Specificity for interval-valued fuzzy sets

In this paper some axiomatic definitions about specificity for interval-valued fuzzy sets are proposed. Some examples of measures of specificity for interval-valued fuzzy sets are showed. It is also defined a extension of the notion of alpha cut for interval-valued fuzzy sets and a generalized similarity for interval-valued fuzzy relations. An axiomatic definition of specificity of interval-valued fuzzy sets under the knowledge of a generalized similarity is proposed.