Combining different prioritization methods in the analytic hierarchy process synthesis

A multicriteria approach for combining prioritization methods within the analytic hierarchy process (AHP) is proposed. The leading assumption is that for each particular decision problem and related hierarchy, AHP must not necessarily employ only one prioritization method (e.g. eigenvector method). If more available methods are used to identify the best estimates of local priorities for each comparison matrix in the hierarchy, then the estimate of final alternatives' priorities should also be the best possible, which is in natural concordance with an additive compensatory structure of the AHP synthesis. The most popular methods for deriving priorities from comparison matrices are identified as candidates (alternatives) to participate in AHP synthesis: additive normalization, eigenvector, weighted least-squares, logarithmic least-squares, logarithmic goal programming and fuzzy preference programming. Which method will be used depends on the result of multicriteria evaluation of their priority vectors' performance with regard to suggested deviation and rank reversal measures. Two hierarchies with matrices of size 3-6 are used to illustrate an approach.