Zhang Zhuo, Wang Hongfei, Zhang Jianting, Jiang Wen
School of Electronics and Information, Northwestern Polytechnical University, Xi'an 710072, China.
No. 91977 Unit of People's Liberation Army of China, Beijing 100036, China.
Entropy (Basel). 2023 Jun 12;25(6):925. doi: 10.3390/e25060925.
Measuring the correlation between belief functions is an important issue in Dempster-Shafer theory. From the perspective of uncertainty, analyzing the correlation may provide a more comprehensive reference for uncertain information processing. However, existing studies about correlation have not combined it with uncertainty. In order to address the problem, this paper proposes a new correlation measure based on belief entropy and relative entropy, named a belief correlation measure. This measure takes into account the influence of information uncertainty on their relevance, which can provide a more comprehensive measure for quantifying the correlation between belief functions. Meanwhile, the belief correlation measure has the mathematical properties of probabilistic consistency, non-negativity, non-degeneracy, boundedness, orthogonality, and symmetry. Furthermore, based on the belief correlation measure, an information fusion method is proposed. It introduces the objective weight and subjective weight to assess the credibility and usability of belief functions, thus providing a more comprehensive measurement for each piece of evidence. Numerical examples and application cases in multi-source data fusion demonstrate that the proposed method is effective.
在证据理论中，度量信度函数之间的相关性是一个重要问题。从不确定性的角度来看，分析相关性可以为不确定信息处理提供更全面的参考。然而，现有的关于相关性的研究尚未将其与不确定性相结合。为了解决这个问题，本文提出了一种基于信度熵和相对熵的新的相关性度量方法，称为信度相关性度量。该度量考虑了信息不确定性对其相关性的影响，能够为量化信度函数之间的相关性提供更全面的度量。同时，信度相关性度量具有概率一致性、非负性、非退化性、有界性、正交性和对称性等数学性质。此外，基于信度相关性度量，提出了一种信息融合方法。该方法引入客观权重和主观权重来评估信度函数的可信度和可用性，从而为每一条证据提供更全面的度量。多源数据融合中的数值算例和应用案例表明，所提方法是有效的。
