On Families of Bounded Specificity Measures

In this paper we propose bounding conditions that characterize different families of specificity measures. The proposed conditions are associated to particular semantics that provide us with different criteria for choosing the most appropriate specificity measure for a certain use. In particular, we distinguish predicate-like measures, mostly useful for providing a fuzzy classification of fuzzy sets between specific and non-specific, and index-like measures, which are more appropriate for providing an order relation between fuzzy sets in terms of their specificity. An intermediate class of measures is also studied, where different bounds are associated to values of the cardinality of fuzzy sets for which specificity is expected to be 0.