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Complex Evidence Theory (CET), an extension of the traditional D-S evidence theory, has garnered academic interest for its capacity to articulate uncertainty through Complex Basic Belief Assignment (CBBA) and to perform uncertainty reasoning using complex combination rules. Nonetheless, quantifying uncertainty within CET remains a subject of ongoing research. To enhance decision-making, a method for Complex Pignistic Belief Transformation (CPBT) has been introduced, which allocates CBBAs of multi-element focal elements to subsets. CPBT's core lies in the fractal-inspired redistribution of the complex mass function. This paper presents an experimental simulation and analysis of CPBT's generation process along the temporal dimension, rooted in fractal theory. Subsequently, a novel Fractal-Based Complex Belief (FCB) entropy is proposed to gauge the uncertainty of CBBA. The properties of FCB entropy are examined, and its efficacy is demonstrated through various numerical examples and practical application.

Dempster rule of combination (DRC) is widely used for uncertainty reasoning in intelligent information system, which is generalized to complex domain recently. However, as the increase of identification framework elements, the computational complexity of Dempster Rule of Combination increases exponentially. To address this issue, we propose a novel quantum Dempster rule of combination (QDRC) by means of Toffoli gate. The QDRC combination process is completely implemented using quantum circuits., Comment: 13 pages, 2 figures

Time series forecasting is a hot spot in recent years. Visibility Graph (VG) algorithm is used for time series forecasting in previous research, but the forecasting effect is not as good as deep learning prediction methods such as methods based on Artificial Neural Network (ANN), Convolutional Neural Network (CNN) and Long Short-Term Memory Network (LSTM). The visibility graph generated from specific time series contains abundant network information, but the previous forecasting method did not effectively use the network information to forecast, resulting in relatively large prediction errors. To optimize the forecasting method based on VG, this article proposes the Deep Visibility Series (DVS) module through the bionic design of VG and the expansion of the past research. By applying the bionic design of biological vision to VG, DVS has obtained superior forecasting accuracy. At the same time, this paper applies the DVS forecasting method to the construction cost index forecast, which has practical significance.

The construction cost index is an important indicator of the construction industry. Predicting CCI has important practical significance. This paper combines information fusion with machine learning, and proposes a multi-feature fusion (MFF) module for time series forecasting. The main contribution of MFF is to improve the prediction accuracy of CCI, and propose a feature fusion framework for time series. Compared with the convolution module, the MFF module is a module that extracts certain features. Experiments have proved that the combination of MFF module and multi-layer perceptron has a relatively good prediction effect. The MFF neural network model has high prediction accuracy and prediction efficiency, which is a study of continuous attention.

Evidence theory is that the extension of probability can better deal with unknowns and inaccurate information. Uncertainty measurement plays a vital role in both evidence theory and probability theory. Approximate Entropy (ApEn) is proposed by Pincus to describe the irregularities of complex systems. The more irregular the time series, the greater the approximate entropy. The ApEn of the network represents the ability of a network to generate new nodes, or the possibility of undiscovered nodes. Through the association of network characteristics and basic probability assignment (BPA) , a measure of the uncertainty of BPA regarding completeness can be obtained. The main contribution of paper is to define the integrity of the basic probability assignment then the approximate entropy of the BPA is proposed to measure the uncertainty of the integrity of the BPA. The proposed method is based on the logical network structure to calculate the uncertainty of BPA in evidence theory. The uncertainty based on the proposed method represents the uncertainty of integrity of BPA and contributes to the identification of the credibility of BPA.

Quantum theory is the focus of current research. Likelihood functions are widely used in many fields. Because the classic likelihood functions are too strict for extreme data in practical applications, Yager proposed soft ordered weighted average (OWA) operator. In the quantum method, probability is represented by Euler's function. How to establish a connection between quantum theory and OWA is also an open question. This article proposes OWA opreator under quantum theory, and discusses the relationship between quantum soft OWA operater and classical soft OWA operator through some examples. Similar to other quantum models, this research has more extensive applications in quantum information.

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.

Time series has attracted a lot of attention in many fields today. Time series forecasting algorithm based on complex network analysis is a research hotspot. How to use time series information to achieve more accurate forecasting is a problem. To solve this problem, this paper proposes a weighted network forecasting method to improve the forecasting accuracy. Firstly, the time series will be transformed into a complex network, and the similarity between nodes will be found. Then, the similarity will be used as a weight to make weighted forecasting on the predicted values produced by different nodes. Compared with the previous method, the proposed method is more accurate. In order to verify the effect of the proposed method, the experimental part is tested on M1, M3 datasets and Construction Cost Index (CCI) dataset, which shows that the proposed method has more accurate forecasting performance.

In this paper, we propose a generalized intelligent quality-based approach for fusing multi-source information. The goal of the proposed approach intends to fuse the multi-complex-valued distribution information while maintaining a high quality of the fused result by considering the usage of credible information sources., Comment: 5 pages

In this paper, we generalize the belief function on complex plane from another point of view. We first propose a new concept of complex mass function based on the complex number, called complex basic belief assignment, which is a generalization of the traditional mass function in Dempster-Shafer evidence theory. On the basis of the de nition of complex mass function, the belief function and plausibility function are generalized. In particular, when the complex mass function is degenerated from complex numbers to real numbers, the generalized belief and plausibility functions degenerate into the traditional belief and plausibility functions in DSE theory, respectively., Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1907.00716, arXiv:1906.11409

Dempster-Shafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in modeling uncertainties without prior information. However, the existing evidence theory is insufficient to consider the situations where it has no capability to express the fluctuations of data at a given phase of time during their execution, and the uncertainty and imprecision which are inevitably involved in the data occur concurrently with changes to the phase or periodicity of the data. In this paper, therefore, a generalized Dempster-Shafer evidence theory is proposed. To be specific, a mass function in the generalized Dempster-Shafer evidence theory is modeled by a complex number, called as a complex basic belief assignment, which has more powerful ability to express uncertain information. Based on that, a generalized Dempster's combination rule is exploited. In contrast to the classical Dempster's combination rule, the condition in terms of the conflict coefficient between the evidences K<1 is released in the generalized Dempster's combination rule. Hence, it is more general and applicable than the classical Dempster's combination rule. When the complex mass function is degenerated from complex numbers to real numbers, the generalized Dempster's combination rule degenerates to the classical evidence theory under the condition that the conflict coefficient between the evidences K is less than 1. In a word, this generalized Dempster-Shafer evidence theory provides a promising way to model and handle more uncertain information., Comment: 9 pages, 5 figures

In this paper, an evidential distance measure is proposed which can measure the difference or dissimilarity between complex basic belief assignments (CBBAs), in which the CBBAs are composed of complex numbers. When the CBBAs are degenerated from complex numbers to real numbers, i.e., BBAs, the proposed distance will degrade into the Jousselme et al.'s distance. Therefore, the proposed distance provides a promising way to measure the differences between evidences in a more general framework of complex plane space., Comment: 4 pages, 2 figures. arXiv admin note: text overlap with arXiv:1906.11409