Peer-Reviewed Journal Details
Mandatory Fields
Gursoy B.;Mason O.;Sergeev S.
2013
April
Linear Algebra and Its Applications
The analytic hierarchy process, max algebra and multi-objective optimisation
Published
()
Optional Fields
Analytic hierarchy process (AHP) Generalised spectral radius Max algebra Multi-objective optimization SR-matrix Subeigenvector
438
7
2911
2928
The analytic hierarchy process (AHP) is widely used for decision making involving multiple criteria. Elsner and van den Driessche (2004, 2010) [10,11] introduced a max-algebraic approach to the single criterion AHP. We extend this to the multi-criteria AHP, by considering multi-objective generalisations of the single objective optimisation problem solved in these earlier papers. We relate the existence of globally optimal solutions to the commutativity properties of the associated matrices; we relate min-max optimal solutions to the generalised spectral radius; and we prove that Pareto optimal solutions are guaranteed to exist. © 2012 Elsevier Inc. All rights reserved.
0024-3795
10.1016/j.laa.2012.11.020
Grant Details