Theory of the Analytic Hierarchy Process. Part 2.1

Abstract

Highlights are given of the decision making theory the Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP) both of which deal with the measurement of tangible and intangible criteria in relative terms by using paired comparisons. The fundamental scale of absolute numbers for representing judgments is introduced and the principal right eigenvector is shown to be the necessary vector of priorities derived from the possibly inconsistent matrix of comparisons of homogeneous elements. A method of synthesis of priorities is proposed. Rank preservation and reversal are discussed. When independent, the alternatives can be rated one at a time with respect to the criteria using intensities. Negative priorities are also introduced. This paper will be followed soon by two other papers.