Geometry of decision making and the vector space formulation of the analytic hierarchy process

Abstract

We extend the conventional Analytic Hierarchy Process (AHP) to an Euclidean vector space and develop formulations for aggregation of the alternative preferences with the criteria preferences. Relative priorities obtained from such a formulation are almost identical with the ones obtained using conventional AHP. Each decision is represented by a preference vector indicating the orientation of the decision maker's mind in the decision space spanned by the decision alternatives. This adds a geometric meaning to the decision making processes. We utilise the measure of similarity between any two decision makers and apply it for analysing decisions in a homogeneous group. We propose an aggregation scheme for calculating the group preference from individual preferences using a simple vector addition procedure that satisfies Pareto optimality condition. The results agree very well with the ones of conventional AHP.