This paper proposes a fuzzy-based approach to edge detection in gray-level images. The proposed fuzzy edge detector involves two phases - global contrast intensification and local fuzzy edge detection. In the first phase, a modified Gaussian membership function is chosen to represent each pixel in the fuzzy plane. A global contrast intensification operator, containing three parameters, viz., intensification parameter t, fuzzifier f_h and the crossover point x_c, is used to enhance the image. The entropy function is optimized to obtain the parameters f_h and x_c using the gradient descent function before applying the local edge operator in the second phase. The local edge operator is a generalized Gaussian function containing two exponential parameters, α and β. These parameters are obtained by the similar entropy optimization method. By using the proposed technique, a marked visible improvement in the important edges is observed on various test images over common edge detectors.