Relationships between entropy and similarity measure of interval-valued intuitionistic fuzzy sets

The concept of entropy of interval-valued intuitionistic fuzzy set (IvIFS) is first introduced. The close relationships between entropy and the similarity measure of interval-valued intuitionistic fuzzy sets are discussed in detail. We also obtain some important theorems by which entropy and similarity measure of IvIFSs can be transformed into each other based on their axiomatic definitions. Simultaneously, some formulae to calculate entropy and similarity measure of IvIFSs are put forward. © 2010 Wiley Periodicals, Inc.