Representatives-Based Interval Analytic Hierarchy Process

In the analytic hierarchy process (AHP), a decision problem is structured hierarchically as criteria and alternatives. Both criteria priority weights and alternatives' local evaluations are obtained from pairwise comparison matrices. In this study, we reconsider a pairwise comparison matrix among alternatives since comparing tasks is burdensome for a decision maker as the increase of alternatives. We introduce two representative alternatives, which are unique to a decision maker. So, it is practical for a decision maker to compare each representative alternative to all the alternatives. Although the number of given comparisons is less than the conventional method, we estimate the lack of comparisons of pairs of alternatives from a possibilistic view. In the comparison matrix, each alternative has two kinds of comparisons, and each representative alternative is compared to all the alternatives. To reflect the two kinds of inconsistency among comparisons, we denote the evaluation of an alternative as an interval. We formulate the problem to derive the interval evaluations from the proposed comparison matrix.