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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]

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]