A new concept of the inclusion measure for intuitionistic fuzzy sets is proposed by the axiomatic definition. Also, the distance measures, similarity measures and information entropy are recalled and summarized. Most of important, some relationships among distance measure, information entropy, and inclusion measure of IFSs are then investigated. Finally, we obtain some important theorems by which the distance measure, information entropy and inclusion measure of IFSs and interval-valued intuitionistic fuzzy set can be deduced based on their corresponding axiomatic definitions. Simultaneously, some new formulae to calculate distance measure, information entropy and inclusion measure of IFSs are presented.
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