| In this thesis, under the conditions that every choice set is normal and that the involved t-norms are left-continuous, we fuzzify the work done by Arrow and Bandyopadhyay and obtain some results about the rationality characterization of fuzzy choice functions. The main research is summarized as follows:Firstly, we present a brief review over rationality conditions and the rationality characterization of crisp choice functions in the literature, and give a detailed introduction to the work done by Arrow and Bandyopadhyay concerning the characterization of choice functions.Then we turn to the study on the rationality characterization of fuzzy choice functions. For this purpose, we extend some results obtained by Ma and Georgescu concerning the relationships between rationality conditions under t-norm min to a general t-norm. Afterwards, we fuzzify Arrow's five rationality conditions and investigate the relationships between thesefuzzified conditions and obtain a sufficient condition to characterize T-transitive rationality of a fuzzy choice function. Meanwhile, some examples are given to illustrate that some Arrow's results don't hold anymore in the fuzzy case. Finally, we fuzzify Bandyopadhyay's rationality conditions and discuss the relationships between these fuzzified conditions with which we characterize T-transitive rationality, T-pseudo-transitive rationality, T-quasi-transitive rationality and acyclic rationality of fuzzy choice functions. The necessary and sufficient conditions for the characterization of acyclic rationality and T-transitive rationality are given. Generally speaking, we only obtain some sufficient conditions for T-quasi-transitive rationality and T-pseudo-transitive rationality. However, a necessary condition for T-quasi-transitive rationality is available if the involved negation is the intuition-istic negation. Again, some examples are provided to illustrate that some results in the crisp case can not be extended to the fuzzy case.
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