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A MIP-based approach to learn MR-Sort models with single-peaked preferences

Author

Listed:
  • Pegdwendé Minoungou

    (Université Paris-Saclay
    IBM)

  • Vincent Mousseau

    (Université Paris-Saclay)

  • Wassila Ouerdane

    (Université Paris-Saclay)

  • Paolo Scotton

    (IBM Research – Zurich)

Abstract

The Majority Rule Sorting (MR-Sort) method assigns alternatives evaluated on multiple criteria to one of the predefined ordered categories. The Inverse MR-Sort problem (Inv-MR-Sort) consists in computing MR-Sort parameters that match a dataset. Existing learning algorithms for Inv-MR-Sort consider monotone preference on criteria. We extend this problem to the case where the preference on criteria are not necessarily monotone, but possibly single-peaked (or single-valley). We propose a mixed-integer programming based algorithm that learns from the training data the preference on criteria together with the other MR-Sort parameters. Numerical experiments investigate the performance of the algorithm, and we illustrate its use on a real-world case study.

Suggested Citation

  • Pegdwendé Minoungou & Vincent Mousseau & Wassila Ouerdane & Paolo Scotton, 2023. "A MIP-based approach to learn MR-Sort models with single-peaked preferences," Annals of Operations Research, Springer, vol. 325(2), pages 795-817, June.
    • Handle: RePEc:spr:annopr:v:325:y:2023:i:2:d:10.1007_s10479-022-05007-5
    DOI: 10.1007/s10479-022-05007-5
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    References listed on IDEAS

    as
    1. 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.
    2. Doumpos, M. & Marinakis, Y. & Marinaki, M. & Zopounidis, C., 2009. "An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method," European Journal of Operational Research, Elsevier, vol. 199(2), pages 496-505, December.
    3. Zopounidis, Constantin & Doumpos, Michael, 2002. "Multicriteria classification and sorting methods: A literature review," European Journal of Operational Research, Elsevier, vol. 138(2), pages 229-246, April.
    4. 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.
    5. Butler, John & Jia, Jianmin & Dyer, James, 1997. "Simulation techniques for the sensitivity analysis of multi-criteria decision models," European Journal of Operational Research, Elsevier, vol. 103(3), pages 531-546, December.
    6. 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.
    7. 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.
    8. Ghaderi, Mohammad & Ruiz, Francisco & Agell, Núria, 2017. "A linear programming approach for learning non-monotonic additive value functions in multiple criteria decision aiding," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1073-1084.
    9. Wang, Hailiang & Zhou, Mingtian & She, Kun, 2015. "Induction of ordinal classification rules from decision tables with unknown monotonicity," European Journal of Operational Research, Elsevier, vol. 242(1), pages 172-181.
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