Pan Qian, Zhou Deyun, Tang Yongchuan, Li Xiaoyang, Huang Jichuan
School of Electronics and Information, Northwestern Polytechnical University, Xi'an 710072, China.
First Military Representative Office of Air Force Equipment Department, People's Liberation Army Air Force, Chengdu 610013, China.
Entropy (Basel). 2019 Feb 10;21(2):163. doi: 10.3390/e21020163.
Dempster-Shafer evidence theory (DST) has shown its great advantages to tackle uncertainty in a wide variety of applications. However, how to quantify the information-based uncertainty of basic probability assignment (BPA) with belief entropy in DST framework is still an open issue. The main work of this study is to define a new belief entropy for measuring uncertainty of BPA. The proposed belief entropy has two components. The first component is based on the summation of the probability mass function (PMF) of single events contained in each BPA, which are obtained using plausibility transformation. The second component is the same as the weighted Hartley entropy. The two components could effectively measure the discord uncertainty and non-specificity uncertainty found in DST framework, respectively. The proposed belief entropy is proved to satisfy the majority of the desired properties for an uncertainty measure in DST framework. In addition, when BPA is probability distribution, the proposed method could degrade to Shannon entropy. The feasibility and superiority of the new belief entropy is verified according to the results of numerical experiments.
邓普斯特-谢弗证据理论（DST）在众多应用中处理不确定性方面已展现出巨大优势。然而，在DST框架下如何用信度熵量化基本概率分配（BPA）基于信息的不确定性仍是一个未解决的问题。本研究的主要工作是定义一种新的信度熵来度量BPA的不确定性。所提出的信度熵有两个组成部分。第一部分基于每个BPA中单个事件的概率质量函数（PMF）之和，这些单个事件的概率质量函数是通过似真度变换获得的。第二部分与加权哈特利熵相同。这两个部分可以分别有效地度量DST框架中发现的不一致不确定性和非特异性不确定性。所提出的信度熵被证明满足DST框架中不确定性度量的大多数期望属性。此外，当BPA为概率分布时，所提出的方法可以退化为香农熵。根据数值实验结果验证了新信度熵的可行性和优越性。
