In this paper, we describe the results of a study on the edge enhancement of X-ray images by using their fuzzy system representation. A set of gray scale X-ray images was generated using the EGS4 computer code. An aluminum plate or a lead plate with three parallel strips taken out has been used as the object with the thickness and the width of the plate, and the gap between the two strips varied. We started with a comparative study on a set of the fuzzy sets for their applicability as the input fuzzy sets for the fuzzy system representation of the gray scale images. Then we describe how the fuzzy system is used to sharpen the edges. Our algorithm is based on adding the magnitude of the gradient not to the pixel value of concern but rather to the nearest neighboring pixel in the direction of the gradient. We show that this algorithm is better in maintaining the spatial resolution of the original image after the edge enhancement.