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Fuzzy inference systems have been widely applied in robotic control. Previous studies proposed various methods to tune the fuzzy rules and the parameters of the membership functions (MFs). Training the systems with only supervised learning requires a large amount of input-output data, and the performance of the trained system is confined by that of the target system. Training the systems with only reinforcement learning (RL) does not require prior knowledge but is time-consuming, and the initialization of the system remains a problem. In this paper, a supervised-reinforced successive training framework is proposed for a multi-continuous-output fuzzy inference system (MCOFIS). The parameters of the fuzzy inference system are first tuned by a limited number of input-output data from an existing controller with supervised training and then are utilized to initialize the system in the reinforcement training stage. The proposed framework is applied in a robotic odor source searching task and the evaluation results demonstrate that the performance of the fuzzy inference system trained by the successive framework is superior to the systems trained by only supervised learning or RL. The system trained by the proposed framework can achieve around a 10% higher success rate compared to the systems trained by only supervised learning or RL.