Time series prediction based on high-order intuitionistic fuzzy cognitive maps with variational mode decomposition

In reality, time series subject to the internal/external influence are usually characterized by nonlinearity, uncertainty, and incompleteness. Therefore, how to model the features of time series in nondeterministic environments is still an open problem. In this article, a novel high-order intuitionistic fuzzy cognitive map (HIFCM) is proposed, where intuitionistic fuzzy set (IFS) is introduced into fuzzy cognitive maps with temporal high-order structure. By means of IFS, the ability of model for the representation of uncertainty can be effectively improved. In order to capture the fluctuation features of series data, variational mode decomposition is utilized to decompose time series into sequences of various frequencies, based on which fine feature structures on different scales can be obtained. Each concept of HIFCM corresponds to one decomposed sequence such that casual reasoning can be achieved among the obtained features in various frequencies of time series. All parameters are learned by the particle swarm optimization algorithm. Finally, the performance of the method is verified on the public datasets, and experimental results show the feasibility and effectiveness of the proposed method.