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Fuzzy neural networks have been successfully applied to generate predictive rules for exchange rate forecasting. This paper presents a methodology to forecast the daily and weekly GBP/USD exchange rate by extracting fuzzy rules based on the neural network with weighted fuzzy membership functions (NEWFM) and the minimized number of input features using the distributed non-overlap area measurement method. NEWFM supports the analysis of the time series of the daily and weekly exchange rate based on the defuzzyfication of weighted average method which is the fuzzy model suggested by Takagi and Sugeno. NEWFM classifies upward and downward cases of next daypsilas and next weekpsilas GBP/USD exchange rate using the recent 32 days and 32 weeks of CPPn,m (Current Price Position of day n and week n : a percentage of the difference between the price of day n and week n and the moving average of the past m days and m weeks from day n-1 and week n-1) of the daily and weekly GBP/USD exchange rate, respectively. In this paper, the Haar wavelet function is used as a mother wavelet. The most important five and four input features among CPPn,m and 38 numbers of wavelet transformed coefficients produced by the recent 32 days and 32 weeks of CPPn,m are selected by the non-overlap area distribution measurement method, respectively. The data sets cover a period of approximately ten years starting from 2 January 1990. The proposed method shows that the accuracy rates are 55.19% for the daily data and 72.58% for the weekly data.