Transitive matrices and their applications
type: Item
instance of: scholarly article
title: Transitive matrices and their applications
zbMATH Open document ID: 0946.15017
DOI: 10.1016/S0024-3795(99)00208-6
author: András Farkas
author: Pál Rózsa
author: Etelka Stubnya
published in: Linear Algebra and its Applications
publication date: 2000-03-21T00:00:00Z
review text: In Section 2, transitive matrices and symmetrically reciprocal (SR) matrices are defined and the spectral properties of these matrices are described. In most of the applied problems, certain pairs of elements of a transitive matrix are perturbed, such that its transitivity is lost, but it remains in SR. In Section 3, the quite simple spectral properties of a perturbed transitive matrix are presented. In Section 4, a controversial aspect of analytic hierarchy process (AHP), the phenomenon of rank reversal is considered. It is proven that a rank reversal is inherent in the AHP, if its input transitive matrix is subjected to certain arbitrarily small perturbations.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1419879
zbMATH Keywords: transitive matrices
zbMATH Keywords: symmetrically reciprocal matrices
zbMATH Keywords: analytic hierarchy process
zbMATH Keywords: spectral density matrix
zbMATH Keywords: perturbations
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
cites work: The description of road surface roughness
cites work: A scaling method for priorities in hierarchical structures
cites work: Axiomatic Foundation of the Analytic Hierarchy Process
cites work: Q4073083
Wikidata QID: Q127725328
description: scientific article; zbMATH DE number 1419879