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Szpilrajn-type extensions of fuzzy quasiorderings

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  • 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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 50547.

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Date of creation: 12 Jul 2013
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Handle: RePEc:pra:mprapa:50547

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Keywords: Quasiordering; order; extension of a quasiordering.;

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  1. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
  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.
  3. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Upper Semicontinuous Extensions of Binary Relations," Cahiers de recherche 2002-01, Universite de Montreal, Departement de sciences economiques.
  4. José Alcantud, 2009. "Conditional ordering extensions," Economic Theory, Springer, vol. 39(3), pages 495-503, June.
  5. 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.
  6. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
  7. Yi, Gyoseob, 1993. "Continuous extension of preferences," Journal of Mathematical Economics, Elsevier, vol. 22(6), pages 547-555.
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