Mathematical properties of dominant analytic hierarchy process and concurrent convergence method

This study discusses the mathematical structure of the dominant AHP and the concurrent convergence method which were originally developed by Kinoshita and Nakanishi. They introduced a new concept of a regulating alternative into an analyzing tool for a simple evaluation problem with a criterion set and an alternative set. Although the original idea of the dominant AHP and the concurrent convergence method is unique, the dominant AHP and the concurrent convergence method are not sufficiently analyzed in mathematical theory. This study shows that the dominant AHP consists of a pair of evaluation rules satisfying a certain property of overall evaluation vectors. This study also shows that the convergence of concurrent convergence method is guaranteed theoretically.