A New Hybrid Recurrent Intuitionistic Fuzzy Time Series Forecasting Method

Classical time series methods are widely employed to analyze linear time series with a limited number of observations; however, their effectiveness relies on several strict assumptions. In contrast, artificial neural networks are particularly suitable for forecasting problems due to their data-driven nature and ability to address both linear and nonlinear challenges. Furthermore, recurrent neural networks feed the output back into the network as input, utilizing this feedback mechanism to enrich the information provided to the model. This study proposes a novel recurrent hybrid intuitionistic forecasting method utilizing a modified pi–sigma neural network, principal component analysis (PCA), and simple exponential smoothing (SES). In the proposed framework, lagged time series variables and principal components derived from the membership and non-membership values of an intuitionistic fuzzy clustering method are used as inputs. A modified particle swarm optimization (PSO) algorithm is employed to train this new hybrid network. By integrating PCA, modified pi–sigma neural networks (MPS-ANNs), and SES within a recurrent hybrid structure, the model simultaneously captures linear and nonlinear dynamics, thereby enhancing forecasting accuracy and stability. The performance of the proposed model is evaluated using diverse financial and environmental datasets, including CMC-Open (I–IV), NYC water consumption, OECD freshwater use, and ROW series. Comparative results indicate that the proposed method achieves superior accuracy and stability compared to other fuzzy-based approaches.