School of Electronics and Information, Northwestern Polytechnical University, Xi'an 710072, China.
Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, China.
Sensors (Basel). 2018 Jun 11;18(6):1902. doi: 10.3390/s18061902.
Quantification of uncertain degree in the Dempster-Shafer evidence theory (DST) framework with belief entropy is still an open issue, even a blank field for the open world assumption. Currently, the existed uncertainty measures in the DST framework are limited to the closed world where the frame of discernment (FOD) is assumed to be complete. To address this issue, this paper focuses on extending a belief entropy to the open world by considering the uncertain information represented as the FOD and the nonzero mass function of the empty set simultaneously. An extension to Deng’s entropy in the open world assumption (EDEOW) is proposed as a generalization of the Deng’s entropy and it can be degenerated to the Deng entropy in the closed world wherever necessary. In order to test the reasonability and effectiveness of the extended belief entropy, an EDEOW-based information fusion approach is proposed and applied to sensor data fusion under uncertainty circumstance. The experimental results verify the usefulness and applicability of the extended measure as well as the modified sensor data fusion method. In addition, a few open issues still exist in the current work: the necessary properties for a belief entropy in the open world assumption, whether there exists a belief entropy that satisfies all the existed properties, and what is the most proper fusion frame for sensor data fusion under uncertainty.
在 Dempster-Shafer 证据理论（DST）框架中，使用置信熵对不确定度进行量化仍然是一个悬而未决的问题，甚至对于开放世界假设也是一个空白领域。目前，DST 框架中存在的不确定性度量方法仅限于封闭世界的假设，其中分辨框架（FOD）被假设为完整的。为了解决这个问题，本文重点关注通过同时考虑不确定信息表示为 FOD 和非零空集质量函数，将置信熵扩展到开放世界。提出了一种在开放世界假设下的 Deng 熵扩展（EDEOW）作为 Deng 熵的推广，并且在必要时可以退化到封闭世界中的 Deng 熵。为了测试扩展置信熵的合理性和有效性，提出了一种基于 EDEOW 的信息融合方法，并将其应用于不确定环境下的传感器数据融合。实验结果验证了扩展度量以及改进后的传感器数据融合方法的有用性和适用性。此外，目前的工作中仍然存在一些悬而未决的问题：开放世界假设下置信熵的必要属性、是否存在满足所有现有属性的置信熵，以及在不确定环境下传感器数据融合的最合适融合框架是什么。
