Consistency properties for fuzzy choice functions: An analysis with the ̷lukasiewicz t-norm

Abstract

In continuation of the research in Alcantud and Díaz [1], we investigate the relationships between consistency axioms in the framework of fuzzy choice functions. In order to help disclose the role of a t-norm in such analyses, we start to study the situation that arises when we use other t-norms instead. We conclude that unless we impose further structure on the domain of application for the choices, the use of the ̷Lukasiewicz t-norm as a replacement for the minimum t-norm does not guarantee a better performance.