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Handling Uncertainty in the Analytic Hierarchy Process: a Stochastic Approach

This paper describes a methodology for handling the propagation of uncertainty in the analytic hierarchy process (AHP). In real applications, the pairwise comparisons are usually subject to judgmental errors and are inconsistent and conflicting with each other. Therefore, the weight point estimates provided by the eigenvector method are necessarily approximate. This uncertainty associated with subjective judgmental errors may affect the rank order of decision alternatives. A new stochastic approach is presented to capture the uncertain behavior of the global AHP weights. This approach could help decision makers gain insight into how the imprecision in judgment ratios may affect their choice toward the best solution and how the best alternative(s) may be identified with certain confidence. The proposed approach is applied to the example problem introduced by Saaty for the best high school selection to illustrate the concepts introduced in this paper and to prove its usefulness and practicality.