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On The Consistency Of Some Crisp Choice Functions Based On A Strongly Complete Fuzzy Pre-Order

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  • SIMEON FOTSO

    ()
    (Département de Mathématiques, Ecole Normale Supérieure de Yaoundé, Université de Yaoundé I, B.P. 47 Yaoundé, Cameroun)

  • LOUIS AIME FONO

    ()
    (Département de Mathématiques et Informatique, Faculté des Sciences, Université de Douala, B.P. 24157 Douala, Cameroun)

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    Abstract

    This paper presents the first part of a general study of the structure of nine preference-based choice functions introduced by Barrett et al.2 More precisely, we show that, as for crisp total pre-orders, first and last alternatives exist in a finite set of alternatives equipped with a strongly complete fuzzy pre-order. We use that result to characterize each of those crisp choice functions for crisp total pre-orders and strongly complete fuzzy pre-orders. We study, by means of those characterizations, the consistency of those preference-based choice functions when preferences are strongly complete fuzzy pre-orders (thereby crisp total pre-orders), that is, we check if each choice function satisfies or violates each of six consistency conditions introduced by Sen.11

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 08 (2012)
    Issue (Month): 02 ()
    Pages: 257-272

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    Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:02:p:257-272

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    Related research

    Keywords: Binary fuzzy relation; transitivity; strong completeness; crisp choice function; consistency condition;

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