Fuzzy time series forecasting models can be divided into two subclasses which are first order and high order. In high order models, all lagged variables exist in the model according to the model order. Thus, some of these can exist in the model although these lagged variables are not significant in explaining fuzzy relationships. If such lagged variables can be removed from the model, fuzzy relationships will be defined better and it will cause more accurate forecasting results. In this study, a new fuzzy time series forecasting model has been proposed by defining a partial high order fuzzy time series forecasting model in which the selection of fuzzy lagged variables is done by using genetic algorithms. The proposed method is applied to some real life time series and obtained results are compared with those obtained from other methods available in the literature. It is shown that the proposed method has high forecasting accuracy.