As it known in many studies, the fuzzy time series methods do not need assumptions such as stationary and the linearity required for classical time series approaches, so there is a huge field of study on fuzzy time series methods in the time series literature. Fuzzy time series literature has the studies which use both the various models of artificial neural networks and the different optimization methods of artificial intelligence jointly. In this study, a new fuzzy time series algorithm based on an ARMA-type recurrent Pi-Sigma artificial neural network is introduced. It is expected that the proposed method increases the forecasting performance for many real-life time series because of using more input which is the error term obtained from Pi-Sigma artificial neural network with recurrent structure. Therefore, it can be considered that the proposed
method is based on an ARMA-type fuzzy time series forecasting model. In the proposed method, the training of recurrent ARMA-type Pi-Sigma neural network is performed by particle swarm optimization. The proposed method has been applied to a real-data set as well as simulated data sets of a real-life time series, and the obtained results have been compared with some other methods in the literature.