A further study on rationality conditions of fuzzy choice functions

The investigation of rationality plays a central role in the study of fuzzy choice functions. In this paper, we deal with some important rationality conditions of fuzzy choice functions, including Weak (Strong) Fuzzy Congruence Axiom, Weak (Strong) Axiom of Fuzzy Revealed Preference, fuzzy versions of famous crisp conditions α, β, γ and δ etc. in the framework of the Banerjee choice function. We systematically investigate the relationships between these conditions under the assumption that every involved choice set is normal and verify some equivalence results for arbitrary t-norms. As a result, a fuzzy version of the Arrow–Sen theorem is presented. The research makes a significant difference compared with the current investigation in the framework of the Georgescu choice function.