Determining interval lengths for fuzzy time series forecasting model based on index of fuzzy sets by combining hedge algebra and particle swarm optimization

Abstract

Researchers frequently use fuzzy time series (FTS) forecasting models to estimate future values since they do not rely on the same rigid assumptions as traditional forecasting techniques. There are generally four factors that determine the performance of the FTS forecasting model (1) determining the length of intervals in the universe of discourse, (2) fuzzification rules or feature representation of crisp time series, (3) establishing fuzzy relation groups (FRGs) and (4) creating defuzzification rule to get crisp forecasted value. Considering the first factor and the fourth factor, we propose the hybrid FTS forecasting model combining particle swarm optimization (PSO) and hedge algebra (HA) to improve forecasting accuracy. Where the hedge algebra is utilized as a tool for partitioning the universe of discourse into intervals of different lengths. Then, the times series data are fuzzified into fuzzy sets, the fuzzy relationship groups are established and forecasting output value based on the index of fuzzy sets is calculated. Ultimately, the suggested model collaborates with PSO to obtain the optimal intervals determined by HA. To test the proposed model, we conduct a simulated study on two widely used real-time series and compare the performance with some recently developed models. Error statistics, such as MSE and RMSE show that the proposed model performs better than the comparing models.