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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]

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]