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.

本文的主要贡献是为熵测度提供了一个公理化的定义，并为区间值直觉模糊集（IVIFS）提供了一种构建方法。我们给出了定义IVIFS熵的新思路：从图形表示形式，我们通过引入满足某些特定条件的距离函数，来考虑给定IVIFS及其对应的两个区间模糊集（IVFS）之间的差异。距离函数和距离度量之间的关系也已说明。基于距离函数，我们给出了一种在IVIFS上构造熵测度的方法。然后，引入了有关IVIFS的许多新熵。此外，