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A linear programming approach for learning non-monotonic additive value functions in multiple criteria decision aiding

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  • Ghaderi, Mohammad
  • Ruiz, Francisco
  • Agell, Núria

Abstract

A new framework for preference disaggregation in multiple criteria decision aiding is introduced. The proposed approach aims to infer non-monotonic additive preference models from a set of indirect pairwise comparisons. The preference model is presented as a set of marginal value functions and the discriminatory power of the inferred preference model is maximized against its complexity. To infer a value function that is compatible with the supplied preference information, the proposed methodology leads to a linear programming optimization problem that is easy to solve. The applicability and effectiveness of the new methodology is demonstrated in a thorough experimental analysis covering a broad range of decision problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:259:y:2017:i:3:p:1073-1084
    DOI: 10.1016/j.ejor.2016.11.038
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    Cited by:

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    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.
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    15. Susmaga, Robert & Szczȩch, Izabela & Zielniewicz, Piotr & Brzezinski, Dariusz, 2023. "MSD-space: Visualizing the inner-workings of TOPSIS aggregations," European Journal of Operational Research, Elsevier, vol. 308(1), pages 229-242.
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    17. Ghaderi, Mohammad & Kadziński, Miłosz, 2021. "Incorporating uncovered structural patterns in value functions construction," Omega, Elsevier, vol. 99(C).
    18. Yue Qi & Ralph E. Steuer, 2020. "On the analytical derivation of efficient sets in quad-and-higher criterion portfolio selection," Annals of Operations Research, Springer, vol. 293(2), pages 521-538, October.
    19. Subrata Mitra & Balram Avittathur, 2018. "Application of linear programming in optimizing the procurement and movement of coal for an Indian coal-fired power-generating company," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 45(3), pages 207-224, September.
    20. Mohammad Ghaderi & Milosz Kadzinsky, 2019. "Accounting for structural patterns in construction of value functions: a convex optimization approach," Economics Working Papers 1634, Department of Economics and Business, Universitat Pompeu Fabra.
    21. Wachowicz, Tomasz & Roszkowska, Ewa, 2022. "Can holistic declaration of preferences improve a negotiation offer scoring system?," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1018-1032.
    22. Sarah Ben Amor & Fateh Belaid & Ramzi Benkraiem & Boumediene Ramdani & Khaled Guesmi, 2023. "Multi-criteria classification, sorting, and clustering: a bibliometric review and research agenda," Annals of Operations Research, Springer, vol. 325(2), pages 771-793, June.

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