Rational fuzzy and sequential fuzzy choice

In the setting of fuzzy choice theory we explore some relationships among known and new consistency axioms, as well as consequences of rationalizability. Then we define the notion of sequential application of fuzzy choice functions, and investigate its normative implications under related concepts of rationalizability. In particular, the fuzzy Binariness axiom is verified by sequential fuzzy choice, and the Fuzzy Arrow Axiom (when the set of alternatives is finite) is preserved by the newly defined sequential procedure. The latter property ensures that full-rationality is preserved too.