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Consistency properties for fuzzy choice functions: an analysis with the Łukasiewicz T-norm. (English) Zbl 1432.91037

Summary: 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.

MSC:

91B06 Decision theory
91B08 Individual preferences
03E72 Theory of fuzzy sets, etc.
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