Li Jiapeng, Pan Qian
School of Automation, Northwestern Polytechnical University, Xi'an 710072, China.
School of Electronics and Information, Northwestern Polytechnical University, Xi'an 710072, China.
Entropy (Basel). 2020 Jun 20;22(6):691. doi: 10.3390/e22060691.
Dempster-Shafer theory has been widely used in many applications, especially in the measurement of information uncertainty. However, under the D-S theory, how to use the belief entropy to measure the uncertainty is still an open issue. In this paper, we list some significant properties. The main contribution of this paper is to propose a new entropy, for which some properties are discussed. Our new model has two components. The first is Nguyen entropy. The second component is the product of the cardinality of the frame of discernment (FOD) and Dubois entropy. In addition, under certain conditions, the new belief entropy can be transformed into Shannon entropy. Compared with the others, the new entropy considers the impact of FOD. Through some numerical examples and simulation, the proposed belief entropy is proven to be able to measure uncertainty accurately.
Dempster-Shafer理论已在许多应用中广泛使用，尤其是在信息不确定性的度量方面。然而，在D-S理论下，如何使用信度熵来度量不确定性仍然是一个未解决的问题。在本文中，我们列出了一些重要性质。本文的主要贡献是提出了一种新的熵，并讨论了其一些性质。我们的新模型有两个组成部分。第一个是阮熵。第二个组成部分是识别框架（FOD）的基数与Dubois熵的乘积。此外，在某些条件下，新的信度熵可以转化为香农熵。与其他熵相比，新熵考虑了FOD的影响。通过一些数值例子和仿真，证明了所提出的信度熵能够准确地度量不确定性。
