complete transitivity. Identifying and adjusting of outliers are proven to be identical with the robust priority estimation method. Inconsistency adjustment using the complete transitivity convergence algorithm in a single stage can be applied in the multi-criteria decision problems with high calculation economy.