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Learning the Parameters of a Non Compensatory Sorting Model

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Algorithmic Decision Theory (ADT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9346))

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Abstract

We consider a multicriteria sorting procedure based on a majority rule, called MR-Sort. This procedure allows to sort each object of a set, evaluated on multiple criteria, in a category selected among a set of pre-defined and ordered categories. With MR-Sort, the ordered categories are separated by profiles which are vectors of performances on the different attributes. Using the MR-Sort rule, an object is assigned to a category if it is at least as good as the category lower profile and not better than the category upper profile. To determine whether an object is as good as a profile, the weights of the criteria on which the object performances are better than the profile performances are summed up and compared to a threshold. If the sum of weights is at least equal to the threshold, then the object is considered at least as good as the profile. In view of increasing the expressiveness of the model, we substitute additive weights by a capacity to represent the power of coalitions of criteria. This corresponds to the Non-Compensatory Sorting model characterized by Bouyssou and Marchant. In the paper we describe a mixed integer program and a heuristic algorithm that enable to learn the parameters of this model from assignment examples.

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References

  1. Bouyssou, D., Marchant, T.: An axiomatic approach to noncompensatory sorting methods in MCDM, I: the case of two categories. Eur. J. Oper. Res. 178(1), 217–245 (2007)

    Article  Google Scholar 

  2. Bouyssou, D., Marchant, T.: An axiomatic approach to noncompensatory sorting methods in MCDM, II: more than two categories. Eur. J. Oper. Res. 178(1), 246–276 (2007)

    Article  Google Scholar 

  3. Leroy, A., Mousseau, V., Pirlot, M.: Learning the parameters of a multiple criteria sorting method based on a majority rule. In: Brafman, R. (ed.) ADT 2011. LNCS, vol. 6992, pp. 219–233. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Sobrie, O., Mousseau, V., Pirlot, M.: Learning a majority rule model from large sets of assignment examples. In: Perny, P., Pirlot, M., Tsoukiàs, A. (eds.) ADT 2013. LNCS, vol. 8176, pp. 336–350. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  5. Jacquet-Lagrèze, E., Siskos, Y.: Assessing a set of additive utility functions for multicriteria decision making: the UTA method. Eur. J. Oper. Res. 10, 151–164 (1982)

    Article  Google Scholar 

  6. Doumpos, M., Zopounidis, C.: Multicriteria Decision Aid Classification Methods. Kluwer Academic Publishers, Dordrecht (2002)

    MATH  Google Scholar 

  7. Fishburn, P.C.: Noncompensatory preferences. Synth. 33(1), 393–403 (1976)

    Article  Google Scholar 

  8. Bouyssou, D.: Some remarks on the notion of compensation in MCDM. Eur. J. Oper. Res. 26, 150–160 (1986)

    Article  MathSciNet  Google Scholar 

  9. Grabisch, M.: The application of fuzzy integrals in multicriteria decision making. Eur. J. Oper. Res. 89(3), 445–456 (1996)

    Article  Google Scholar 

  10. Yu, W.: Aide multicritère à la décision dans le cadre de la problématique du tri: méthodes et applications. Ph.D. thesis, LAMSADE, Université Paris Dauphine, Paris (1992)

    Google Scholar 

  11. Roy, B., Bouyssou, D.: Aide multicritère à la décision: méthodes et cas. Economica, Paris (1993)

    MATH  Google Scholar 

  12. Bouyssou, D., Pirlot, M.: A characterization of concordance relations. Eur. J. Oper. Res. 167(2), 427–443 (2005)

    Article  MathSciNet  Google Scholar 

  13. Bouyssou, D., Pirlot, M.: Further results on concordance relations. Eur. J. Oper. Res. 181, 505–514 (2007)

    Article  MathSciNet  Google Scholar 

  14. Chateauneuf, A., Jaffray, J.: Derivation of some results on monotone capacities by Möbius inversion. In: Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 1986. Lecture Notes in Computer Science, vol. 286, pp. 95–102. Springer, Heidelberg (1986)

    Chapter  Google Scholar 

  15. Mousseau, V., Słowiński, R.: Inferring an ELECTRE TRI model from assignment examples. J. Global Optim. 12(1), 157–174 (1998)

    Article  MathSciNet  Google Scholar 

  16. Mousseau, V., Figueira, J., Naux, J.P.: Using assignment examples to infer weights for ELECTRE TRI method: some experimental results. Eur. J. Oper. Res. 130(1), 263–275 (2001)

    Article  Google Scholar 

  17. The, A.N., Mousseau, V.: Using assignment examples to infer category limits for the ELECTRE TRI method. J. Multi-criteria Decis. Anal. 11(1), 29–43 (2002)

    Article  Google Scholar 

  18. Dias, L., Mousseau, V., Figueira, J., Clímaco, J.: An aggregation/disaggregation approach to obtain robust conclusions with ELECTRE TRI. Eur. J. Oper. Res. 138(1), 332–348 (2002)

    Article  Google Scholar 

  19. Doumpos, M., Marinakis, Y., Marinaki, M., Zopounidis, C.: An evolutionary approach to construction of outranking models for multicriteria classification: the case of the ELECTRE TRI method. Eur. J. Oper. Res. 199(2), 496–505 (2009)

    Article  Google Scholar 

  20. Cailloux, O., Meyer, P., Mousseau, V.: Eliciting ELECTRE TRI category limits for a group of decision makers. Eur. J. Oper. Res. 223(1), 133–140 (2012)

    Article  MathSciNet  Google Scholar 

  21. Zheng, J., Metchebon, S., Mousseau, V., Pirlot, M.: Learning criteria weights of an optimistic Electre Tri sorting rule. Comput. OR 49, 28–40 (2014)

    Article  Google Scholar 

  22. Hüllermeier, E., Tehrani, A.F.: Efficient learning of classifiers based on the 2-additive choquet integral. In: Moewes, C., Nürnberger, A. (eds.) Computational Intelligence in Intelligent Data Analysis. SCI, vol. 445, pp. 17–29. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  23. Tehrani, A.F., Cheng, W., Dembczynski, K., Hüllermeier, E.: Learning monotone nonlinear models using the choquet integral. Mach. Learn. 89(1–2), 183–211 (2012)

    MathSciNet  MATH  Google Scholar 

  24. Ersek Uyanık, E., Sobrie, O., Mousseau, V., Pirlot, M.: Listing the families of sufficient coalitions of criteria involved in sorting procedures. In: DA2PL 2014 Workshop From Multiple Criteria Decision Aid to Preference Learning, pp. 60–70, Paris, France (2014)

    Google Scholar 

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Author information

Authors and Affiliations

  1. LGI, CentraleSupelec, Grande Voie des Vignes, 92295, Châteney-Malabry, France

    Olivier Sobrie & Vincent Mousseau

  2. Faculté Polytechnique, Université de Mons, 9, Rue de Houdain, 7000, Mons, Belgium

    Olivier Sobrie & Marc Pirlot

Authors
  1. Olivier Sobrie
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  2. Vincent Mousseau
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  3. Marc Pirlot
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Corresponding author

Correspondence to Olivier Sobrie .

Editor information

Editors and Affiliations

  1. University of New South Wales, Kensington, Australia

    Toby Walsh

Appendices

A MIP Learning the Parameters of a MR-Sort Model

(12)

B MIP Learning the Parameters of a 2-Additive NCS Model

(13)

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Sobrie, O., Mousseau, V., Pirlot, M. (2015). Learning the Parameters of a Non Compensatory Sorting Model. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_10

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  • DOI: https://doi.org/10.1007/978-3-319-23114-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23113-6

  • Online ISBN: 978-3-319-23114-3

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