# Fuzzy Tracking and Control Algorithm for an SSVEP-Based BCI System
## 3 Results and Discussion
### Performance of the Fuzzy Tracking and Control Algorithm  
This subsection reports that fifteen healthy subjects (11 males and four females) aged between 21 and 23 were asked to participate for evaluating the fuzzy tracking and control algorithm. To collect  
Figure 4: Membership function of fuzzifier (fuzzy set A).  
Figure 5: Membership function of defuzzifier (fuzzy set B).  
the training data, we developed a visual stimulation procedure comprised of five sets of stimulation sequences. Each set of stimulation sequence consisted of three stimulation frequencies that were randomly generated from the five given frequencies (6 Hz, 6.67 Hz, 10.00 Hz, 8.57 Hz, and 7.50 Hz). Each set of stimulation sequence consisting of three stimulation frequencies followed the following procedure: Each set began with a five-second countdown delay followed by a series of a ten-second visual stimulation and ten seconds of rest. Afterwards, one minute of compulsory rest time was provided for the subject after every set of stimulation sequence. The acquired EEG signals during every ten-second visual stimulation were then blocked into ten non-overlapping frames, and the duration of each frame was one second.  
Because the membership functions of fuzzification and defuzzification can greatly affect the accuracy, validating the factors of membership functions such as their shapes and the ranges is crucial. For fuzzy-based approaches, the triangular function, trapezoidal function, generalized bell curve function, symmetric Gaussian function, and a two-sided version of the Gaussian are widely used [22]. Therefore, these five functions were selected as the membership functions and denoted as TriaMF, TrapMF, GbellMF, GaussMF, and Gauss2 MF, respectively. The range of each membership function in fuzzification and defuzzification was examined from 5 to 50, and the results are shown in Figure 6. The results show that the recognition rates converged when the range of the membership function was greater than 20 for each membership function. When the range of the membership function did not suffice to model the features, the recognition rates were seriously degraded.  
Figure 6: Recognition rates for (**a**) TriaMF; (**b**) TrapMF; (**c**) GbellMF; (**d**) GaussMF; and (**e**) Gauss2 MF. RD, RF, and RR are the output range of defuzzification, the input range of fuzzification, and recognition rate, respectively.  
The optimal recognition rates for the five membership functions are shown in Table 2. The results indicate that the recognition rates for different membership functions were similar. The computational time of the proposed approach was not affected by the RD or the RF, but it was greatly affected by membership functions with different levels of complexity. Since TrapMF, GbellMF, GaussMF, and Gauss2 MF are second-order polynomial equations; their computational complexity are similar. However, the computational complexity of TraiMF was lower than those of the other membership functions. The difference between the optimal recognition rate (GaussMF) and the pessimal recognition rate (TriaMF) was only 0.6%; such a level of error can be ignored in numerous applications. Therefore, the TriaMF was very suitable for real-time applications and was selected in this study.