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A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package

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  • Grabisch, Michel
  • Kojadinovic, Ivan
  • Meyer, Patrick

Abstract

The application of multi-attribute utility theory whose aggregation process is based on the Choquet integral requires the prior identification of a capacity. The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed. All the reviewed methods have been implemented within the Kappalab R package. Their application is illustrated on a detailed example.

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File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(07)00233-0
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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 186 (2008)
Issue (Month): 2 (April)
Pages: 766-785

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Handle: RePEc:eee:ejores:v:186:y:2008:i:2:p:766-785
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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  1. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  2. Marichal, Jean-Luc, 2004. "Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral," European Journal of Operational Research, Elsevier, vol. 155(3), pages 771-791, June.
  3. Michel Grabisch & Christophe Labreuche & Jean-Claude Vansnick, 2003. "On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria," Post-Print hal-00272780, HAL.
  4. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
  5. Karatzoglou, Alexandros & Smola, Alexandros & Hornik, Kurt & Zeileis, Achim, 2004. "kernlab - An S4 Package for Kernel Methods in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i09).
  6. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
  7. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
  8. Alain Chateauneuf & Jean-Yves Jaffray, 2008. "Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of Mobius Inversion," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00649208, HAL.
  9. Kojadinovic, Ivan, 2007. "Minimum variance capacity identification," European Journal of Operational Research, Elsevier, vol. 177(1), pages 498-514, February.
  10. Marichal, Jean-Luc & Roubens, Marc, 2000. "Determination of weights of interacting criteria from a reference set," European Journal of Operational Research, Elsevier, vol. 124(3), pages 641-650, August.
  11. Fujimoto, Katsushige & Kojadinovic, Ivan & Marichal, Jean-Luc, 2006. "Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices," Games and Economic Behavior, Elsevier, vol. 55(1), pages 72-99, April.
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Cited by:

  1. Doumpos, Michael & Zopounidis, Constantin, 2011. "Preference disaggregation and statistical learning for multicriteria decision support: A review," European Journal of Operational Research, Elsevier, vol. 209(3), pages 203-214, March.
  2. Angilella, Silvia & Greco, Salvatore & Matarazzo, Benedetto, 2010. "Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral," European Journal of Operational Research, Elsevier, vol. 201(1), pages 277-288, February.
  3. Greco, Salvatore & Mousseau, Vincent & Słowiński, Roman, 2014. "Robust ordinal regression for value functions handling interacting criteria," European Journal of Operational Research, Elsevier, vol. 239(3), pages 711-730.
  4. Zhang, Ling & Zhang, Luping & Zhou, Peng & Zhou, Dequn, 2015. "A non-additive multiple criteria analysis method for evaluation of airline service quality," Journal of Air Transport Management, Elsevier, vol. 47(C), pages 154-161.
  5. Lorenza Campagnolo & Carlo Carraro & Fabio Eboli & Luca Farnia, 2015. "Assessing SDGs: A New Methodology to Measure Sustainability," Working Papers 2015.89, Fondazione Eni Enrico Mattei.
  6. Paugam, Luc, 2011. "Valorisation et reporting du goodwill : enjeux théoriques et empiriques," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/8007 edited by Casta, Jean-François, October.
  7. Luc Paugam & Jean-François Casta, 2010. "Mesurer le capital organisationnel comme combinaison de ressources," Post-Print halshs-00494560, HAL.
  8. Silvia Bortot & Ricardo Alberto Marques Pereira, 2011. "Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process," DISA Working Papers 2011/06, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.
  9. Constantin Zopounidis & Michael Doumpos, 2013. "Multicriteria decision systems for financial problems," TOP- An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 241-261, July.
  10. Feng, Cheng-Min & Wu, Pei-Ju & Chia, Kai-Chieh, 2010. "A hybrid fuzzy integral decision-making model for locating manufacturing centers in China: A case study," European Journal of Operational Research, Elsevier, vol. 200(1), pages 63-73, January.
  11. Silvia Bortot & Ricardo Alberto Marques Pereira & Thuy Nguyen, 2015. "On the binomial decomposition of OWA functions, the 3-additive case in n dimensions," Working Papers 360, ECINEQ, Society for the Study of Economic Inequality.
  12. Alessio Bonetti & Silvia Bortot & Mario Fedrizzi & Silvio Giove & Ricardo Alberto Marques Pereira & Andrea Molinari, 2011. "Modelling group processes and effort estimation in Project Management using the Choquet integral: an MCDM approach," DISA Working Papers 2011/12, Department of Computer and Management Sciences, University of Trento, Italy, revised Sep 2011.
  13. M. Ferrara & F. Lamperti & R. Mavilia, 2016. "Looking for best performers: a pilot study towards the evaluation of science parks," Scientometrics, Springer;Akadémiai Kiadó, vol. 106(2), pages 717-750, February.
  14. Silvia Bortot & Ricardo Alberto Marques Pereira & Thuy H. Nguyen, 2015. "Welfare functions and inequality indices in the binomial decomposition of OWA functions," DEM Discussion Papers 2015/08, Department of Economics and Management.
  15. Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio, 2016. "Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression," Omega, Elsevier, vol. 61(C), pages 2-18.
  16. van de Kuilen, G. & Wakker, P.P., 2011. "The midweight method to measure attitudes towards risk and ambiguity," Other publications TiSEM c58a6884-24cc-4cab-ae2f-a, Tilburg University, School of Economics and Management.
  17. Silvia Bortot & Mario Fedrizzi & Silvio Giove, 2011. "Modelling fraud detection by attack trees and Choquet integral," DISA Working Papers 2011/09, Department of Computer and Management Sciences, University of Trento, Italy, revised 31 Aug 2011.
  18. Jean-François Casta & Luc Paugam & Hervé Stolowy, 2011. "Non-additivity in accounting valuation: Internally generated goodwill as an aggregation of interacting assets," Post-Print halshs-00541525, HAL.

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