A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations

Fuzzy time series approaches, which do not require the strict assumptions of traditional time series approaches, generally consist of three stages. These are called as the fuzzification of crisp time series observations, the identification of fuzzy relationships and the defuzzification. All of these stages play a very important role on the forecasting performance of the model. Although there are many studies contributing to the stages of fuzzification and determining fuzzy relationships, the number of the studies about the defuzzification stage, which is very important at least as much as the others, is limited. None of them considered the number of recurrence of the fuzzy relationships in the stage of defuzzification. However it is very reasonable to take into account since fuzzy relations and their recurrence number are reflected the nature of the time series. Then the information obtained from the fuzzy relationships can be used in the defuzzification stage. In this study, we take into account the recurrence number of the fuzzy relations in the stage of defuzzification. Then this new approach has been applied to the real data sets which are often used in other studies in literature. The results are compared to the ones obtained from other techniques. Thus it is concluded that the results present superior forecasts performance.