Fuzzy time series-Markov chain forecasting with particle swarm optimization algorithm

The concept of forecasting with fuzzy time series have been increasingly developed to solve various problems. The length of the interval and defuzzification are two important factors that affect the accuracy of forecasting results. In this paper, the author combines the fuzzy time series-Markov chain with particle swarm optimization algorithm. Markov chain rule was implemented in the defuzzification for handling the repeated fuzzy sets and determining the proper weights. Meanwhile, the particle swarm optimization was applied for determining the appropriate length of intervals of the fuzzy time series by considering the universe of discourse as a search space and intervals as particles. The author uses the Average Forecasting Error Rate (AFER) value to see the level of accuracy of forecasting. The proposed method was applied to predict the opening stock price of PT. Astra International Tbk. and showed a very good accuracy with an AFER value of 0.9555%.