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Axioms 2018, 7(4), 78; https://doi.org/10.3390/axioms7040078

Consistency Properties for Fuzzy Choice Functions: An Analysis with the Łukasiewicz T-Norm

1
UNIMODE Research Units, Department of Statistics and O. R., University of Oviedo, E33003 Oviedo, Spain
2
BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), Campus Unamuno, University of Salamanca, E37007 Salamanca, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 10 August 2018 / Revised: 22 October 2018 / Accepted: 25 October 2018 / Published: 29 October 2018
Full-Text   |   PDF [249 KB, uploaded 29 October 2018]

Abstract

We focus on the relationships among some consistency axioms in the framework of fuzzy choice functions. In order to help disclose the role of the t-norm in existing analyses, we start to study the situation that arises when we replace the standard t-norm with other t-norms. Our results allow us to conclude that unless we impose further structure on the domain of application for the choices, the use of the Łukasiewicz t-norm as a replacement for the standard t-norm does not guarantee a better performance. View Full-Text
Keywords: fuzzy choice function; choice function; consistency; fuzzy arrow axiom; triangular norm fuzzy choice function; choice function; consistency; fuzzy arrow axiom; triangular norm
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Díaz, S.; Alcantud, J.C.R.; Montes, S. Consistency Properties for Fuzzy Choice Functions: An Analysis with the Łukasiewicz T-Norm. Axioms 2018, 7, 78.

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