In the fog computing model of the IoT, subprocesses of an application process to handle sensor data are performed on fog nodes. Since the IoT is scalable, we have to reduce the electric energy consumption. In the tree-based fog computing (TBFC) model, fog nodes are hierarchically structured. In this paper, we propose a fault-tolerant TBFC (FTBFC) model. In addition, we newly propose a pair of fault-tolerant strategies. In one data transmission strategy, data processed by disconnected fog nodes is sent to a new parent fog node. Here, we propose a minimum energy (ME) algorithm to select a new parent fog node whose energy consumption is minimum. In another subprocess transmission strategy, the subprocess of the faulty fog node is sent to another fog node. In the evaluation, the energy consumption and execution time of a new parent fog node can be reduced by the ME algorithm.