Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process
AbstractWe propose to extend the aggregation scheme of Saaty's AHP, from the standard weighted averaging to the more general Choquet integration. In our model, a measure of inconsistency between criteria is derived from the main pairwise comparison matrix and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean in the consistency case. In the general inconsistency case, however, the new aggregation scheme based on Choquet integration tends to attenuate (resp. emphasize) the priority values of the criteria with higher (resp. lower) average inconsistency with the remaining criteria.
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Bibliographic InfoPaper provided by Department of Computer and Management Sciences, University of Trento, Italy in its series DISA Working Papers with number 2011/06.
Length: 32 pages
Date of creation: Jun 2011
Date of revision: 29 Jul 2011
Postal: DISA Università degli Studi di Trento via Inama, 5 I-38122 Trento TN Italy
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-15 (All new papers)
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- Grabisch, M. & Roubens, M., 1998.
"An Axiomatic Approach to the Concept of Interaction Among Players in Cooperative Games,"
Liege - Groupe d'Etude des Mathematiques du Management et de l'Economie
9818, UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie.
- Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer, vol. 28(4), pages 547-565.
- Berrah, L. & Mauris, G. & Montmain, J., 2008. "Monitoring the improvement of an overall industrial performance based on a Choquet integral aggregation," Omega, Elsevier, vol. 36(3), pages 340-351, June.
- Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008.
"A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package,"
European Journal of Operational Research,
Elsevier, vol. 186(2), pages 766-785, April.
- repec:hal:cesptp:halshs-00625708 is not listed on IDEAS
- repec:hal:cesptp:halshs-00267932 is not listed on IDEAS
- repec:hal:cesptp:hal-00188165 is not listed on IDEAS
- Fedrizzi, Michele & Giove, Silvio, 2007.
"Incomplete pairwise comparison and consistency optimization,"
European Journal of Operational Research,
Elsevier, vol. 183(1), pages 303-313, November.
- Michele Fedrizzi & Silvio Giove, 2006. "Incomplete pairwise comparison and consistency optimization," Working Papers 144, Department of Applied Mathematics, Università Ca' Foscari Venezia.
- Cliville, Vincent & Berrah, Lamia & Mauris, Gilles, 2007. "Quantitative expression and aggregation of performance measurements based on the MACBETH multi-criteria method," International Journal of Production Economics, Elsevier, vol. 105(1), pages 171-189, January.
- Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
- repec:hal:cesptp:halshs-00625706 is not listed on IDEAS
- Miranda, P. & Grabisch, M. & Gil, P., 2005.
"Axiomatic structure of k-additive capacities,"
Mathematical Social Sciences,
Elsevier, vol. 49(2), pages 153-178, March.
- Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
- Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011.
"A representation of preferences by the Choquet integral with respect to a 2-additive capacity,"
Theory and Decision,
Springer, vol. 71(3), pages 297-324, September.
- Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
- repec:hal:cesptp:halshs-00496558 is not listed on IDEAS
- Thomas L. Saaty, 1986. "Axiomatic Foundation of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 32(7), pages 841-855, July.
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