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

[img]
Preview
Download (2MB) | Preview


Share your research

Twitter Facebook LinkedIn GooglePlus Email more...



Add this article to your Mendeley library


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:

Repository Staff Only(login required)

View Item Item control page

Document Downloads

More statistics for this item...