Summary: The Arrow index of a fuzzy choice function \(C\) is a measure of the degree to which \(C\) satisfies the Fuzzy Arrow Axiom, a fuzzy version of the classical Arrow Axiom. The main result of this paper shows that the Arrow index \({\mathcal A}(C)\) characterizes the degree to which \(C\) is full rational. We also obtain a method for computing \({\mathcal A}(C)\). The Arrow index allows to rank the fuzzy choice functions with respect to their rationality. Thus, if for solving a decision problem several fuzzy choice functions are proposed, by the Arrow index the most rational one will be chosen.