The Analytic Hierarchy Process without the theory of oskar perron

Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States

Publication date: Jan, 2014

Journal: International Journal of the Analytic Hierarchy Process
Vol.: 5- Issue: 2

Abstract: It is known and has been mathematically proven that the principal eigenvector is necessary for deriving priorities from judgments in the Analytic Hierarchy Process (AHP). According to the work of Oskar Perron, the principal eigenvector can be obtained as the limiting power of a positive matrix. In this paper we show that the principal eigenvector does not need the theory of Perron for its existence based on the fact that the principal eigenvalue and corresponding principal eigenvector are transparently obtained for a consistent matrix. By perturbation theory the result is obtained for a near consistent matrix.

Keywords: Perron, AHP, Eigenvector, Pairwise comparison matrix solution, Analytic Hierarchy Process