<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Pairwise comparison matrices are of key importance in multi-attribute decision analysis. A matrix is incomplete if some of the elements are missing. The eigenvector method, to derive the weights of criteria, can be generalized for the incomplete case by using the least inconsistent completion of the matrix. If inconsistency is indexed by CR, defined by Saaty, it leads to the minimization of the Perron eigenvalue. This problem can be transformed to a convex optimization problem. The paper presents a method based on the Newton iteration, univariate and multivariate. Numerical examples are also given.</p></abstract>

Pairwise comparison matrices are of key importance in multi-attribute decision analysis. A matrix is incomplete if some of the elements are missing. The eigenvector method, to derive the weights of criteria, can be generalized for the incomplete case by using the least inconsistent completion of the matrix. If inconsistency is indexed by CR, defined by Saaty, it leads to the minimization of the Perron eigenvalue. This problem can be transformed to a convex optimization problem. The paper presents a method based on the Newton iteration, univariate and multivariate. Numerical examples are also given.

Minimization of the Perron eigenvalue of incomplete pairwise comparison matrices by Newton iteration

Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, Hungary

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Pairwise comparison matrices are of key importance in multi-attribute decision analysis. A matrix is incomplete if some of the elements are missing. The...

Minimization of the Perron eigenvalue of incomplete pairwise comparison matrices by Newton iteration

Published Online: Jun 08, 2015

Page range: 58 - 71

Received: Jan 24, 2015

DOI: https://doi.org/10.1515/ausi-2015-0012

© Kristóf Ábele-Nagy

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.