A Novel Scale for Inconsistency Reduction in the Pair-Wise Comparison Matrices

Linguistic pairwise comparison of the attributes forms the basis for prioritization of the attributes and also aids in calculating the weights for each attribute for final decision making in the Analytical Hierarchy Process (AHP). This process may sometimes lead to inconsistencies in the pairwise comparison matrix, and the acceptability of the method is checked with respect to a measure known as Consistency Ratio (CR), whose upper limit is fixed as 0.1. The present work attempts to develop a new methodology in which the pairwise attribute comparison matrix is formed in such a manner that the decision maker can safely eliminate the process of consistency check. In this endeavor, a new scale called as 'Relative Percentage Supremacy' (RPS) scale with three variations namely, High, Moderate and Low is introduced and employed. The proposed methodology is successfully applied to Saaty's 'Distance', 'Optics', 'National Wealth' and 'Weights Estimation' problems for which the actual weights are available. Also, the method has been applied on Saaty's 'Buying a House' problem and a comparison of the results with the results of already existing scales is done. The Relative Percentage Supremacy scale with Moderate value is found to yield results close to the Saaty's actual values in the majority of the time and the applicability of the other variations are also discussed.