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.
Highlights
Choice functions are a pre-eminent tool in the abstract theory of decision making
The first implication that we study under H1 and H2 is whether the fuzzy Arrow axiom guarantees the fuzzy Chernoff condition in the context of the Łukasiewicz implicator
The analysis of the consistency of choices is an important challenge that aspires to establish the limits of rational behavior from a theoretical point of view
Summary
Choice functions are a pre-eminent tool in the abstract theory of decision making. They have been deeply studied from many perspectives. Particular emphasis is put on disclosing their relationship with models like preferences (binary relations) or utility functions In this interaction, the axioms of consistency draw a bridge between abstract choices and rational behavior. Stochastic choice functions (e.g., Bandyopadhyay, Dasgupta and Pattanaik [3,4], Machina [5]) or correspondences (e.g., Alcantud [6]) replace the deterministic with stochastic or probabilistic behavior They permit the analysis of their rationality to be reproduced through adapted axioms of consistency. It is important to have precise knowledge about the various forms that rationality axioms can adopt Their relationships with different specifications of the underlying fuzzy concepts, like implications, is a natural field for investigation.
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