The characterization of Wϕ-transitive rationality and acyclic rationality of fuzzy choice functions

Abstract

The objective of the paper is to extend Bandyopadhyay's results on rationality conditions of crisp choice functions. By fuzzifying the rationality conditions in the crisp case, we present a necessary and sufficient condition for the acyclic rationality and a characterization theorem for the Wϕ-transitive rationality under a strong De Morgan triple. As a result, some rationality characterizations in the crisp choice functions are generalized.