Tang Yongchuan, Chen Yong, Zhou Deyun
School of Microelectronics, Northwestern Polytechnical University, Xi'an 710072, China.
School of Big Data and Software Engineering, Chongqing University, Chongqing 401331, China.
Entropy (Basel). 2022 Nov 2;24(11):1596. doi: 10.3390/e24111596.
Dempster-Shafer evidence theory is widely used in modeling and reasoning uncertain information in real applications. Recently, a new perspective of modeling uncertain information with the negation of evidence was proposed and has attracted a lot of attention. Both the basic probability assignment (BPA) and the negation of BPA in the evidence theory framework can model and reason uncertain information. However, how to address the uncertainty in the negation information modeled as the negation of BPA is still an open issue. Inspired by the uncertainty measures in Dempster-Shafer evidence theory, a method of measuring the uncertainty in the negation evidence is proposed. The belief entropy named Deng entropy, which has attracted a lot of attention among researchers, is adopted and improved for measuring the uncertainty of negation evidence. The proposed measure is defined based on the negation function of BPA and can quantify the uncertainty of the negation evidence. In addition, an improved method of multi-source information fusion considering uncertainty quantification in the negation evidence with the new measure is proposed. Experimental results on a numerical example and a fault diagnosis problem verify the rationality and effectiveness of the proposed method in measuring and fusing uncertain information.
邓普斯特-谢弗证据理论在实际应用中对不确定信息的建模与推理方面有着广泛应用。近来，一种基于证据否定来对不确定信息进行建模的新视角被提出，并引起了广泛关注。在证据理论框架下，基本概率赋值（BPA）及其否定都能够对不确定信息进行建模与推理。然而，如何处理以BPA否定形式建模的否定信息中的不确定性仍是一个悬而未决的问题。受邓普斯特-谢弗证据理论中不确定性度量的启发，提出了一种度量否定证据中不确定性的方法。采用了在研究者中备受关注的名为邓熵的信度熵，并对其进行改进以度量否定证据的不确定性。所提出的度量基于BPA的否定函数进行定义，能够量化否定证据的不确定性。此外，还提出了一种改进的多源信息融合方法，该方法利用新度量考虑了否定证据中的不确定性量化。在一个数值示例和一个故障诊断问题上的实验结果验证了所提方法在度量和融合不确定信息方面的合理性与有效性。
