Fuzzy Time Series (FTS), based on fuzzy set theory, models’ data using linguistic labels to handle incomplete data, and has been widely applied in forecasting student enrollment, traffic safety, and energy prices. However, the subjective determination of time intervals and fuzziness parameters reduces prediction accuracy, especially for highly volatile datasets. This study proposes a novel FTS model that employs Particle Swarm Optimization (PSO) to simultaneously optimize the fuzziness parameters of Hedge Algebra (HA) and interval lengths of the universe of discourse, obviating manual tuning. A new defuzzification formula based on fuzzy set indices further enhances forecasting accuracy. Evaluations on University of Alabama enrollments, Belgian traffic accident fatalities, and Vietnamese gasoline prices demonstrate superior performance, with RMSE reductions up to 20-30% over existing methods [e.g., 70.9 for enrollments with 14 intervals], excelling in incomplete data scenarios. This automated and adaptive model improves forecasting performance and supports decision-making not only in education and energy management but also effectively across various domains.
