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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 intervalvalued fuzzy relations. An axiomatic definition of specificity of interval-valued fuzzy sets under the knowledge of a generalized similarity is given.
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