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A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

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  • Ben Amor, Sarah
  • Martel, Jean-Marc

Abstract

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:237:y:2014:i:3:p:1165-1169
    DOI: 10.1016/j.ejor.2014.03.036
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    References listed on IDEAS

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    1. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    2. 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.
    3. Tommi Meskanen & Hannu Nurmi, 2006. "Distance from Consensus: A Theme and Variations," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 117-132, Springer.
    4. Wade Cook & Moshe Kress & Lawrence Seiford, 1986. "Information and preference in partial orders: A bimatrix representation," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 197-207, June.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Wade D. Cook & Moshe Kress, 1985. "Ordinal Ranking with Intensity of Preference," Management Science, INFORMS, vol. 31(1), pages 26-32, January.
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    2. Boris Mirkin & Trevor I. Fenner, 2019. "Distance and Consensus for Preference Relations Corresponding to Ordered Partitions," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 350-367, July.

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