Result: Max-algebra and pairwise comparison matrices
Title:
Max-algebra and pairwise comparison matrices
Authors:
Source:
Linear Algebra and its Applications. 385:47-62
Publisher Information:
Elsevier BV, 2004.
Publication Year:
2004
Subject Terms:
Numerical computation of eigenvalues and eigenvectors of matrices, Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, Max-eigenvector, analytic hierarchy process (AHP), Matrices over special rings (quaternions, finite fields, etc.), analytically hierarchy process, Decision theory, 01 natural sciences, SR-matrix, Positive matrices and their generalizations, cones of matrices, ranking, max-eigenvector, Discrete Mathematics and Combinatorics, Ranking, Geometry and Topology, 0101 mathematics, Analytic hierarchy process (AHP)
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0024-3795
DOI:
10.1016/s0024-3795(03)00476-2
Access URL:
https://zbmath.org/2083506
https://doi.org/10.1016/s0024-3795(03)00476-2
https://www.sciencedirect.com/science/article/pii/S0024379509005199
https://www.infona.pl/resource/bwmeta1.element.elsevier-34bca296-028e-366b-8c37-1a065babc042
https://www.sciencedirect.com/science/article/abs/pii/S0024379509005199
https://doi.org/10.1016/s0024-3795(03)00476-2
https://www.sciencedirect.com/science/article/pii/S0024379509005199
https://www.infona.pl/resource/bwmeta1.element.elsevier-34bca296-028e-366b-8c37-1a065babc042
https://www.sciencedirect.com/science/article/abs/pii/S0024379509005199
Rights:
Elsevier Non-Commercial
"In Copyright" Rights Statement
"In Copyright" Rights Statement
Accession Number:
edsair.doi.dedup.....dbe0afc0d66e93e8dc1e151945c1a6b2
Database:
OpenAIRE
Further Information
Instead of the Perron eigenvector, the max-eigenvector of a symmetrically reciprocal matrix \(A\) is used in order to construct a transitive matrix that is closest to \(A\) in a relative error measure and gives more consistent rankings in the analytical hierarchy process. In this respect, some properties of the max-eigenvector are discussed and a procedure of its calculation is formulated. Three examples illustrate the entire approach.