ON THE CONSISTENCY OF SOME CRISP CHOICE FUNCTIONS BASED ON A STRONGLY COMPLETE FUZZY PRE-ORDER-Reference-Cited by-同舟云学术

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

Published:2012-06-14 Issue:02 Volume:08 Page:257-272
ISSN:1793-0057
Container-title:New Mathematics and Natural Computation
language:en
Short-container-title:New Math. and Nat. Computation

Author:

FOTSO SIMEON¹,FONO LOUIS AIME²

Affiliation:

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

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

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

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics,Computer Science Applications,Human-Computer Interaction

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793005712400145

Reference11 articles.

1. On choosing rationally when preferences are fuzzy

2. Fuzzy revealed preference theory

3. Utility function of fuzzy preferences on a countable set under max-*-transitivity

4. On strict lower and upper sections of weakly complete fuzzy pre-orders based on co-implication

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