Developing a Fuzzy Time Series Forecasting Model Based on Hedge Algebras and Particle Swarm Optimization

Abstract

In recent years, numerous fuzzy time series (FTS) forecasting models have been widely used. One of the important factors for obtaining high forecasting accuracy in fuzzy time series model is that the lengths of intervals in the universe of discourse. In this study, a hybrid forecasting model which uses hedge algebra (HA) and particle swarm optimization (PSO) is proposed to determine optimal lengths of intervals in FTS models. In that, HA is utilized as a tool to partition the universe of discourse into intervals with unequal-size corresponding to the semantic intervals calculated from the linguistic terms. After processing of generating the intervals, we define fuzzy sets based on the observation data of times series and use them to establish fuzzy relationship groups. Then, the proposed model is combined with the PSO technique to find the appropriate length of each interval with view to reaching the better forecasting accuracy rate. The performance of the proposed model is evaluated with the historical data of enrolments at the University of Alabama. The simulated results obtained indicate that the proposed model achieves higher forecasting accuracy compared other existing forecasting models and it can obtain better quality solutions for both the 1st-order and high-order FTS model.
 HIGHLIGHTS
 
 In fuzzy time series forecasting model, the length of intervals and the order of fuzzy relationships are two critical factors for forecasting accuracy
 Hedge algebra and PSO are utilized as a tool to partition the universe of discourse into intervals with unequal - size corresponding to the semantic intervals calculated from the linguistic terms
 The defuzzification principles are used to calculate the forecasting results based on the fuzzy relationship groups
 
 GRAPHICAL ABSTRACT