In this paper enhancement of a digital image is done by detecting the noisy and noiseless region of the image. The noisy regions are smoothed and the noiseless regions are sharpened. After detecting and removing the noise, finally the contrast and edges are preserved and enhanced. The fuzzy set is represented by a membership function that will be used by the filtering method, which is a fuzzy averaging of neighboring pixels. Key Words: Image Enhancement, Fuzzy set, noise reduction, edge preservation.