In the context of time series analysis, forecasting time series is known as an important sub-study field within the associated scientific fields. At this point, especially forecasting chaotic systems has been a remarkable research approach. As being associated with the works on forecasting chaotic systems, some application areas are very interested in benefiting from advantages of forecasting time series. For instance, forecasting electroencephalogram (EEG) time series enables researchers to learn more about future status of the brain activity in terms of any physical or pathological case. In this sense, this work introduces an ANFIS-VOA hybrid system, which is based on ANFIS and a new optimization algorithm called as vortex optimization algorithm (VOA). Generally, the system provides a basic, strong enough, alternative forecasting solution way for EEG time series. The performed evaluation applications have shown that the ANFIS-VOA approach here provided effective enough solution way for forecasting EEG time series, as a result of learning-reasoning infrastructure achieved by the combination of two different artificial intelligence techniques.