The edge detection has been so far under a lot of studies on its methods, as a very important part of image recognition. Never the less the correct detection of the edge has been yet a difficult problem because of the various scopes of detection according to the applied field. One of those problems to be solved is the edge detection in images with noise. This paper presents an efficient method which removes noise and detect edge in the same framework based on fuzzy logic. The method consists of two steps. First, an efficient filtering is applied to eliminate the noise from original image. The filtering is performed by utilizing fuzzy MIN-MAX operator in three directions such as vertical, horizontal and diagonal angle of 3${ imes}$3 mask. Second, edges are detected by using extended fuzzy Shanon Function.