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arXiv · 1207.6572

The Analytic Hierarchy Process, Max Algebra and Multi-objective Optimisation

Buket Benek Gursoy·Oliver Mason·Sergei Sergeev
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Abstract

The Analytic Hierarchy Process (AHP) is widely used for decision making involving multiple criteria. Elsner and van den Driessche 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.

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Buket Benek Gursoy, Oliver Mason, Sergei Sergeev. 2012-07-27. The Analytic Hierarchy Process, Max Algebra and Multi-objective Optimisation. https://doi.org/10.1016/j.laa.2012.11.020

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