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Szpilrajn-type extensions of fuzzy quasiorderings

Author

Listed:
  • Alcantud, José Carlos R.
  • Díaz, Susana

Abstract

The problem of embedding incomplete into complete relations has been an important topic of research in the context of crisp relations. After Szpilrajn’s result, several variations have been published. Alcantud studied in 2009 the case where the extension is asked to satisfy some order conditions between elements. He first studied and solved a particular formulation where conditions are imposed in terms of strict preference only, which helps to precisely identify which quasiorderings can be extended when we allow for additional conditions in terms of indifference too. In this contribution we generalize both results to the fuzzy case.

Suggested Citation

  • Alcantud, José Carlos R. & Díaz, Susana, 2013. "Szpilrajn-type extensions of fuzzy quasiorderings," MPRA Paper 50547, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:50547
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    References listed on IDEAS

    as
    1. Yi, Gyoseob, 1993. "Continuous extension of preferences," Journal of Mathematical Economics, Elsevier, vol. 22(6), pages 547-555.
    2. Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 115-134, March.
    3. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
    4. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2002. "Upper semicontinuous extensions of binary relations," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 231-246, May.
    5. José Alcantud, 2009. "Conditional ordering extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 495-503, June.
    6. 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.
    7. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-390, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Quasiordering; order; extension of a quasiordering.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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