New symmetric belief α-divergence and belief entropy via belief-plausibility transformation for multi-source information fusion

Dempster-Shafer evidence theory, a powerful tool for managing imperfect information, has been extensively used in various fields of multi-source information fusion. However, how to effectively quantify the difference between evidences and the uncertainty within each evidence remains a challenge. In this paper, we introduce two new symmetric belief $\alpha$-divergences based on belief-plausibility transformation to measure the difference between evidences. These divergences exhibit key properties such as nonnegativity, nondegeneracy and symmetry. We also show that they reduce to well-known divergences like ${\chi }^2$, Jeffreys, Hellinger, Jensen-Shannon and arithmetic-geometric in specific cases. Additionally, we propose a new belief entropy, derived from the belief-plausibility transformation, to quantify the uncertainty inherent in evidence. Leveraging both the divergences and entropy, we develop a new multi-source information fusion method that assesses the credibility and informational volume of each evidence, providing deeper insights into the importance of each evidence. To demonstrate the effectiveness of our method, we apply it to plant disease detection and fault diagnosis, where it outperforms existing techniques.