An improved belief Hellinger divergence for Dempster-Shafer theory and its application in multi-source information fusion

Dempster-Shafer theory (DST), as a generalization of Bayesian probability theory, is a useful technique for achieving multi-source information fusion under uncertain environments. Nevertheless, when a high degree of conflict exists between pieces of evidence, unreasonable results are often generated using Dempster's combination rule. How to fuse highly conflicting information is still an open problem. In this study, we first propose an improved belief Hellinger divergence measure, which can fully consider the uncertainty in basic probability assignments, to quantify the conflict level between evidence. Second, some properties (i.e., nonnegativity, nondegeneracy, symmetry, and trigonometric inequality) of the proposed divergence measure are discussed. Then, we present a novel multi-source information fusion strategy, in which the credibility of the evidence is determined based on external discrepancy and internal ambiguity. Additionally, we consider the decay of credibility when fusing evidence across different times. Finally, applications in fault diagnosis and Iris dataset classification are presented to demonstrate the effectiveness of our method. The results indicate that our approach is more reasonable and can identify the target with a higher belief degree.