Fuzzy time series forecasting based on hesitant fuzzy sets, particle swarm optimization and support vector machine-based hybrid method

In this paper, we propose hesitant fuzzy sets-based hybrid time series forecasting method using particle swarm optimization and support vector machine. Length of unequal intervals, weights of intervals and process of defuzzification are major factors that affect the forecasting accuracy of hesitant fuzzy sets-based time series models. The proposed hybrid fuzzy time series forecasting method uses hesitant fuzzy sets which are constructed using fuzzy sets with equal and unequal length intervals. Particle swarm optimization and linear programming are used to optimize length of unequal intervals and weights of equal and unequal intervals. The proposed hybrid method of time series forecasting uses support vector machine for setting input-target pattern for defuzzification. Outperformance of proposed hybrid method of time series forecasting method is revealed by applying it on widely used time series data of enrollments of the University of Alabama, market share price of State Bank of India share at Bombay stock exchange and car sell in Quebec City of Canada. Validity of the proposed hybrid fuzzy time series forecasting method is verified using values of Willmott index and tracking signal.