Appropriate task offloading management strategy is a challenging problem for high delay-sensitive and heavy-task applications. This paper proposes a fuzzy-based mobile edge manager with task partitioning, which can handle the multi-criteria decision-making process by considering multiple parameters in the MEC network framework and make appropriate offloading decisions for incoming tasks of IoT applications. Considering that the mobile devices are becoming more and more powerful, this paper also takes WLAN delay and the computing power of mobile devices into account, forming a three-level fuzzy logic system. In addition, since many tasks of Internet of Things applications are composed of several independent modules, this paper also sets two optimal task partitioning ratios, which have symmetry, so that each module can be independently executed in each layer of the MEC network. In addition, results will return to the mobile devices after execution, so as to minimize the service time and improve QoS. Finally, several indexes such as task failure rate and service time are simulated, and the results show that the proposed scheme has better performance compared with the other four comparison schemes, especially for high-latency sensitivity and heavy-task applications.