Multisource information fusion is a comprehensive and interdisciplinary subject. Dempster-Shafer (D-S) evidence theory copes with uncertain information effectively. Pattern classification is the core research content of pattern recognition, and multisource information fusion based on D-S evidence theory can be effectively applied to pattern classification problems. However, in D-S evidence theory, highly-conflicting evidence may cause counterintuitive fusion results. Belief divergence theory is one of the theories that are proposed to address problems of highly-conflicting evidence. Although belief divergence can deal with conflict between evidence, none of the existing belief divergence methods has considered how to effectively measure the discrepancy between two pieces of evidence with time evolutionary. In this study, a novel fractal belief Rényi (FBR) divergence is proposed to handle this problem. We assume that it is the first divergence that extends the concept of fractal to R/'enyi divergence. The advantage is measuring the discrepancy between two pieces of evidence with time evolution, which satisfies several properties and is flexible and practical in various circumstances. Furthermore, a novel algorithm for multisource information fusion based on FBR divergence, namely FBReD-based weighted multisource information fusion, is developed. Ultimately, the proposed multisource information fusion algorithm is applied to a series of experiments for pattern classification based on real datasets, where our proposed algorithm achieved superior performance.

Information can be quantified and expressed by uncertainty, and improving the decision level of uncertain information is vital in modeling and processing uncertain information. Dempster-Shafer evidence theory can model and process uncertain information effectively. However, the Dempster combination rule may provide counter-intuitive results when dealing with highly conflicting information, leading to a decline in decision level. Thus, measuring conflict is significant in the improvement of decision level. Motivated by this issue, this paper proposes a novel method to measure the discrepancy between bodies of evidence. First, the model of dynamic fractal probability transformation is proposed to effectively obtain more information about the non-specificity of basic belief assignments (BBAs). Then, we propose the higher-order fractal belief Rényi divergence (HOFBReD). HOFBReD can effectively measure the discrepancy between BBAs. Moreover, it is the first belief Rényi divergence that can measure the discrepancy between BBAs with dynamic fractal probability transformation. HoFBReD has several properties in terms of probability transformation as well as measurement. When the dynamic fractal probability transformation ends, HoFBReD is equivalent to measuring the Rényi divergence between the pignistic probability transformations of BBAs. When the BBAs degenerate to the probability distributions, HoFBReD will also degenerate to or be related to several well-known divergences. In addition, based on HoFBReD, a novel multisource information fusion algorithm is proposed. A pattern classification experiment with real-world datasets is presented to compare the proposed algorithm with other methods. The experiment results indicate that the proposed algorithm has a higher average pattern recognition accuracy with all datasets than other methods. The proposed discrepancy measurement method and multisource information algorithm contribute to the improvement of decision level.