The Seven Pillars of the Analytic Hierarchy Process

Abstract

The seven pillars of the AHP, some highlights of which are discussed in the paper, are: 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 judgments; 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 unidimensional normalized ratio scale, that is thus an absolute “dominance” scale, free of a measurement unit; 6) allowing rank preservation (ideal mode) or allowing rank reversal (distributive mode); and 7) group decision making using a mathematically justifiable way for synthesizing individual judgments which allows the construction of a cardinal group decision compatible with the individual preferences.