Person re-identification (Re-ID) is an important research field in computer vision and pedestrian detection. However, there are many complex and highly uncertain factors in the real world, such as occlusion, appearance similarity, and motion blur. These factors pose serious challenges to obtaining accurate and robust feature representation. In order to deploy person Re-ID algorithms on mobile devices and other terminal systems, it is necessary to consider both model complexity and recognition accuracy. To address these uncertainties and enhance the real-time detection accuracy of person Re-ID, we propose a lightweight attention network based on fuzzy logic (FLA-Net). In the backbone network, a pair of complementary attention mechanisms are embedded to capture the discriminative features of pedestrians. Additionally, fuzzy logic is introduced into the attention module to re-weight the feature maps, optimizing the accuracy and robustness of feature representation by adjusting the fuzzy membership degree of pixel values in local regions. Finally, we employ the local horizontal pooling operation to extract fine-grained information from the network, facilitating the capture of discriminative pedestrian features. Experimental analysis of the public datasets Market1501 and DukeMTMC-reID demonstrates that FLA-Net is superior to the state-of-the-art lightweight person Re-ID methods.