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Gursoy, Buket, 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 |
| Related URLs: | |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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