Brain-computer interface (BCI) provides direct communication and control between the human brain and physical devices. It is achieved by converting EEG signals into control commands. Such interfaces have significantly improved the lives of disabled individuals suffering from neurological disorders-such as stroke, amyotrophic lateral sclerosis (ALS), and spinal cord injury-by extending their movement range and thereby promoting self-independence. Brain-controlled mobile robots, however, often face challenges in safety and control performance due to the inherent limitations of BCIs. This paper proposes a shared control scheme for brain-controlled mobile robots by utilizing fuzzy logic to enhance safety, control performance, and robustness. The proposed scheme is developed by combining a self-learning neuro-fuzzy (SLNF) controller with an obstacle avoidance controller (OAC). The SLNF controller robustly tracks the user's intentions, and the OAC ensures the safety of the mobile robot following the BCI commands. Furthermore, SLNF is a model-free controller that can learn as well as update its parameters online, diminishing the effect of disturbances. The experimental results prove the efficacy and robustness of the proposed SLNF controller including a higher task completion rate of 94.29% (compared to 79.29%, and 92.86% for Direct BCI and Fuzzy-PID, respectively), a shorter average task completion time of 85.31 s (compared to 92.01 s and 86.16 s for Direct BCI and Fuzzy-PID, respectively), and reduced settling time and overshoot.