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A Distance-Based Collective Preorder Integrating the Relative Importance of the Group's Members

Author

Listed:
  • Khaled Jabeur

    (Université Laval)

  • Jean-Marc Martel

    (Université Laval)

  • Slim Ben Khélifa

    (École Supérieure de Commerce de Tunis)

Abstract

In this paper, we propose an aggregation procedure, which includes two steps. In the first one, the group's members elaborate individually a preorder (total or partial) on the alternatives set. These preorders can be obtained, for example, by applying a multicriterion aggregation procedure such as ELECTRE III, PROMETHEE I or II. In the second step, these individual preorders (total or partial) are aggregated into a collective preorder (total or partial). For this purpose, we first built a distance measure between pairs of binary relations in order to quantify the divergence between two preorders. Then we determine, for each pair of alternatives, the relative importance coefficients of the group's members by using a method based on subjective and objective components. These coefficients and the distance measure are finally exploited by an iterative algorithm in order to elaborate a collective preorder synthesizing the individual preorders.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:grdene:v:13:y:2004:i:4:d:10.1023_b:grup.0000042894.00775.75
    DOI: 10.1023/B:GRUP.0000042894.00775.75
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    References listed on IDEAS

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    1. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    2. Freixas, Josep & Marciniak, Dorota & Pons, Montserrat, 2012. "On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 367-375.
    3. Alessandro Luè & Alberto Colorni, 2015. "Conflict Analysis for Environmental Impact Assessment: A Case Study of a Transportation System in a Tourist Area," Group Decision and Negotiation, Springer, vol. 24(4), pages 613-632, July.
    4. Chun-xiang Guo & Ying Peng, 2015. "Lattice Order Group Decision Making with Interval Probability Based on Prospect Theory," Group Decision and Negotiation, Springer, vol. 24(5), pages 753-775, September.
    5. Cook, Wade D., 2006. "Distance-based and ad hoc consensus models in ordinal preference ranking," European Journal of Operational Research, Elsevier, vol. 172(2), pages 369-385, July.
    6. 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.
    7. Suzana de Suzana Dantas Daher & Adiel Teixeira Almeida, 2012. "The Use of Ranking Veto Concept to Mitigate the Compensatory Effects of Additive Aggregation in Group Decisions on a Water Utility Automation Investment," Group Decision and Negotiation, Springer, vol. 21(2), pages 185-204, March.
    8. Siskos, Eleftherios & Tsotsolas, Nikos, 2015. "Elicitation of criteria importance weights through the Simos method: A robustness concern," European Journal of Operational Research, Elsevier, vol. 246(2), pages 543-553.
    9. 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.
    10. Fu-Ling Cai & Xiuwu Liao & Kan-Liang Wang, 2012. "An interactive sorting approach based on the assignment examples of multiple decision makers with different priorities," Annals of Operations Research, Springer, vol. 197(1), pages 87-108, August.
    11. Freixas, Josep & Kurz, Sascha, 2013. "The golden number and Fibonacci sequences in the design of voting structures," European Journal of Operational Research, Elsevier, vol. 226(2), pages 246-257.
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    13. 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.

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