A Measure of Referential Success Based on Alpha-Cuts

Abstract

In this paper we propose a measure of the referential success of a referring expression, defined by a collection of fuzzy properties, with respect to a certain object. The measure yields the degree to which the object is univocally identified by the referring expression among a collection of objects in a certain context. We consider the alpha-cuts of the fuzzy subset of objects that satisfy the referring expression as crisp versions of the problem, and we obtain the final measure by measuring the subset of levels in [0,1] where the referring expression has referential success in the crisp sense.