Improving the Analytical Hierarchy Process Methodology Through Implementation of Consistency Ratio-Based Weights for Multi-Expert Judgement
Open AccessThe Analytical Hierarchy Process (AHP) is a methodology for multi-criteria decision making where complex decision problems are disaggregated into pairwise comparisons. A critical procedure in AHP is the confirmation of an expert’s logical validity through the calculation of a consistency ratio (Saaty, 2008). For analysis where multiple experts are utilized to establish the judgement scale, variability in consistency is not accounted for on an individual basis. Furthermore, inconsistent feedback results in either reduction of the dataset, or reevaluation of the survey by the expert; both conditions confounding the methodology. Developing a Consistency Ratio-Based Weight (CRW AHP) for multi-expert judgement provides improvements in aggregated consistency. This proposed methodology augments the analysis to increase the impact of judgement from experts with favorable consistency scores, while eliminating the conditions for data loss. The AHP methodology, in any multi-criteria decision problem being supported by feedback from more than one expert, benefits from the proposed improvements because the conditions for data loss or re-surveying are avoided. Industry utilization for the proposed method can range from the selection process of drug therapies to studies in accident precursors; topics addressed as part of the overall research validation strategy. The CRW AHP methodology requires the definition of a hierarchical structure to set criteria for assessment. Experts are then surveyed to generate a priority matrix representing assessment of all pairwise comparisons, and a max eigenvalue is calculated to represent an intermediate criteria weight. These results are tested for consistency to ensure an appropriate level of transitivity and reciprocity has been achieved by the expert being surveyed. Based on the consistency ratios of all experts, a weight is then calculated to augment the max eigenvalues prior to aggregation. The intent of the methodology is to increase the aggregated consistency ratio without retraining or normalizing the experts as part of an re-surveying effort. The results of the research provided four key deductions regarding the analytical functionality of the CRW AHP methodology. First, with a p-value of 0.047 per paired T test, a statistically significant difference between the calculated consistency ratios between CRW AHP and AHP was measured (α=0.05). The consistency ratio from the CRW AHP method was lower, and thus more consistent when compared to AHP. Second, with a p-value of 0.167 per paired T test, no statistical difference between the standard error for the calculated criteria weights between the two methodologies was measured (α=0.05). Third, with a p-value of 0.156 per equivalence testing, the two methodologies resulted in non-equivalent results when calculating criteria weights as part of the AHP assessment. Lastly, with a p-value of 0.014 per two-sample T test, a statistically significant bimodal correlation between consistency ratios and negative versus positive AHP outcomes was measured. The research efforts have helped define a novel methodology for utilizing an expert’s consistency ratio to calculate weights for proportionally adjusted aggregation of max eigenvalues in an AHP analysis. Furthermore, the CRW AHP methodology enables intaking non-normalized or non-reevaluated expert judgement without requiring training or modulation of pairwise comparisons during the survey process. CRW AHP therefore offers a novel and efficient method of addressing issues with inconsistency without incurring additional costs associated with data loss or re-surveying.
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