Edge detection is a crucial task in image processing. Owing to the similarity in property between edges and noise, which demonstrates abrupt changes in image grayscale values, traditional edge detection methods are insufficient in detecting weak edges. Therefore, a local multi-threshold fuzzy inference method (LMFI) is introduced. Considering the binarization processing prior to conducting a fuzzy inference, to retain more edge information, a local threshold processing method and a triple threshold processing method are proposed. To reduce noise interference, an improved sigma filter and an improved fuzzy inference strategy are presented. The experimental results show that the effect of weak edge detection is improved by LMFI, when compared to conventional methods such as the original fuzzy inference algorithm and Canny edge detection algorithm.