Time series classification (TSC) is a critical area with broad applications. In the field of evidence theory, quantum evidence theory (QET) offers a promising framework for onedimensional TSC tasks, leveraging the capabilities of quantum basic probability amplitude (QBPA) to capture two-dimensional uncertainty. However, as the first step for the application of QET to TSC, how to construct QBPA still remains an open issue. In this paper, a novel approach to generate QBPA is devised. Specifically, we first apply the discrete Fourier transform (DFT) to the original data, extracting two-dimensional features embedded in the magnitude and phase from the frequency domain based on the front-few multi-frequency components, achieved by setting a threshold frequency index (TFI) to limit the frequencies considered. Next, we introduce the complex dual gaussian fuzzy number (CDGFN) as a carrier for QBPA, effectively representing two-dimensional uncertainty in the data. A CDGFN-based multisource information fusion (CDGFN-MSIF) algorithm for decision-making is proposed to combine information from different frequency components. Finally, the decisionmaking algorithm is validated on multiple time series datasets. Experimental results highlight the superior performance of the proposed approach over other state-of-the-art models, demonstrating its effectiveness and enhanced classification accuracy.

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.

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.

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.

Complex evidence theory (CET) is an effective method for uncertainty reasoning in knowledge-based systems with good interpretability that has recently attracted much attention. However, approaches to improve the performance of uncertainty reasoning in CET-based expert systems remains an open issue. One key to performance improvement is the adequate management of conflict from multisource information. In this paper, a generalized correlation coefficient, namely, the complex evidential correlation coefficient (CECC), is proposed for the complex mass functions or complex basic belief assignments (CBBAs) in CET. On this basis, a complex conflict coefficient is proposed to measure the conflict between CBBAs; when CBBAs turn into classic BBAs, the complex correlation and conflict coefficients will degrade into traditional coefficients. The complex conflict coefficient satisfies nonnegativity, symmetry, boundedness, extreme consistency, and insensitivity to refinement properties, which are desirable for conflict measurement. Several numerical examples validate through comparisons the superiority of the complex conflict coefficient. In this context, a weighted discounting multisource information fusion algorithm, which is called the CECC-WDMSIF, is designed based on the CECC to improve the performance of CET-based expert systems. By applying the CECC-WDMSIF method to the pattern classification of diverse real-world datasets, it is demonstrated that the proposed CECC-WDMSIF outperforms well-known related approaches with higher classification accuracy and robustness.

In decision-making systems, how to address uncertainty plays an important role for the improvement of system performance in uncertainty reasoning. Dempster—Shafer evidence (DSE) theory is an effective method to address uncertainty in decision-making problems by means of basic belief assignments (BBAs) and Dempster's combination rule. In the DSE theory, divergence measure between BBAs, which is beneficial for conflict information management in decision making, remains an open issue. In this paper, several generalized evidential divergences (EDs) are proposed and studied to measure the difference and discrepancy between BBAs in DSE theory, which have more universal applicability in decision theory. On this basis, a uniform BJS divergence-based decision-making algorithm is devised to improve the decision level. Furthermore, the extensions of weighted BJS to decision-making algorithms are discussed by considering not only subjective weights but also objective weights. Notably, this is the first work to propose the weighted BJS divergence in DSE theory providing a promising way to analyze decision-making problems from different perspectives. Finally, the proposed BJS-based decision-making algorithm is applied to pattern classification. The results validate that the proposed decision-making algorithm is beneficial for diverse real-world datasets and outperforms several well-known related works and demonstrates higher classification accuracy as well as robustness.

The complex evidence theory is an effective methodology for multiattribute decision-making. Since difference measure between multiattribute plays an important role for conflict management in the process of multiattribute decision-making, how to measure discrepancy between complex basic belief assignments (CBBAs) in complex evidence theory is still an open issue. In this context, a new distance measurement (complex belief distance—CBD) is proposed in this paper by taking advantages of complex belief function and complex plausibility function, called complex belief interval-based distance. In addition, we compare the proposed CBD with the related work to illustrate its superiority. Next, based on CBD, we devise a novel multiattribute decision-making algorithm for pattern recognition. Finally, we apply the method to problems of medical diagnosis to verify the effectiveness of the proposed method.

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%.

Complex evidence theory, a generalization of Dempster–Shafer evidence theory, is an effective uncertainty reasoning for decision fusion in complex-valued domain. In particular, the generation of complex basic belief assignment (CBBA) is a key issue for uncertainty modeling in complex evidence theory. In this paper, we first construct complex interval number (CIN) model. In this context, we propose a novel CBBA generation method to model uncertainty in the framework of complex planes. Furthermore, we propose a novel decision-making algorithm on the basis of the CIN-based CBBA generation method. Through an application in pattern recognition on several real-world data sets, the efficiency of the proposed decision-making algorithm is verified.

An open issue of the Dempster combination rule is the conflicting management, which is very important in multisource data fusion, such as group decision making and target recognition. To address this issue, an improved method to generate basic probability assignment is presented. Then, a new combination method to assign the conflicting mass function without the normalization is proposed to handle a highly conflicting environment. Compared with other methods, this proposed method is convenient in computing and has better accuracy to predict potential possibilities especially when disposing of extreme status. Some numerical examples and real benchmark data collected in UCI database are illustrated to verify the validity and rationality of the proposed method.

In multisource information fusion, the weight assignment is critical to improve the fusion performance, especially under uncertainty and conflict situations. As for uncertainty, the probability distribution is a desirable method to model uncertainty. In this context, a novel dynamic weight allocation method is first proposed, which considers three situations: nonconflict, general conflict, and high conflict. In particular, according to the degree of conflict, different weight allocations are considered by means of generalized information quality and negation operation. After that, a novel dynamic weight allocation method is proposed that contains three subalgorithms: NonC algorithm, BNC algorithm, and BIC algorithm. In addition, a novel multisource information fusion method is presented based on the newly designed dynamic weight allocation method. Besides, some numerical examples illustrate its feasibility. Finally, an application in target recognition demonstrates the practicability of the proposed fusion method.

Within the framework of evidence theory, the confidence functions of different information can be combined into a combined confidence function to solve uncertain problems. The Dempster combination rule is a classic method of fusing different information. This paper proposes a similar confidence function for the time point in the time series. The Dempster combination rule can be used to fuse the growth rate of the last time point, and finally a relatively accurate forecast data can be obtained. Stock price forecasting is a concern of economics. The stock price data is large in volume, and more accurate forecasts are required at the same time. The classic methods of time series, such as ARIMA, cannot balance forecasting efficiency and forecasting accuracy at the same time. In this paper, the fusion method of evidence theory is applied to stock price prediction. Evidence theory deals with the uncertainty of stock price prediction and improves the accuracy of prediction. At the same time, the fusion method of evidence theory has low time complexity and fast prediction processing speed.

For the sake of great ability of handling uncertain information, Dempster-Shafer evidence theory is extensively used in information fusion. Nevertheless, when there exists highly inconsistent evidences, using classical Dempster's combination rule may lead to counter-intuitive results. To address this issue, a new conflicting evidences combination method based on distance function and Tsallis entropy is proposed. Numerical examples are used to illustrate the feasibility and efficiency of the proposed method. Further, an fault diagnosis problem is used as an example to show the effectiveness and superiority of the proposed method. The proposed method outperforms other methods that the proposed method recognize the target by the probability 99.49%, which is higher than other methods.

It is necessary to take the information quality into consideration in information fusion. However, existing information quality has a limitation due to the ignorance of the credibility of information source. In this paper, the generalized information quality (GIQ) been proposed considering the association among the collected sensor reports, first. Then, the ordered weighting aggregation (OWA) operator of probability distribution based on the GIQ is presented. Numerical example and real application in fault diagnosis are used to illustrate the efficiency of the proposed method. The proposed GIQ and OWA algorithm has the advantage in fault tolerance and reduce the impact of conflict data in data fusion process, due to the consideration of the credibility of each sensor report. The proposed method has the promising aspects in uncertainty data aggregation.

Multicriteria decision-making problems have been applied to many applications for its practicality. Nevertheless, when the evaluated satisfactions are more complex, such as interval-valued distributions, how to reasonably obtain the aggregation results of alternatives is still an open issue. In this paper, an interval-valued exceedance method is proposed to solve such a question based on the Golden Rule representative value and probabilistic exceedance method. Due to good performance of expressing uncertain information, the Golden Rule representative value method is used to order interval-valued satisfactions after an effective normalization process. In addition, a quantifier-based ordered weighted averaging operator is also introduced to consider the preferences of decision makers. A realistic application of supplier selection is shown to illustrate the practicality of the proposed method.

How to deal with matrix game under uncertainty is an open issue. Compared with the Dempster-Shafer structure, the insignificant deviation caused by the subjectivity of the expert is effectively eliminated generalized Dempster-Shafer structures. In this paper, a new matrix game with payoffs of generalized Dempster-Shafer structures is presented. Generalized Dempster-Shafer structures presents probability nonspecificity and inaccuracy as interval values. Then payoff is determined by linear programming. A zero-sum matrix game is illustrated the efficiency of the proposed method.