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Fuzzy preorders: conditional extensions, extensions and their representations

Author

Listed:
  • J. C. R. Alcantud

    (University of Salamanca)

  • S. Díaz

    (University of Oviedo)

Abstract

The crisp literature provides characterizations of the preorders that admit a total preorder extension when some pairwise order comparisons are imposed on the extended relation. It is also known that every preorder is the intersection of a collection of total preorders. In this contribution we generalize both approaches to the fuzzy case. We appeal to a construction for deriving the strict preference and the indifference relations from a weak preference relation, that allows to obtain full characterizations in the conditional extension problem. This improves the performance of the construction via generators studied earlier.

Suggested Citation

  • J. C. R. Alcantud & S. Díaz, 2016. "Fuzzy preorders: conditional extensions, extensions and their representations," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 371-396, December.
    • Handle: RePEc:spr:fuzodm:v:15:y:2016:i:4:d:10.1007_s10700-016-9230-3
    DOI: 10.1007/s10700-016-9230-3
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    References listed on IDEAS

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    1. José Alcantud, 2009. "Conditional ordering extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 495-503, June.
    2. Donaldson, David & Weymark, John A., 1998. "A Quasiordering Is the Intersection of Orderings," Journal of Economic Theory, Elsevier, vol. 78(2), pages 382-387, February.
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