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Steady-state Visually Evoked Potential (SSVEP) based Electroencephalogram (EEG) signal is utilized in brain-computer interface paradigms, diagnosis of brain diseases, and measurement of the cognitive status of the human brain. However, various artifacts such as the Electrocardiogram (ECG), Electrooculogram (EOG), and Electromyogram (EMG) are present in the raw EEG signal, which adversely affect the EEG-based appliances. In this research, Adaptive Neuro-fuzzy Interface Systems (ANFIS) and Hilbert-Huang Transform (HHT) are primarily employed to remove the artifacts from EEG signals. This work proposes Adaptive Noise Cancellation (ANC) and ANFIS based methods for canceling EEG artifacts. A mathematical model of EEG with the aforementioned artifacts is determined to accomplish the research goal, and then those artifacts are eliminated based on their mathematical characteristics. ANC, ANFIS, and HHT algorithms are simulated on the MATLAB platform, and their performances are also justified by various error estimation criteria using hardware implementation.