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Interaction of Criteria and Robust Ordinal Regression in Bi-polar PROMETHEE Methods

  • Salvatore Corrente
  • José Rui Figueira
  • Salvatore Greco
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)

Abstract

In this paper we consider the bipolar approach to Multiple Criteria Decision Analysis (MCDA). In particular we aggregate positive and negative preferences by means of the bipolar PROMETHEE method. To elicit preferences we consider Robust Ordinal Regression (ROR) that has been recently proposed to derive robust conclusions through the use of the concepts of possible and necessary preferences. It permits to take into account the whole set of preference parameters compatible with the preference information given by the Decision Maker (DM).

Keywords

Multiple criteria outranking methods Interaction between criteria Bi-polar Choquet integral 

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References

  1. 1.
    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
  2. 2.
    Brans, J., Maréchal, B.: PROMETHEE Methods. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys. Springer, Berlin (2005)Google Scholar
  3. 3.
    Brans, J., Vincke, P.: A preference ranking organisation method: The PROMETHEE method for MCDM. Management Science 31(6), 647–656 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Choquet, G.: Theory of Capacities. Annales de l’Institute Fourier 5, 131–295 (1953/1954)Google Scholar
  5. 5.
    Figueira, J., Greco, S., Ehrgott, M.: Multiple Criteria Decision Analysis: State of the Art Surveys. Springer, Berlin (2005)zbMATHGoogle Scholar
  6. 6.
    Figueira, J.R., Greco, S., Słowiński, R.: Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method. European Journal of Operational Research 195(2), 460–486 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Grabisch, M., Labreuche, C.: Bi-capacities-I: definition, Möbius transform and interaction. Fuzzy Sets and Systems 151(2), 211–236 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Grabisch, M., Labreuche, C.: Bi-capacities-II: the Choquet integral. Fuzzy Sets and Systems 151(2), 237–259 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Greco, S., Kadzinski, M., Słowiński, R.: Extreme ranking analysis in Robust Ordinal Regression. Omega 40(4), 488–501 (2012)CrossRefGoogle Scholar
  10. 10.
    Greco, S., Kadziński, M., Mousseau, V., Słowiński, R.: ELECTREGKMS: Robust Ordinal Regression for outranking methods. European Journal of Operational Research 214(1), 118–135 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    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
  12. 12.
    Greco, S., Figueira, J.R.: Dealing with interaction between bi-polar multiple criteria preferences in outranking methods. Research Report 11-2003, INESC-Coimbra, Portugal (2003)Google Scholar
  13. 13.
    Greco, S., Figueira, J.R., Roy, B.: Electre methods with interaction between criteria: An extension of the concordance index. European Journal of Operational Research 199(2), 478–495 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Greco, S., Grabish, M., Pirlot, M.: Bipolar and bivariate models in multicriteria decision analysis: Descriptive and constructive approaches. International Journal of Intelligent Systems 23(9), 930–969 (2008)zbMATHCrossRefGoogle Scholar
  15. 15.
    Marichal, J., Roubens, M.: Determination of weights of interacting criteria from a reference set. European Journal of Operational Research 124(3), 641–650 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Mousseau, V., Figueira, J., Dias, L., Gomes da Silva, C., Clímaco, J.: Resolving inconsistencies among constraints on the parameters of an MCDA model. European Journal of Operational Research 147, 72–93 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Roy, B., Mousseaui, V.: A theoretical framework for analysing the notion of relative importance of criteria. Journal of Multi-Criteria Decision Analysis 5, 145–159 (1996)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Salvatore Corrente
    • 1
  • José Rui Figueira
    • 2
  • Salvatore Greco
    • 1
  1. 1.Department of Economics and BusinessUniversity of CataniaCataniaItaly
  2. 2.CEG-IST, Instituto Superior TécnicoLisboaPortugal

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