A necessary and sufficient condition for the existence of Orlovsky's choice set

Abstract

In a previous paper [2], the authors proved that a property of ‘acyclity’ in fuzzy preference relations was anecessary and sufficientcondition for the existence of unfuzzy nondominated alternatives when such aset of alternatives is finite. In this paper, a general property of ‘foundation’ is proved to be anecessary and sufficientcondition, without requiring finiteness on the set of alternatives. Both concepts are based on classical results in crisp binary relations.