ARTIFICIAL NEURAL-NETWORK REPRESENTATIONS FOR HIERARCHICAL PREFERENCESTRUCTURES

In this paper, we introduce two artificial neural network formulations that can be used to assess the preference ratings from the pairwise c omparison matrices of the Analytic Hierarchy Process. First, we introd uce a modified Hopfield network that can determine the vector of prefe rence ratings associated with a positive reciprocal comparison matrix. The dynamics of this network are mathematically equivalent to the pow er method, a widely used numerical method for computing the principal eigenvectors of square matrices. However, this Hopfield network repres entation is incapable of generalizing the preference patterns, and con sequently is not suitable for approximating the preference ratings if the pairwise comparison judgments are imprecise. Second, we present a feed-forward neural network formulation that does have the ability to accurately approximate the preference ratings. We use a simulation exp eriment to verify the robustness of the feed-forward neural network fo rmulation with respect to imprecise pairwise judgments. From the resul ts of this experiment, we conclude that the feed-forward neural networ k formulation appears to be a powerful tool for analyzing discrete alt ernative multicriteria decision problems with imprecise or fuzzy ratio -scale preference judgments. Copyright (C) 1996 Elsevier Science Ltd