Evaluation Techniques for Paired Ratio-Comparison Matrices in a Hierarchical Decision Model

A hierarchical decision model for the ranking of discrete alternatives has been proposed by T. Saaty. This procedure has achieved some popularity in the operations research community. Among the components of the model is the deduction of a vector of weights from a matrix of paired ratio comparisons. We consider several evaluation techniques for this purpose including the Perron-Frobenius right eigenvector which was recommended by Saaty. In the absence of any theoretical basis for choice of a particular evaluation technique, these techniques are subjected to a variety of numerical tests. Among the conclusions, there seems to be no basis for preference for the Perron-Frobenius right eigenvector. Thus, there is no reason to believe that use of the model as originally proposed is generating desirable solutions. However, a nonlinear least-squares fit, initialized with a heuristic evaluation technique, performs very well. Before reliable use can be made of the overall decision model, theoretical, numerical, and empirical development of all the components should be furthered.