Oil in both aspects of quantity and the value, is the most important tradable commodity in the world and due to the dependence of economic activities on this energy source, it’s the most strategic global commodity too so that any change in oil prices can affect the global economy. Therefore the economists are always looking to identify and predict the behavior of oil prices have been. However, the need to find the methods that can predict the oil prices, with less error, is quite clear. In this regard, the econometric methods have made rapid progress and other rival methods have appeared in this field, which the fuzzy logic is one of them. This paper compares two techniques, fuzzy logic and ARFIMA to predict daily North Sea Brent oil prices over the period 1998-2011.To optimize fuzzy method first input membership functions and then output membership functions were optimized. Optimization the output membership functions cause minimizing error. The results show fuzzy logic has more advantages than ARFIMA_EGARCH method.