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A fuzzy logic based filter is presented for speckle reduction of synthetic aperture radar (SAR) images. The filtering method is composed of two stages. The first stage computes a fuzzy edge for each pixel in the filter window. The second stage uses these fuzzy edges to weight the contributions of neighboring pixel values and performs fuzzy filtering. Both stages are on the basis of fuzzy logic which makes use of membership functions. In order to effectively reduce heavy noise, the fuzzy filter can be applied iteratively. The multiplicative noise model of full-developed speckle is employed to construct the membership functions of fuzzy sets. The fuzzy filter is tested on two RADARSAT-1 images and a simulated SAR image. Experimental results are compared to other filters by numerical measures and visual inspection. As was expected, the new filter averages the homogeneous areas better and preserves edges better.