The analytic hierarchy process, max algebra and multi-objective optimisation


Gursoy, Buket and Mason, Oliver and Sergeev, Sergei (2013) The analytic hierarchy process, max algebra and multi-objective optimisation. Linear Algebra and its Applications, 438 (7). pp. 2911-2928. ISSN 0024-3795

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Abstract

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.

Item Type: Article
Keywords: Analytic hierarchy process (AHP); SR-matrix; Max algebra; Subeigenvector; Generalised spectral radius; Multi-objective optimization;
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID: 6066
Identification Number: 10.1016/j.laa.2012.11.020
Depositing User: Oliver Mason
Date Deposited: 23 Apr 2015 10:25
Journal or Publication Title: Linear Algebra and its Applications
Publisher: Elsevier
Refereed: Yes
URI:

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