Addressing the challenge of the security recognition through electroencephalogram (EEG) biometrics, we propose an EEG recognition system named EEG-FE rrRS. Leveraging a fuzzy extractor, this system aims to facilitate personalized recognition in the scenarios such as the unmanned aerial vehicle (UAV) and metaverse that require human-computer interaction. This robust and reusable fuzzy extractor framework capitalizes on EEG characteristics for biometric identification and it can be divided into two parts: an EEG signal processing module and a proprietary fuzzy extractor scheme containing the secure sketch and the strong extractor. By employing EEG-FE rrRS, a unique digital identity can be established for each user. The security of the proposed fuzzy extractor is proved from the perspective of entropy loss. Furthermore, the simulations have been conducted to evaluate the performance of EEGFE rrRS, showcasing its highly promising recognition accuracy. Specifically, the recognition rate of the system on the motor imagery database has reached 0.92% FRR and 0.08% FAR, respectively. While on the SEED database, the recognition rate has achieved 0% FRR and 0% FAR, respectively.