Fuzzy time series forecasting method based on Gustafson-Kessel fuzzy clustering

Fuzzy time series forecasting methods do not require constraints found in conventional approaches. In addition, due to uncertainty that they contain, many time series to be forecasted should be considered as fuzzy time series. Fuzzy time series forecasting models consist of three steps as fuzzification, identification of fuzzy relations and defuzzification. Although most of the time series encountered in real life contain seasonal component, only few of these fuzzy time series approaches analyze seasonal fuzzy time series. Even though all these studies have various advantages, their biggest disadvantage is to take into consideration only the fuzzy set having the highest membership value rather than the membership value of observations belonging to each fuzzy set. This situation conflicts to fuzzy set theory and causes the loss of information thus, negatively affects on the forecasting performance. In this study, a seasonal fuzzy time series forecasting model, in which Gustafson-Kessel fuzzy clustering technique in fuzzification stage is initially used and membership values are taken into account in both the determining fuzzy relations and the defuzzification stages is proposed. The proposed method is applied to real life seasonal time series and substantial results are obtained.