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A stochastic method for exploiting outranking relations in multicriteria choice problems

Author

Listed:
  • Luis C. Dias

    (University of Coimbra)

  • Humberto Rocha

    (University of Coimbra)

Abstract

The multicriteria decision aiding field offers many methods to support decision makers in comparing a list of alternatives. Among these, outranking methods such as ELECTRE are appreciated for avoiding full compensation among criteria, but outranking relations are difficult to exploit due to incompleteness and lack of transitivity. This work focuses on choice problems, proposing a stochastic exploitation method to select the most preferred alternative. It builds on the concept of Markov solution, which has become popular to select a winner in tournaments and voting problems. The proposed method can be used to exploit crisp outranking relations, valued outranking relations, or stochastic outranking relations. This can be a valuable addition to the toolbox for exploiting outranking relations as this work shows that solutions can be computed without much effort and guarantee some essential properties.

Suggested Citation

  • Luis C. Dias & Humberto Rocha, 2023. "A stochastic method for exploiting outranking relations in multicriteria choice problems," Annals of Operations Research, Springer, vol. 321(1), pages 165-189, February.
    • Handle: RePEc:spr:annopr:v:321:y:2023:i:1:d:10.1007_s10479-022-04903-0
    DOI: 10.1007/s10479-022-04903-0
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    References listed on IDEAS

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    1. Dias, Luis C. & Lamboray, Claude, 2010. "Extensions of the prudence principle to exploit a valued outranking relation," European Journal of Operational Research, Elsevier, vol. 201(3), pages 828-837, March.
    2. Govindan, Kannan & Kadziński, Miłosz & Ehling, Ronja & Miebs, Grzegorz, 2019. "Selection of a sustainable third-party reverse logistics provider based on the robustness analysis of an outranking graph kernel conducted with ELECTRE I and SMAA," Omega, Elsevier, vol. 85(C), pages 1-15.
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    4. Luis C. Dias & Vincent Mousseau, 2018. "Eliciting Multi-Criteria Preferences: ELECTRE Models," International Series in Operations Research & Management Science, in: Luis C. Dias & Alec Morton & John Quigley (ed.), Elicitation, chapter 0, pages 349-375, Springer.
    5. Bertrand Mareschal & Jean Pierre Brans & Philippe Vincke, 1986. "How to select and how to rank projects: the Prométhée method," ULB Institutional Repository 2013/9307, ULB -- Universite Libre de Bruxelles.
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    8. Leyva López, Juan Carlos & Solano Noriega, Jesús Jaime & Figueira, José Rui & Liu, Jun & Gastélum Chavira, Diego Alonso, 2021. "Non-dominated sorting genetic-based algorithm for exploiting a large-sized fuzzy outranking relation," European Journal of Operational Research, Elsevier, vol. 293(2), pages 615-631.
    9. Fernandez, Eduardo & Leyva, Juan Carlos, 2004. "A method based on multiobjective optimization for deriving a ranking from a fuzzy preference relation," European Journal of Operational Research, Elsevier, vol. 154(1), pages 110-124, April.
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