Mixed-Order Fuzzy Time Series Forecast

Fuzzy time series forecasting has gained significant attention for its accuracy, robustness, and interpretability, making it widely applicable in practical prediction tasks. In classical fuzzy time series models, the lag order plays a crucial role, with variations in order often leading to markedly different forecasting results. To obtain the best performance, we propose a mixed-order fuzzy time series model, which incorporates fuzzy logical relationships (FLRs) of different orders into its rule system. This approach mitigates the uncertainty in fuzzy forecasting caused by empty FLRs and FLR groups while fully exploiting the fitting advantages of different-order FLRs. Theoretical analysis is provided to establish the mathematical foundation of the mixed-order model, and its superiority over fixed-order models is demonstrated. Simulation studies reveal that the proposed model outperforms several classical time series models in specific scenarios. Furthermore, applications to real-world datasets, including a COVID-19 case study and a TAIEX financial dataset, validate the effectiveness and applicability of the proposed methodology.