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Learning non-compensatory sorting models using efficient SAT/MaxSAT formulations

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  • Tlili, Ali
  • Belahcène, Khaled
  • Khaled, Oumaima
  • Mousseau, Vincent
  • Ouerdane, Wassila

Abstract

The Non-Compensatory Sorting model aims at assigning alternatives evaluated on multiple criteria to one of the predefined ordered categories. Computing parameters of the Non-Compensatory Sorting model compatible to a set of reference assignments is computationally demanding. To overcome this problem, two formulations based on Boolean satisfiability have recently been proposed to learn the parameters of the Non-Compensatory Sorting model from perfect preference information, i.e. when the set of reference assignments can be completely represented in the model. In this paper, two popular variants of the Non-Compensatory Sorting model are considered, the Non-Compensatory Sorting model with a unique profile and the Non-Compensatory Sorting model with a unique set of sufficient coalitions. For each variant, we start by extending the formulation based on a separation principle to the multiple category case. Moreover, we extend the two formulations to handle inconsistency in the preference information using the Maximum satisfiability problem language. A computational study is proposed to compare the efficiency of both formulations to learn the two Non-Compensatory Sorting models (with a unique profile and with a unique set of sufficient coalitions) from noiseless and noisy preference information.

Suggested Citation

  • Tlili, Ali & Belahcène, Khaled & Khaled, Oumaima & Mousseau, Vincent & Ouerdane, Wassila, 2022. "Learning non-compensatory sorting models using efficient SAT/MaxSAT formulations," European Journal of Operational Research, Elsevier, vol. 298(3), pages 979-1006.
  • Handle: RePEc:eee:ejores:v:298:y:2022:i:3:p:979-1006
    DOI: 10.1016/j.ejor.2021.08.017
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    1. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2010. "Multiple criteria sorting with a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1455-1470, December.
    2. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
    3. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    4. Almeida-Dias, J. & Figueira, J.R. & Roy, B., 2010. "Electre Tri-C: A multiple criteria sorting method based on characteristic reference actions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 565-580, August.
    5. Jacquet-Lagreze, E. & Siskos, J., 1982. "Assessing a set of additive utility functions for multicriteria decision-making, the UTA method," European Journal of Operational Research, Elsevier, vol. 10(2), pages 151-164, June.
    6. Arcidiacono, Sally Giuseppe & Corrente, Salvatore & Greco, Salvatore, 2021. "Robust stochastic sorting with interacting criteria hierarchically structured," European Journal of Operational Research, Elsevier, vol. 292(2), pages 735-754.
    7. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02898131, HAL.
    8. Liu, Jiapeng & Liao, Xiuwu & Kadziński, Miłosz & Słowiński, Roman, 2019. "Preference disaggregation within the regularization framework for sorting problems with multiple potentially non-monotonic criteria," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1071-1089.
    9. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    10. Mousseau, Vincent & Figueira, Jose & Dias, Luis & Gomes da Silva, Carlos & Climaco, Joao, 2003. "Resolving inconsistencies among constraints on the parameters of an MCDA model," European Journal of Operational Research, Elsevier, vol. 147(1), pages 72-93, May.
    11. Herrera-Viedma, E. & Herrera, F. & Chiclana, F. & Luque, M., 2004. "Some issues on consistency of fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 154(1), pages 98-109, April.
    12. Patrice Perny, 1998. "Multicriteria filtering methods based onconcordance and non-discordance principles," Annals of Operations Research, Springer, vol. 80(0), pages 137-165, January.
    13. Almeida-Dias, J. & Figueira, J.R. & Roy, B., 2012. "A multiple criteria sorting method where each category is characterized by several reference actions: The Electre Tri-nC method," European Journal of Operational Research, Elsevier, vol. 217(3), pages 567-579.
    14. Kadziński, Miłosz & Tervonen, Tommi & Rui Figueira, José, 2015. "Robust multi-criteria sorting with the outranking preference model and characteristic profiles," Omega, Elsevier, vol. 55(C), pages 126-140.
    15. Tervonen, Tommi & Figueira, José Rui & Lahdelma, Risto & Dias, Juscelino Almeida & Salminen, Pekka, 2009. "A stochastic method for robustness analysis in sorting problems," European Journal of Operational Research, Elsevier, vol. 192(1), pages 236-242, January.
    16. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02917994, HAL.
    17. Liu, Jiapeng & Kadziński, Miłosz & Liao, Xiuwu & Mao, Xiaoxin & Wang, Yao, 2020. "A preference learning framework for multiple criteria sorting with diverse additive value models and valued assignment examples," European Journal of Operational Research, Elsevier, vol. 286(3), pages 963-985.
    18. Salvatore Corrente & Michael Doumpos & Salvatore Greco & Roman Słowiński & Constantin Zopounidis, 2017. "Multiple criteria hierarchy process for sorting problems based on ordinal regression with additive value functions," Annals of Operations Research, Springer, vol. 251(1), pages 117-139, April.
    19. Kadziński, Miłosz & Ciomek, Krzysztof, 2021. "Active learning strategies for interactive elicitation of assignment examples for threshold-based multiple criteria sorting," European Journal of Operational Research, Elsevier, vol. 293(2), pages 658-680.
    20. Kadziński, Miłosz & Ghaderi, Mohammad & Dąbrowski, Maciej, 2020. "Contingent preference disaggregation model for multiple criteria sorting problem," European Journal of Operational Research, Elsevier, vol. 281(2), pages 369-387.
    21. Blaszczynski, Jerzy & Greco, Salvatore & Slowinski, Roman, 2007. "Multi-criteria classification - A new scheme for application of dominance-based decision rules," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1030-1044, September.
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    Cited by:

    1. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2023. "Multiple criteria sorting models and methods—Part I: survey of the literature," 4OR, Springer, vol. 21(1), pages 1-46, March.
    2. Ali Tlili & Oumaima Khaled & Vincent Mousseau & Wassila Ouerdane, 2023. "Interactive portfolio selection involving multicriteria sorting models," Annals of Operations Research, Springer, vol. 325(2), pages 1169-1195, June.
    3. Wenfeng Zhu & Hengjie Zhang & Jing Xiao, 2023. "Coming to Consensus on Classification in Flexible Linguistic Preference Relations: The Role of Personalized Individual Semantics," Group Decision and Negotiation, Springer, vol. 32(5), pages 1237-1271, October.

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