Time Series Forecasting Using Improved Empirical Fourier Decomposition and High-Order Intuitionistic FCM: Applications in Smart Manufacturing Systems

Fuzzy Cognitive Maps (FCMs) have been proven effective in modeling and predicting stationary time series, yet challenges persist when dealing with time-varying nonstationary time series characterized by dynamic statistical features. This paper presents a robust hybrid predictive approach, which combines an Improved version of Empirical Fourier Decomposition (IEFD) with High-Order Intuitionistic Fuzzy Cognitive Maps (HIFCM), termed IEFD-HIFCM, to address these challenges in time series forecasting, focusing on manufacturing applications. IEFD-HIFCM offers three key contributions to overcome existing limitations in the FCM-based time series forecasting literature. First, we introduce IEFD to extract features from the original time series that later to be fed into the HIFCM, addressing the shortcomings of established methods such as Empirical Wavelet Transform, Variational Mode Decomposition, and Fourier Decomposition. Second, by using HIFCM, the approach possesses an answer for uncertainty by considering the degree of hesitation between nodes in the cognitive map. Third, this paper combines Elastic-net with an enhanced version of the grey wolf optimizer to optimize the weights and parameters of HIFCM as a whole, rectifying the issue with earlier FCM-based predictors that optimize individual components separately. IEFD-HIFCM's performance is validated through comparisons with state-of-the-art methods using a mathematically generated non-stationary signal. Additionally, the proposed approach is tested on four real-world smart manufacturing and supply chain datasets, yielding highly accurate results. These results demonstrate the effectiveness of IEFD-HIFCM in enhancing time series forecasting accuracy and reducing forecasting errors.