Fuyuan Xiao’s research while affiliated with Chongqing University and other places

In multisource information fusion (MSIF), Dempster–Shafer evidence (DSE) theory offers a useful framework for reasoning under uncertainty. However, measuring the divergence between belief functions within this theory remains an unresolved challenge, particularly in managing conflicts in MSIF, which is crucial for enhancing decision-making level. In this paper, several divergence and distance functions are proposed to quantitatively measure discrimination between belief functions in DSE theory, including the reverse evidential KullbackLeibler (REKL) divergence, evidential Jeffrey's (EJ) divergence, evidential JensenShannon (EJS) divergence, evidential $\chi ^{2}$ (E $\chi ^{2}$ ) divergence, evidential symmetric $\chi ^{2}$ (ES $\chi ^{2}$ ) divergence, evidential triangular (ET) discrimination, evidential Hellinger (EH) distance, and evidential total variation (ETV) distance. On this basis, a generalized f -divergence, also called the evidential f -divergence (Ef divergence), is proposed. Depending on different kernel functions, the Ef divergence degrades into several specific classes: EKL, REKL, EJ, EJS, E $\chi ^{2}$ and ES $\chi ^{2}$ divergences, ET discrimination, and EH and ETV distances. Notably, when basic belief assignments (BBAs) are transformed into probability distributions, these classes of Ef divergence revert to their classical counterparts in statistics and information theory. In addition, several Ef-MSIF algorithms are proposed for pattern classification based on the classes of Ef divergence. These Ef-MSIF algorithms are evaluated on real-world datasets to demonstrate their practical effectiveness in solving classification problems. In summary, this work represents the first attempt to extend classical f -divergence within the DSE framework, capitalizing on the distinct properties of BBA functions. Experimental results show that the proposed Ef-MSIF algorithms improve classification accuracy, with the best-performing Ef-MSIF algorithm achieving an overall performance difference approximately 1.22 times smaller than the suboptimal method and 14.12 times smaller than the worst-performing method.

Data fusion is a prevalent technique for assembling imperfect raw data coming from multiple sources to capture reliable and accurate information. Dempster–Shafer evidence theory is one of useful methodologies in the fusion of uncertain multisource information. The existing literature lacks a thorough and comprehensive review of the recent advances of Dempster– Shafer evidence theory for data fusion. Therefore, the state of the art has to be surveyed to gain insight into how Dempster–Shafer evidence theory is beneficial for data fusion and how it evolved over time. In this paper, we first provide a comprehensive review of data fusion methods based on Dempster–Shafer evidence theory and its extensions, collectively referred to as classical evidence theory, from three aspects of uncertainty modeling, fusion, and decision making. Next, we study and explore complex evidence theory for data fusion in both closed world and open world contexts that benefits from the frame of complex plane modelling. We then present classical and complex evidence theory framework-based multisource data fusion algorithms, which are applied to pattern classification to compare and demonstrate their applicabilities. The research results indicate that the complex evidence theory framework can enhance the capabilities of uncertainty modeling and reasoning by generating constructive interference through the fusion of appropriate complex basic belief assignment functions modeled by complex numbers. Through analysis and comparison, we finally propose several challenges and identify open future research directions in evidence theorybased data fusion.

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 R $\acute{e}$ nyi divergence, a novel time series complexity measurement algorithm, called belief R $\acute{e}$ nyi divergence of divergence (BR $\acute{e}$ DOD), is proposed. Specifically, the BR $\acute{e}$ 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 BR $\acute{e}$ 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.

Uncertainty modeling and reasoning in intelligent systems are crucial for effective decision-making, such as complex evidence theory (CET) being particularly promising in dynamic information processing. Within CET, the complex basic belief assignment (CBBA) can model uncertainty accurately, while the complex rule of combination can effectively reason uncertainty with multiple sources of information, reaching a consensus. However, determining CBBA, as the key component of CET, remains an open issue. To mitigate this issue, we propose a novel method for generating CBBA using high-level features extracted from Box–Cox transformation and discrete Fourier transform (DFT). Specifically, our method deploys complex Gaussian fuzzy number (CGFN) to generate CBBA, which provides a more accurate representation of information. The proposed method is applied to pattern classification tasks through a multisource information fusion algorithm, and it is compared with several well-known methods to demonstrate its effectiveness. Experimental results indicate that our proposed CGFN-based method outperforms existing methods, by achieving the highest average classification rate in multisource information fusion for pattern classification tasks. We found the Box–Cox transformation contributes significantly to CGFN by formatting data in a normal distribution, and DFT can effectively extract high-level features. Our method offers a practical approach for generating CBBA in CET, precisely representing uncertainty and enhancing decision-making in uncertain scenarios.

Dempster–Shafer (D–S) evidence theory is used to process multisource data fusion and uncertainty problems. When faced with strongly contradictory evidence, there are always some surprising phenomena. We propose a new generalized distance based on Li et al.’s Hellinger distance in this study to assess the distinction between basic probability assignments (BPAs) to solve this problem.The basic structure of Li et al.’s Hellinger distance was kept in the generalized Hellinger distance, and certain advancements were achieved. The generalized Hellinger distance considers the differences between both focal elements and the subsets of the sets of belief functions, enabling a wider range of applications for it. Additionally, we present the proof of generalized Hellinger distance satisfied nonnegativeness, symmetry, definiteness and triangle inequality. Through several comparative examples, we know that the new distance has better universality than some well-known works. Finally, we suggest a novel generalized Hellinger distance-based multisource data fusion approach and use it to solve a real-word pattern classification problem.