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Many edge detection schemes suffer from the lack of image quality at the global level. Global properties are more vital in grayscale images due to loss of hue and texture. This paper proposes a novel fuzzy-based Gaussian edge detector that uses both global and local image properties for grayscale images. In the global contrast intensification phase, each pixel in an image is represented in the fuzzy domain using a modified Gaussian membership function. A nonlinear contrast intensification function containing three parameters is used to further enhance the image. In the local phase, we present a novel fuzzy parameterized Gaussian-type edge detector mask containing two fuzzifier parameters, which are chosen based on experimental selection rules. Optionally, the fuzzy image entropy function can be used to optimize all the parameters through simple gradient descent technique. In experiments conducted on various classic images, this algorithm showed notable visual improvement on both strong and weak edges in comparison with common edge detectors.