The Trend-Fuzzy-Granulation-Based Adaptive Fuzzy Cognitive Map for Long-Term Time Series Forecasting

One drawback of using the existing one-step forecasting models for long-term time series prediction is the cumulative errors caused by iterations. In order to overcome this shortcoming, this article proposes a trend-fuzzy-granulation-based adaptive fuzzy cognitive map (FCM) for long-term time series forecasting. Different from the original FCM-based forecasting models, a class of trend fuzzy information granules is built to represent the trend, fluctuation range, and trend persistence of various segments of time series, which are more instrumental and comprehensive than simple magnitude information. Thus, the proposed forecasting model is a granular model according to the form of its inputs and outputs. In an original FCM-based forecasting model, the causal relationships among concepts remain unchanged throughout the training of the whole dataset, however, in reality, the causal relationships may change with the state of concepts. Therefore, it is unreasonable to use the invariable causal relationships which often result in poor predictions. In view of this, we construct an adaptive FCM where different causal relationships are built to forecast concepts of different states. This is the first time to forecast trend fuzzy information granules using an adaptive FCM. Compared with the existing classical forecasting models, the proposed forecasting model achieves superior performance which is verified through a series of experimental studies.