Analyzing analytic hierarchy process matrices by regression

In the analytic hierarchy process (AHP) the decision maker makes comparisons between pairs of attributes or alternatives. In real applications the comparisons are subject to judgmental errors. Many AHP-matrices reported in the literature are found to be such that the logarithm of the comparison ratio can be sufficiently well modeled by a normal distribution with a constant variance. On the basis of this model we present the formulae for the evaluation of the standard deviations of the estimates of the AHP-weights obtained by regression analysis. In order to eliminate the effect of an outlier in the comparison ratios a robust regression technique is elaborated, and compared with the eigenvector method and the logarithmic least squares regression. A dissimilarity matrix approach is presented for the statistical simultaneous comparisons of the AHP-weights. The results are illustrated by simulation experiments.