A Sensitivity Study of T. Saaty’s Analytic Hierarchy Process

The sensitivity of four approximate Saaty estimates for a priority vector in the Analytic Hierarchy Process (AHP) was studied using MATLAB tools. This method involves structuring the problem hierarchically, conducting pairwise comparisons of elements, and calculating the priority vector at each level of hierarchy. To model expert errors in these pairwise comparisons, random variables were introduced into the elements of the consistent Saaty matrix. Purpose: to study the sensitivity of the AHP by calculating coefficients for the linear convolutions of the four Saaty estimates for the priority vector. A linear combination of these estimates was equated to the precise priority vector, and a series of SLAEs n×4 (n = ) for the weight coefficients is resolved using the pseudoinverse matrix method along with Tikhonov regularization. Results: it has been statistically established that the initial two Saaty estimates for the priority vector were insignificant, as their weight coefficients were not substantial and nearly reached zero. In contrast, the weight coefficients of the third and fourth estimates were stable and greater than zero. Practical significance: the results obtained can be applied in a proprietary software product for evaluating alternatives in decision-making without involving the MATLAB commercial engineering calculation environment.