Seasonal Auto Regressive Fractionally Integrated Moving Average (SARFIMA) is a well-known model for forecasting of seasonal time series that follow a long memory process. However, to better boost the accuracy of forecasts inside such data for nonlinear problem, in this study, a combination of Fuzzy Time Series (FTS) with SARFIMA is proposed. To build the proposed model, certain parameters requires to be estimated. Therefore, a reliable Evolutionary Algorithm namely Particle Swarm Optimization (PSO) is employed. As a case study, a seasonal long memory time series, i.e., short term load consumption historical data, is selected. In fact, Short Term Load Forecasting (STLF) plays a key role in energy management systems (EMS) and in the decision making process of every power supply organization. In order to evaluate the proposed method, some experiments, using eight datasets of half-hourly load data from England and France for the year 2005 and four data sets of hourly load data from Malaysia for the year 2007, are designed. Although the focus of this research is STLF, six other seasonal long memory time series from several interesting case studies are employed to better evaluate the performance of the proposed method. The results are compared with some novel FTS methods and new state-of-the-art forecasting methods. The analysis of the results indicates that the proposed method presents higher accuracy than its counterparts, representing an efficient hybrid method for load forecasting problems.