Integrating hedge algebras and optimization techniques to reduce forecasting errors in fuzzy time series model

Accurate forecasting in fuzzy time series (FTS) models is essential for applica-tions such as financial markets, traffic fatalities, and academic enrollments. How-ever, a persistent challenge in FTS forecasting is the determination of optimal interval lengths in the universe of discourse (UD), which significantly impacts prediction accuracy. This study introduces a novel hybrid approach that inte-grates Hedge Algebra (HA) with Particle Swarm Optimization (PSO) and Simu-lated Annealing (SA) to enhance forecasting accuracy. HA enables adaptive, non-uniform interval partitioning based on linguistic semantics, while PSO and SA jointly refine these intervals to reduce forecasting errors. Unlike convention-al FTS models with fixed partitioning, our approach leverages HA’s mathemati-cal structure alongside PSO’s global search and SA’s local refinement to en-hance adaptability and robustness. The model is evaluated on diverse datasets, including enrollment data, traffic fatalities, and gasoline prices, demonstrating superior forecasting accuracy over existing FTS models, as measured by Mean Squared Error (MSE) and Root Mean Squared Error (RMSE).