A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure

In this contribution, we generalize recent results on the entropy of interval-valued fuzzy sets (IVFSs) based on the intuitionistic distance and its relationship with similarity measure. The intuitionistic distance provides us with a new axiomatic definition of entropy of IVFSs. Based on the set of new axioms, we also prove some theorems that entropy and similarity measure for IVFSs can be transformed by each other in a general way. The contribution ends by deriving a formula that creates a variety of new entropies by the use of given entropies of IVFSs. (c) 2012 Elsevier B.V. All rights reserved.