ON THE CONSISTENCY OF SOME CRISP CHOICE FUNCTIONS BASED ON A STRONGLY COMPLETE FUZZY PRE-ORDER

Simeon Fotso () and Louis Aime Fono ()
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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

New Mathematics and Natural Computation (NMNC), 2012, vol. 08, issue 02, 257-272

Abstract: This paper presents the first part of a general study of the structure of nine preference-based choice functions introduced by Barrettet al.2More 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

Keywords: Binary fuzzy relation; transitivity; strong completeness; crisp choice function; consistency condition (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S1793005712400145

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