Specificity measures based on fuzzy set inequality

Abstract

Specificity is a measure that tells us to what extent a fuzzy set is a singleton. The variety of application domains of this measure requires different specific forms of calculating it. One way to control the semantic nuances in the way specificity is computed is to generate it from other well-known measures in the Fuzzy Set Theory that have a wide range of evaluation functions with different axiomatics. Following this strategy, in this work we study in depth the inequality measures based on their axiomatics, we establish a method to use them as generators of specificity measures, and we analyze the semantics and the desired properties of specificity measures obtained according to the axioms satisfied by the inequality measures used as generators. As we will see, relevant results have been obtained that relate different families of specificity and inequality measures.