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Software-defined networking (SDN) is an emerging networking technology with a central point, called the controller, on the control plane. This controller communicates with the application and data planes. In fifth-generation (5G) mobile wireless networks and beyond, specific levels of service quality are defined for different traffic types. Ultra-reliable low-latency communication (URLLC) is one of the key services in 5G. This paper presents a fuzzy logic (FL)-based dynamic routing (FLDR) mechanism with congestion avoidance for URLLC on SDN-based 5G networks. By periodically monitoring the network status and making forwarding decisions on the basis of fuzzy inference rules, the FLDR mechanism not only can reroute in real time, but also can cope with network status uncertainty owing to FL's fault tolerance capabilities. Three input parameters, normalized throughput, packet delay, and link utilization, were employed as crisp inputs to the FL control system because they had a more accurate correlation with the network performance measures we studied. The crisp output of the FL control system, i.e., path weight, and a predefined threshold of packet loss ratio on a path were applied to make routing decisions. We evaluated the performance of the proposed FLDR mechanism on the Mininet simulator by installing three additional modules, topology discovery, monitoring, and rerouting with FL, on the traditional control plane of SDN. The superiority of the proposed FLDR over the other existing FL-based routing schemes was demonstrated using three performance measures, system throughput, packet loss rate, and packet delay versus traffic load in the system. [ABSTRACT FROM AUTHOR]