Arrow's Axiom and Full Rationality for Fuzzy Choice Functions

A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function verifies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that these conditions are also equivalent with weak and strong fuzzy congruence axioms WFCA and SFCA. It is studied the Arrow index, a new concept that indicates the degree to which a fuzzy choice function verifies the Fuzzy Arrow Axiom.