## 12 Evolving Fuzzy Techniques for EEG Artifact Removal
### An Important Expansion: Intuitionistic Fuzzy Systems (IFS)  
Adopting an intuitionistic approach to fuzzy TS systems in removing artifacts from EEG signals constitutes a notable advance, adding an evaluation dimension that refines uncertainty management and increases flexibility in dealing with ambiguities in EEG signals. This mathematical advancement enriches the understanding of the uncertainty related to each component of the signal, enhancing the effectiveness in distinguishing artifacts from true neural components. In intuitionistic fuzzy TS systems (ITS), each rule not only evaluates the presence of a characteristic through a degree of membership but also considers a degree of non-membership, thus introducing a bi-valued approach that allows for more sophisticated management of uncertainty. A rule in such a system can be expressed as:  
\[\text{If }c_{1}\text{ is }A_{1}^{I}\text{ and }c_{2}\text{ is }A_{2}^{I}\text{ }\dots\text{ and }c\text{ is }A_{n}^{I}\text{ Then }y=f(c_{1},c_{2},\dots,c_{n}), \tag{40}\]  
where \(A_{1}^{I}\), \(A_{2}^{I}\), \(\dots\), \(A_{n}^{I}\) are intuitionistic fuzzy sets, \(c_{1}\), \(c_{2}\), \(\dots c_{n}\) are the characteristics of the EEG signal, and \(y\) is the artifact removal action calculated by a function \(f\). Every intuitionistic fuzzy set, \(A^{I}\), is characterized by a membership function, \(\mu_{A^{I}}(c_{i})\), which measures the degree to which \(x\) belongs to \(A^{I}\) and a non-membership function, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ref.** & **Domain** & **Method** & **Conclusions** \\ \hline \multirow{3}{*}{[145]} & \multirow{3}{*}{Internal external} & \multirow{3}{*}{TS and PSI} & The system delivers virtually impeccable performance, consistently achieving near-perfect results in its operational metrics. This performance is characterized by exceptional accuracy and reliability across a range of applications, demonstrating its robustness and effectiveness in meeting stringent quality standards. \\ \cline{3-4}  & & & The system exhibits close to perfect performance, achieving nearly optimal results in its functionality. This exceptional level of performance is quantitatively evident through high accuracy rates and minimal error margins across various tests and applications, underscoring its effectiveness and reliability in operational environments. \\ \hline \multirow{3}{*}{[147]} & \multirow{3}{*}{Internal external} & \multirow{3}{*}{ANFIS} & The system demonstrates nearly flawless execution, consistently achieving high-precision and minimal errors in its operations. This level of performance is quantitatively reflected in superior accuracy metrics and operational efficiency, highlighting its reliability and effectiveness in executing tasks with exceptional proficiency. \\ \hline \multirow{3}{*}{[148]} & \multirow{3}{*}{Internal external} & \multirow{3}{*}{ANFIS} & The system achieves high accuracy, demonstrating its capability to deliver precise results in real-time applications. This high level of accuracy is quantitatively significant, enhancing its reliability and usability in fast-paced environments. Additionally, the system’s performance indicates a strong potential for broader applications, suggesting that its technology can be effectively adapted and utilized across different settings and tasks, further extending its utility and impact. \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Application TS fuzzy approaches for the removing of internal/external in EEG. \(\
u_{A^{I}}(c_{i})\), which measures the degree to which \(c_{i}\) does not belong to \(A^{I}\). The uncertainty index, \(\pi_{A^{I}}(c_{i})\) for an element \(c_{i}\) regarding a fuzzy set, \(A^{I}\) can be defined as:  
\[\pi_{A^{I}}(c_{i})=1-(\mu_{A^{I}}(c_{i})+\
u_{A^{I}}(c_{i})), \tag{41}\]  
and  
\[0\leq\mu_{A^{I}}(c_{i})+\
u_{A^{I}}(c_{i})\leq 1. \tag{42}\]  
This index measures the uncertainty or ambiguity in the classification of EEG signals, improving the accuracy of the evaluation in cases of indeterminate presence of artifacts.