An approach to construct entropies on interval-valued intuitionistic fuzzy sets by their distance functions

The main contribution of this paper is to give a new axiomatic definition of entropy measure and provide a constructing approach in the context of interval-valued intuitionistic fuzzy set (IVIFS). We give a new idea to define entropy on IVIFS: From the graphical representation, we consider the difference between a given IVIFS and its corresponding two interval fuzzy sets (IVFSs) by introducing a distance function that meets some specific conditions. The relationship between the distance function and the distance measure has also been illustrated. Based on distance functions, we give an approach to construct entropy measures on IVIFS. Then, a plenty of new entropies on IVIFS are introduced. Furthermore, we use a comparative example to show the proposed measures outperform the existing measures and utilize a demonstrative example to explain the application of the entropy measure in the multi-criteria decision making (MCDM), which verify the feasibility of our entropy construction method.