Time series data contains the amount of information to reflect the development process and state of a subject. Especially, the complexity is a valuable factor to illustrate the feature of the time series. However, it is still an open issue to measure the complexity of sophisticated time series due to its uncertainty. In this study, based on the belief Re´nyi divergence, a novel time series complexity measurement algorithm, called belief Re´nyi divergence of divergence (BRe´DOD), is proposed. Specifically, the BRe´DOD algorithm takes the boundaries of time series value into account. What is more, according to the Dempster-Shafer (D-S) evidence theory, the time series is converted to the basic probability assignments (BPAs) and it measures the divergence of a divergence sequence. Then, the secondary divergence of the time series is figured out to represent the complexity of the time series. In addition, the BRe´DOD algorithm is applied to sets of cardiac inter-beat interval time series, which shows the superiority of the proposed method over classical machine learning methods and recent well-known works.

Dempster–Shafer (D-S) evidence theory is invaluable in the domain of multisource information fusion for handing uncertainty problems. However, there may be counter-intuitive phenomenon when facing highly conflicting information. In this paper, a novel symmetric enhanced belief χ 2 ${\chi }^{2}$ divergence measure, called S E B χ 2 $SEB{\chi }^{2}$ , is proposed to measure the discrepancy between basic probability assignments (BPAs). The S E B χ 2 $SEB{\chi }^{2}$ divergence consider the features of BPAs as the influence of both single-element subsets and multielement subsets is taken into account. Furthermore, the S E B χ 2 $SEB{\chi }^{2}$ divergence is proven to be symmetric, nonnegative and nondegenerate, which are desirable properties for conflict management. Then, a new algorithm for multisource information fusion based on the S E B χ 2 $SEB{\chi }^{2}$ divergence measure is derived. Finally, an application for pattern classification is used to illustrate the superiority of the proposed S E B χ 2 $SEB{\chi }^{2}$ divergence measure-based fusion method over other existing well-known and recent related works with a better classification accuracy of 94.39%.