Fundamentals of the Analytic Hierarchy Process

Abstract

The seven pillars of the analytic hierarchy process (AHP) are presented. These include: (1) ratio scales derived from reciprocal paired comparisons; (2) paired comparisons and the psychophysical origin of the fundamental scale used to make the comparisons; (3) conditions for sensitivity of the eigenvector to changes in judgements; (4) homogeneity and clustering to extend the scale from 1–9 to 1-℞; (5) additive synthesis of priorities, leading to a vector of multi-linear forms as applied within the decision structure of a hierarchy or the more general feedback network to reduce multi-dimensional measurements to a uni-dimensional ratio scale; (6) allowing rank preservation (ideal mode) or allowing rank reversal (distributive mode); and (7) group decision making using a mathematically justifiable way for synthesising individual judgements which allows the construction of a cardinal group decision compatible with individual preferences. These properties of the AHP give it both theoretical support and broad application.