Skip to main content
SpringerLink
Log in

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

  • Original Research
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. It should be noted that if the peak is drawn as an extreme value, the single-peaked (or single-valley) criterion actually corresponds to a monotone (gain or cost) criterion.

  2. ASA stands for “American Society of Anesthesiologists”.

References

  • Belahcene, K., Labreuche, C., Maudet, N., Mousseau, V., & Ouerdane, W. (2018). An efficient SAT formulation for learning multiple criteria non-compensatory sorting rules from examples. Computers & Operations Research, 97, 58–71.

    Article  Google Scholar 

  • Black, D. (1948). On the rationale of group decision-making. Journal of Political Economy, 56(1), 23–34.

    Article  Google Scholar 

  • Blaszczynski, J., Greco, S., & Slowinski, R. (2012). Inductive discovery of laws using monotonic rules. Engineering Applications of Artificial Intelligence, 25(2), 284–294.

    Article  Google Scholar 

  • Bouyssou, D., & Marchant, T. (2007). An axiomatic approach to noncompensatory sorting methods in mcdm, i: The case of two categories. European Journal of Operational Research, 178, 217–245.

    Article  Google Scholar 

  • Bouyssou, D., & Marchant, T. (2007). An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories. European Journal of Operational Research, 178(1), 246–276.

    Article  Google Scholar 

  • Butler, J., Jia, J., & Dyer, J. (1997). Simulation techniques for the sensitivity analysis of multi-criteria decision models. European Journal of Operational Research, 103(3), 531–546.

    Article  Google Scholar 

  • Cano, J.-R., Gutierrez, P. A., Krawczyk, B., Wozniak, M., & Garcia, S. (2019). Monotonic classification: An overview on algorithms, performance measures and data sets. Neurocomputing, 341, 168–182.

    Article  Google Scholar 

  • Despotis, D. K., & Zopounidis, C. (1995). Building Additive Utilities in the Presence of Non-Monotonic Preferences (pp. 101–114) Springer.

  • Doumpos, M. (2012). Learning non-monotonic additive value functions for multicriteria decision making. OR Spectrum, 34(1), 89–106.

    Article  Google Scholar 

  • 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, 199(2), 496–505.

    Article  Google Scholar 

  • Doumpos, M., & Zopounidis, C. (2002). Multicriteria decision aid classification methods. Kluwer Academic Publishers.

  • Eckhardt, A., & Kliegr, T. (2012). Preprocessing algorithm for handling non-monotone attributes in the UTA method. In Proceedings of the ECAI-12 workshop on preference learning: Problems and applications in AI (PL-12), eds., Fürnkranz, J., Hüllermeier, E.

  • Feelders, A. (2010). Monotone relabeling in ordinal classification. In G. I. Webb, B. Liu, C. Zhang, D. Gunopulos, X. Wu (Eds.), ICDM 2010, The 10th IEEE international conference on data mining (pp. 803–808). IEEE Computer Society.

  • Figueira, J., Mousseau, V., & Roy, B. (2005). Electre methods. In Multiple criteria decision analysis: State of the art surveys (pp. 133–153). Springer.

  • Ghaderi, M., Ruiz, F., & Agell, N. (2015). Understanding the impact of brand colour on brand image: A preference disaggregation approach. Pattern Recognition Letters, 67, 11–18.

    Article  Google Scholar 

  • Ghaderi, M., Ruiz, F., & Agell, N. (2017). A linear programming approach for learning non-monotonic additive value functions in multiple criteria decision aiding. European Journal of Operational Research, 259(3), 1073–1084.

    Article  Google Scholar 

  • Greco, S., Matarazzo, B., & Slowinski, R. (2001). Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 129(1), 1–47.

    Article  Google Scholar 

  • Guo, M., Liao, X., & Liu, J. (2019). A progressive sorting approach for multiple criteria decision aiding in the presence of non-monotonic preferences. Expert Systems with Applications, 123, 1–17.

    Article  Google Scholar 

  • Gutiérrez, P. A., & García, S. (2016). Current prospects on ordinal and monotonic classification. Progress in Artificial Intelligence, 5(3), 171–179.

    Article  Google Scholar 

  • IBM ILOG Cplex, IBM ILOG CPLEX Optimization Studio CPLEX User’s Manual, Version 12, Release 8, IBM ILOG, 20.1.0 edn., (2017).

  • Kadzinski, M., Martyn, K., Cinelli, M., Slowinski, R., Corrente, S., & Greco, S. (2020). Preference disaggregation for multiple criteria sorting with partial monotonicity constraints: Application to exposure management of nanomaterials. International Journal of Approximate Reasoning, 117, 60–80.

    Article  Google Scholar 

  • Kadzinski, M., Martyn, K., Cinelli, M., Slowinski, R., Corrente, S., & Greco, S. (2021). Preference disaggregation method for value-based multi-decision sorting problems with a real-world application in nanotechnology. Knowledge-Based Systems, 218, 106879.

    Article  Google Scholar 

  • Kadzinski, M., & Martyn, M. (2020). Enriched preference modeling and robustness analysis for the ELECTRE Tri-B method. Annals of Operations Research, 306, 1–35.

    Google Scholar 

  • Kliegr, T. (2009). UTA-NM : Explaining stated preferences with additive non-monotonic utility functions. In Proceedings of ECML PKDD workshop on preference learning.

  • Lazouni, M. A., Chikh, M. A., & Mahmoudi, S. (2013). A new computer aided diagnosis system for pre-anesthesia consultation. Journal of Medical Imaging and Health Informatics, 3(4), 471–479.

    Article  Google Scholar 

  • Leroy, A., Mousseau, V., Pirlot, M. (2011). Learning the parameters of a multiple criteria sorting method. In International conference on algorithmic decision theory (pp. 219–233). Springer.

  • Liu, J., Liao, X., Kadzinski, M., & Slowinski, R. (2019). Preference disaggregation within the regularization framework for sorting problems with multiple potentially non-monotonic criteria. European Journal of Operational Research, 276(3), 1071–1089.

    Article  Google Scholar 

  • Meyer, P., & Olteanu, A. (2017). Integrating large positive and negative performance differences into multicriteria majority-rule sorting models. Computers and Operations Research, 81, 216–230.

    Article  Google Scholar 

  • Meyer, P., & Olteanu, A. (2019). Handling imprecise and missing evaluations in multi-criteria majority-rule sorting. Computers and Operations Research, 110, 135–147.

    Article  Google Scholar 

  • Minoungou, P., Mousseau, V., Ouerdane, W. & Scotton, P. (2020). Learning an MR-sort model from data with latent criteria preference direction. In DA2PL’2020, from multiple criteria Decision Aid to Preference Learning, Trento, Italy.

  • Mousseau, V., & Slowinski, R. (1998). Inferring an ELECTRE TRI model from assignment examples. Journal of Global Optimization, 12(2), 157–174.

    Article  Google Scholar 

  • Nefla, O., Öztürk, M., Viappiani, P., & Brigui-Chtioui, I. (2019). Interactive elicitation of a majority rule sorting model with maximum margin optimization. In ADT 2019, 6th international conference on algorithmic decision theory.

  • Pei, S., & Hu, Q. (2018). Partially monotonic decision trees. Information Sciences, 424, 104–117.

    Article  Google Scholar 

  • Roy, B. (1991). The outranking approach and the foundations of Electre methods. Theory and Decision, 31(1), 49–73.

    Article  Google Scholar 

  • Sobrie, O. (2016). Learning preferences with multiple-criteria models, Ph.D. dissertation, Université de Mons (Faculté Polytechnique) and Université Paris-Saclay (CentraleSupélec).

  • Sobrie, O., Lazouni, M. A., Mahmoudi, S., Mousseau, V., & Pirlot, M. (2016). A new decision support model for preanesthetic evaluation. Computer Methods and Programs in Biomedicine, 133, 183–193.

    Article  Google Scholar 

  • Sobrie, O., Mousseau, V., & Pirlot, M. (2019). Learning monotone preferences using a majority rule sorting model. International Transactions in Operational Research, 26(5), 1786–1809.

    Article  Google Scholar 

  • Wang, H., Zhou, M., & She, K. (2015). Induction of ordinal classification rules from decision tables with unknown monotonicity. European Journal of Operational Research, 242(1), 172–181.

    Article  Google Scholar 

  • Zheng, J., Metchebon Takougang, S., Mousseau, V., & Pirlot, M. (2014). Learning criteria weights of an optimistic Electre Tri sorting rule. Computers and Operations Research, 49, 28–40.

    Article  Google Scholar 

  • Zopounidis, C., & Doumpos, M. (2002). Multicriteria classification and sorting methods: A literature review. European Journal of Operational Research, 138(2), 229–246.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MICS, CentraleSupélec, Université Paris-Saclay, Gif-sur-Yvette, France

    Pegdwendé Minoungou, Vincent Mousseau & Wassila Ouerdane

  2. IBM, Saclay, France

    Pegdwendé Minoungou

  3. IBM Research – Zurich, Rüschlikon, Switzerland

    Paolo Scotton

Authors
  1. Pegdwendé Minoungou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vincent Mousseau
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wassila Ouerdane
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paolo Scotton
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vincent Mousseau.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Minoungou, P., Mousseau, V., Ouerdane, W. et al. A MIP-based approach to learn MR-Sort models with single-peaked preferences. Ann Oper Res 325, 795–817 (2023). https://doi.org/10.1007/s10479-022-05007-5

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-022-05007-5

Keywords

Search

Navigation