SMAA-Choquet: Stochastic Multicriteria Acceptability Analysis for the Choquet Integral

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)


In this paper, we extend the Choquet integral decision model in the same spirit of the Stochastic Multicriteria Acceptability Analysis (SMAA) method that takes into account a probability distribution over the preference parameters of multiple criteria decision methods. In order to enrich the set of parameters (the capacities) compatible with the DM’s preference information on the importance of criteria and interaction between couples of criteria, we put together Choquet integral with SMAA. The sampling of the compatible preference parameters (the capacities) is obtained by a Hit-and-Run procedure. Finally, we evaluate a set of capacities contributing to the evaluation of the rank acceptability indices and of the central preference parameters as done in the SMAA methods.


Multiple criteria decision analysis SMAA Choquet integral 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Angilella, S., Greco, S., Lamantia, F., Matarazzo, B.: Assessing non-additive utility for multicriteria decision aid. European Journal of Operational Research 158(3), 734–744 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Angilella, S., Greco, S., Matarazzo, B.: Non-additive robust ordinal regression: A multiple criteria decision model based on the choquet integral. European Journal of Operational Research 201(1), 277–288 (2010)zbMATHCrossRefGoogle Scholar
  3. 3.
    Bana e Costa, C.A.: A multicriteria decision aid methodology to deal with conflicting situations on the weights. European Journal of Operational Research 26(1), 22–34 (1986)Google Scholar
  4. 4.
    Bana e Costa, C.A.: A methodology for sensitivity analysis in three-criteria problems: A case study in municipal management. European Journal of Operational Research 33(2), 159–173 (1988)Google Scholar
  5. 5.
    Chateauneuf, A., Jaffray, J.Y.: Some characterizations of lower probabilities and other monotone capacities through the use of möbius inversion. Mathematical Social Sciences 17, 263–283 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5(54), 131–295 (1953)MathSciNetGoogle Scholar
  7. 7.
    Figueira, J., Greco, S., Ehrgott, M.: Multiple Criteria Decision Analysis: State of the Art Surveys. Springer, Berlin (2010)Google Scholar
  8. 8.
    Gilboa, I., Schmeidler, D.: Additive representations of non-additive measures and the choquet integral. Ann. Operational Research 52, 43–65 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Grabisch, M.: The application of fuzzy integrals in multicriteria decision making. European Journal of Operational Research 89, 445–456 (1996)zbMATHCrossRefGoogle Scholar
  10. 10.
    Grabisch, M.: k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 92, 167–189 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Greco, S., Matarazzo, B., Giove, S.: The Choquet integral with respect to a level dependent capacity. Fuzzy Sets and Systems 175, 1–35 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Greco, S., Mousseau, V., Słowiński, R.: Ordinal regression revisited: multiple criteria ranking using a set of additive value functions. European Journal of Operational Research 191(2), 416–436 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Keeney, R.L., Raiffa, H.: Decisions with multiple objectives: Preferences and value tradeoffs. J. Wiley, New York (1976)Google Scholar
  14. 14.
    Lahdelma, R., Hokkanen, J., Salminen, P.: SMAA - stochastic multiobjective acceptability analysis. European Journal of Operational Research 106(1), 137–143 (1998)CrossRefGoogle Scholar
  15. 15.
    Lahdelma, R., Salminen, P.: SMAA-2: Stochastic multicriteria acceptability analysis for group decision making. Operations Research 49(3), 444–454 (2001)zbMATHCrossRefGoogle Scholar
  16. 16.
    Marichal, J.L., Roubens, M.: Determination of weights of interacting criteria from a reference set. European Journal of Operational Research 124(3), 641–650 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Murofushi, S., Soneda, T.: Techniques for reading fuzzy measures (iii): interaction index. In: 9th Fuzzy Systems Symposium, Sapporo, Japan, pp. 693–696 (1993)Google Scholar
  18. 18.
    Barba Romero, S., Pomerol, J.C.: Choix multicritère dans l’enterprise. Heres. Collection Informatique (1993)Google Scholar
  19. 19.
    Rota, G.C.: On the foundations of combinatorial theory i. Theory of möbius functions. Wahrscheinlichkeitstheorie und Verwandte Gebiete 2, 340–368 (1964)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)Google Scholar
  21. 21.
    Shapley, L.S.: A value for n-person games. In: Tucker, A.W., Kuhn, H.W. (eds.) Contributions to the Theory of Games II, p. 307. Princeton University Press, Princeton (1953)Google Scholar
  22. 22.
    Smith, R.L.: Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions. Operations Research 32, 1296–1308 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Tervonen, T., Figueira, J.: A survey on stochastic multicriteria acceptability analysis methods. Journal of Multi-Criteria Decision Analysis 15(1-2), 1–14 (2008)zbMATHCrossRefGoogle Scholar
  24. 24.
    Tervonen, T., Van Valkenhoef, G., Basturk, N., Postmus, D.: Efficient weight generation for simulation based multiple criteria decision analysis. In: EWG-MCDA, Tarragona, April 12-14 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Economics and BusinessUniversity of CataniaCataniaItaly

Personalised recommendations