Interval estimation of priorities in the AHP

This paper extends and modifies the Analytic Hierarchy Process (AHP) and the Synthetic Hierarchy Method (SHM) of priority estimation to accommodate random data in the pairwise comparison matrices. It employs a Cauchy distribution to describe the pairwise comparison of alternatives in Saaty matrices, and shows how to modify these matrices in order to handle random data. The use of random data yields Saaty matrices that are not reciprocally symmetrical. Several variants of the AHP are then modified (i) to accommodate reciprocally asymmetric matrices, and (ii) to allow each priority estimate to be expressed on an interval of possible values, rather than as a single discrete point. The merits of interval estimation are illustrated by an example.