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Fuzzy cognitive maps (FCMs) have widely been applied for knowledge representation and reasoning. However, in real life, reasoning is always accompanied with hesitation, which is deriving from the uncertainty and fuzziness. Especially, when processing the online data, since the internal and external interference, the distribution and characteristics of sequence data would be considerably changed along with the passage of time, which further increase the difficulty of modeling. In this article, based on intuitionistic fuzzy set theory, a new dynamic intuitionistic fuzzy cognitive map (DIFCM) scheme is proposed for online data prediction. Combined with a novel detection algorithm of concept drift, the structure of DIFCM can be adaptively updated with the online learning scheme, which can effectively improve the representation of online information by capturing the real-time changes of sequence data. Moreover, in order to tackle with the possible hesitancy in the process of modeling, intuitionistic fuzzy set is applied in the construction of dynamic FCM, where hesitation degree as a quantitative index explicitly expresses the hesitancy. Finally, a series of experiments using public data sets verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The prediction of time series in multi-steps is of significance in reality. However, considering the uncertainty and high noise existing in time series, the long-term forecasting is still an open problem. By means of granular computing, in this article, a novel spatial–temporal fuzzy information granule (STFIG) model is proposed to achieve the multi-step forecasting of time series. From the perspective of time dimension, by using unequal division method, time series is converted into generalized time-varying fuzzy information granules, where the trend information and dispersion degree of sequence data can be quantitatively described. Moreover, in terms of spatial dimension, the fluctuation information of time series is also calculated and involved into information granules, which can further enhance the semantic representation of sequential data. In order to improve the ability of dealing with uncertainties and fuzziness in time series, the interval type-2 fuzzy set is applied in the granules model. By using synthetic data and real-life time series, experiments are carried out to verify the effectiveness of the proposed scheme, where abundant semantic information and better long-term predictive performance can be obtained. [ABSTRACT FROM AUTHOR]

High noise and strong volatility are the typical characteristics of financial time series. Combined with pseudo-randomness, nonsteady and self-similarity exhibiting in different time scales, it is a challenging issue for the pattern analysis of financial time series. Different from the existing works, in this paper, financial time series are converted into granular complex networks, based on which the structure and dynamics of network models are revealed. By using variable-length division, an extended polar fuzzy information granule (FIGs) method is used to construct granular complex networks from financial time series. Considering the temporal characteristics of sequential data, static networks and temporal networks are studied, respectively. As to the static network model, some features of topological structures of granular complex networks, such as distribution, clustering and betweenness centrality are discussed. Besides, by using the Markov chain model, the transfer processes among different granules are investigated, where the fluctuation pattern of data in the coming step can be evaluated from the transfer probability of two consecutive granules. Shanghai composite index and foreign exchange data as two examples in real life are applied to carry out the related discussion. [ABSTRACT FROM AUTHOR]

Time series exist widely in either nature or society such that the research on analysis of time series has great significance. However, considering the nonlinearity and uncertainty, the prediction of time series is still an open problem. In this paper, by means of the intuitionistic fuzzy set theory, we proposed a novel time series prediction scheme based on intuitionistic fuzzy cognitive map. In the previous research, intuitionistic fuzzy cognitive map, as a kind of knowledge-based modeling tool, is mainly used in decision-making field, where concept structure and weight matrix are usually obtained from experience of experts. To tackle with the diversity of time series, the proposed algorithm constructs the conceptual structure of cognitive map and weight matrix directly from raw sequential data, which effectively enlarges the application range by reducing human participation. Moreover, in order to appropriately calculate the hesitation degree, which is the key role for the application of intuitionistic fuzzy sets, we propose a real-time adjustable hesitation degree calculation scheme. By using this proposed method, hesitation degree can be adaptively adjusted by combining Femi formula with dynamic membership degree. A number of experiments are implemented to reveal feasibility and effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

Abstract The prediction of time series has both the theoretical value and practical significance in reality. However, since the high nonlinear and noises in the time series, it is still an open problem to tackle with the uncertainties and fuzziness in the forecasting process. In this article, an evolving recurrent interval type-2 intuitionistic fuzzy neural network (eRIT2IFNN) is proposed for time series prediction and regression problems. The eRIT2IFNN employs interval type-2 intuitionistic fuzzy sets to enhance the modeling of uncertainties by intuitionistic evaluation and noise tolerance of the system. In the eRIT2IFNN, the antecedent part of each fuzzy rule is defined using intuitionistic interval type-2 fuzzy sets, and the consequent realizes the Takagi–Sugeno–Kang type fuzzy inference mechanism. In order to utilize the prior knowledge including intuitionistic information, a local internal feedback is established by feeding the rule firing strength of each rule to itself eRIT2IFNN is fully adaptive to the evolving of sequence data by online learning of structure and parameters. A modified density-based clustering is implemented for the structure learning, where both densities and membership degrees are involved to determine the fuzzy rules. Performance of eRIT2IFNN is evaluated using a set of benchmark problems and compared with existing fuzzy inference systems. Moreover, the eRIT2IFNN is tested for identification of dynamics under both noise-free and noisy environments. Finally, a group of practical financial price-tracking problems including high-frequency data of financial future, commodity future and precious metal are used for the evaluation of the proposed inference system. Highlights • A novel recurrent structure utilizing interval type-2 intuitionistic fuzzy set is proposed. • Self-evolving structure based on density clustering and intuitionistic evaluation. • The uncertain mean of interval type-2 intuitionistic fuzzy set is first constructed. [ABSTRACT FROM AUTHOR]

The volatility features of financial data would considerably change in different periods, that is one of the main factors affecting the applications of machine learning in quantitative trading. Therefore, to effectively distinguish fluctuation patterns of financial markets can provide meaningful information for the trading decision. In this article, a novel intelligent trading system based on deep fuzzy self-organizing map (DFSOM) companied with GRU networks is proposed, where DFSOM is utilized for the clustering of financial data to acquire multiple fluctuation patterns in an unsupervised way. Firstly, in order to capture the trend features and evade the effect of high noises in financial data, the images of extended candlestick charts instead of raw data are processed and the obtained features are applied for the following unsupervised learning, where candlestick charts are produced with both price and volume information. Secondly, by using the candlestick features, a two-layer deep fuzzy self-organizing map is constructed to carry out the clustering, where two-layer models carry out the clustering in multiple time scales to improve the processing of time-dependent information. Thirdly, GRU networks are used to implement the prediction task, based on which an intelligent trading model is constructed. The feasibility and effectiveness of the proposed method are verified by using various real financial datasets. • A novel two-layer structure of deep fuzzy self-organizing map is proposed. • Image-based analysis and intelligent learning for financial time series. • Multiple features fused by using the extended candlestick charts. [ABSTRACT FROM AUTHOR]

In reality, some kinds of time series have the characteristics of high volatility, where fluctuation patterns of sequential data contain rich semantic knowledge and represent the spatial features from two-dimensional perspective. Especially, some non-trivial fluctuations may provide key information for the forecasting of time series. However, how to appropriately represent the fluctuation patterns and achieve the causal reasoning among them remains open. In this work, by learning the causal knowledge of fluctuation patterns, a novel spatial attention fuzzy cognitive map with high-order structure is proposed for the interpretable prediction of time series with high volatility. Firstly, a kind of extended polar fuzzy information granules is utilized to convert time series into granule sequences with interpretable fluctuation features, based on which fuzzy cognitive maps can be constructed by using full data-driven way. Secondly, in order to capture the key fluctuation patterns, the attention mechanism is first introduced into fuzzy cognitive map, where the spatial features of the focused patterns can be taken fully utilized. Thirdly, the high-order structure is involved into the proposed model for the learning of the temporal knowledge existing in the pattern sequences. Finally, real-world financial time series with strong noises and high volatility are empirically utilized to verify the promising performance of the proposed method. • The attention mechanism is first introduced into FCM. • A novel method to construct FCM based on fan-shape FIGs. • A kind of improved fan-shape FIGs in polar coordinates is proposed. • Two-stage training for the sparse learning of the large-scale FCM. [ABSTRACT FROM AUTHOR]

As to the long-term time series forecasting, it is more challenging and practical to obtain the trend information and fluctuation range of sequence data than single-step prediction values. In this article, by means of fuzzy information granules (FIGs) and recurrent fuzzy neural networks, a novel long-term prediction model for time series is proposed. Based on a variable-length division method, generalized zonary time-variant fuzzy information granule (GZT-FIG) is constructed, which can express the variation trend, fluctuation range and dispersion degree of sequence data. Furthermore, in order to improve the anti-noise ability and memory ability, type-2 fuzzy sets and long short-term memory mechanism are introduced into the prediction scheme, based on which a self-evolving interval type-2 LSTM fuzzy neural network (eIT2FNN-LSTM) is provided. Compared with the existing works related to fuzzy-neural models, the involvement of long short-term memory mechanism effectively improves the memory ability to achieve the long-term prediction. In order to verify the validation and effectiveness of the proposed scheme, several groups of experiments, including synthetic sequences and real-life time series, are carried out. The experimental results reveal the better predictive performance and rich semantic information. • A method of unequal dividing the time series based on stepwise linear division is proposed. • A generalized time-variant fuzzy information granule can reflect the trend and the range of data changing. • A distance algorithm to measure the similarity and characterize the correlation degree between two GZT-FIGs. [ABSTRACT FROM AUTHOR]

Most of time series deriving from complex systems in real life is non-stationary, where the data distribution would be influenced by various internal/external factors such that the contexts are persistently changing. Therefore, the concept drift detection of time series has practical significance. In this paper, a novel method called online entropy-based time domain feature extraction (ETFE) for concept drift detection is proposed. Firstly, the empirical mode decomposition based on extrema symmetric extension is used to decompose time series, where features in various time scales can be adaptively extracted. Meanwhile, the end point effect caused by traditional empirical mode decomposition can be avoided. Secondly, by using the entropy calculation, the time-domain features are coarse-grained to quantify the structure and complexity of the time series, among which six kinds of entropy are used for discussion. Finally, a statistical process control method based on generalized likelihood ratio is used to monitor the change of the entropy, which can effectively track the mean and amplitude of the time series. Therefore, the early alarm of concept drift can be given. Synthetic data sets and neonatal electroencephalogram (EEG) recordings with seizures annotations data sets are used to validate the effectiveness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]