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A Distance-Based Collective Weak Ordering

Author

Listed:
  • Slim Ben Khelifa

    (Ecole des Sciences Economiques et Commerciales)

  • Jean-Marc Martel

    (Université Laval)

Abstract

A group decision-making approach can be seen as a two stage process. The first stage allows for multi-cirteria evaluation of the alternatives and the second aims at deriving a collective weak ordering from the partial orderings supplied by the members after the first stage. The problem of combining the weak orderings to form a collective ranking is investigated. An axiomatic structure relating to the concept of distance between binary relations is developed. An algorithm for deriving the collective weak ordering is proposed, based on the idea of ranking first the least dominated alternatives.

Suggested Citation

  • Slim Ben Khelifa & Jean-Marc Martel, 2001. "A Distance-Based Collective Weak Ordering," Group Decision and Negotiation, Springer, vol. 10(4), pages 317-329, July.
    • Handle: RePEc:spr:grdene:v:10:y:2001:i:4:d:10.1023_a:1011257109771
    DOI: 10.1023/A:1011257109771
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    References listed on IDEAS

    as
    1. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    2. Ronald D. Armstrong & Wade D. Cook & Lawrence M. Seiford, 1982. "Priority Ranking and Consensus Formation: The Case of Ties," Management Science, INFORMS, vol. 28(6), pages 638-645, June.
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    Cited by:

    1. Ben Amor, Sarah & Martel, Jean-Marc, 2014. "A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1165-1169.
    2. Jabeur, Khaled & Martel, Jean-Marc, 2007. "An ordinal sorting method for group decision-making," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1272-1289, August.
    3. Andrej Bregar, 2019. "Application of a hybrid Delphi and aggregation–disaggregation procedure for group decision-making," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 7(1), pages 3-32, May.
    4. Jabeur, Khaled & Martel, Jean-Marc, 2007. "A collective choice method based on individual preferences relational systems (p.r.s.)," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1549-1565, March.
    5. Yoo, Yeawon & Escobedo, Adolfo R. & Skolfield, J. Kyle, 2020. "A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1025-1041.
    6. Khaled Jabeur & Jean-Marc Martel & Slim Ben Khélifa, 2004. "A Distance-Based Collective Preorder Integrating the Relative Importance of the Group's Members," Group Decision and Negotiation, Springer, vol. 13(4), pages 327-349, July.
    7. Amor, Sarah Ben & Jabeur, Khaled & Martel, Jean-Marc, 2007. "Multiple criteria aggregation procedure for mixed evaluations," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1506-1515, September.
    8. Khaled Jabeur & Jean-Marc Martel, 2010. "An Agreement Index with Respect to a Consensus Preorder," Group Decision and Negotiation, Springer, vol. 19(6), pages 571-590, November.

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