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Edge detection is an important problem in image processing. This was extensively studied in recent years. In this paper artificial feedforward neural networks are used for identifying edges in gray-scale images. Supervised learning based on the gradient descent algorithm is used. A new method is proposed for neural network training patterns using fuzzy concepts. Fuzzy membership functions are used for improving the generalization capability of neural network. Edge detection in noisy images without applying a noise removal technique poses a difficult problem. The proposed method obtained successful experimental results for digital images. The advantage of our approach is that we use the trained neural network as a filter on both noisy and noise free images.