Entropy, Similarity Measure, Inclusion Measure of Intuitionistic Fuzzy Sets and Their Relationships

In the present paper, we introduce a new axiomatic definition of the inclusion measure for intuitionistic fuzzy sets (IFSs, for short). The close relationships among entropy, similarity measure, and inclusion measure of IFSs are then discussed in detail. Also, we obtain some important theorems by which the entropy, similarity measure and inclusion measure of IFSs can be transformed into each other based on their axiomatic definitions. Moreover, some formulae for calculating the entropy, similarity measure and inclusion measure of IFSs are put forward. Finally, we compare the proposed new entropy, similarity and distance measures with the existing ones.