A generalized χ 2 divergence for multisource information fusion and its application in fault diagnosis

Dempster–Shafer theory is invaluable for handing uncertain problems in multisource information fusion field. But how to fuse highly conflicting information remains a pending issue. To deal with the issue, we propose a novel reinforced belief ${\chi }^2$ divergence measure (named as $\mathrm{??}{\chi }^2$ divergence) to calculate the conflict degree between evidence. The proposed $\mathrm{??}{\chi }^2$ divergence comprehensively considers the effects of the single-element subset and the multielement subset. In addition, the $\mathrm{??}{\chi }^2$ divergence has been proved to be a bounded, nondegenerate, and symmetrical divergence measure. Then, we design a new $\mathrm{??}{\chi }^2$ divergence-based multisource information fusion method. This method combines information volume weights and supports degree weights to modify the evidence before fusion. Finally, an application for fault diagnosis is provided to show that the proposed method is superior to other existing methods.