Driven by diverse intelligent applications, computing capability is moving from the central cloud to the edge of the network in the form of small cloud nodes, forming a distributed computing power network. Tasked with both packet transmission and data processing, it requires joint optimization of communications and computing. Considering the diverse requirements of applications, we develop a dynamic control policy of routing to determine both paths and computing nodes in a distributed computing power network. Different from traditional routing protocols, additional metrics related to computing are taken into consideration in the proposed policy. Based on the multi-attribute decision theory and the fuzzy logic theory, we propose two routing selection algorithms, the Fuzzy Logic-Based Routing (FLBR) algorithm and the low-complexity Pairwise Multi-Attribute Decision-Making (lPMADM) algorithm. Simulation results show that the proposed policy could achieve better performance in average processing delay, user satisfaction, and load balancing compared with existing works.