In this paper we study empirically the validity of measures of referential success for referring expressions involving gradual properties. More specifically, we study the ability of several measures of referential success to predict the success of a user in choosing the right object, given a referring expression. Experimental results indicate that certain fuzzy measures of success are able to predict human accuracy in reference resolution. Such measures are therefore suitable for the estimation of the success or otherwise of a referring expression produced by a generation algorithm, especially in case the properties in a domain cannot be assumed to have crisp denotations.

We introduce the properties to be satisfied by measures of referential success of set referring expressions with fuzzy properties. We define families of measures on the basis of n-cardinality measures and we illustrate some of them with a toy example.