Abstract: This article presents a linear generalized fuzzy operator (LGFO)for fuzzy enhancement of contrast among successive region,and then puts forward a novel bilinear nondestructive algorithm for image edge detection based on the theory of normal fuzzy sets(NFS)and generalized fuzzy sets(GFS). The principle of this algorithm is to achieve space transform among grey image space, normal fuzzy space, and generalized fuzzy space by using left semi-trapezoid fuzzy distribution function and LGFO. By the algorithm, the contrast among successive region for generalized fuzzy space is enhanced fuzzily in the process of space transform. Then the edge is extracted in grey image space. Experiments indicate that by using the algorithm proposed in the paper, extraction of edge is efficient and good in effect, superior to the algorithm of Pal, Chen Wufan and Wang Hui in multi-index.