## 6 Implementation of the Dynamic Fuzzy Logic Controller (Dynamic FLC)
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Optimized Gain Factors for the Input Variable \(E_{k}\) (Error)**} \\ \hline \(c_{i}\) & \(\sigma_{i}\) & \\ \multicolumn{3}{c}{**(Optimized Peak Value)**} & **(Optimized Standard Deviation or the Width of the Curve)** & **Membership Function (MF)** \\ \hline \(c_{E_{1}}=-5000\pm\left(\frac{\lambda_{E}}{p_{E_{1}}}\right)\times gain_{c_{1}}\) & \(\sigma_{E_{1}}=707\pm\left(\frac{\lambda_{E}}{q_{E_{1}}}\right)\times gain_{c_ {1}}\) & NB \\ \(c_{E_{2}}=-3333\pm\left(\frac{\lambda_{E}}{p_{E_{2}}}\right)\times gain_{c_{2}}\) & \(\sigma_{E_{2}}=707\pm\left(\frac{\lambda_{E}}{q_{E_{2}}}\right)\times gain_{c_ {2}}\) & NM \\ \(c_{E_{3}}=-1667\pm\left(\frac{\lambda_{E}}{p_{E_{3}}}\right)\times gain_{c_{3}}\) & \(\sigma_{E_{3}}=707\pm\left(\frac{\lambda_{E}}{q_{E_{3}}}\right)\times gain_{c_ {3}}\) & NS \\ \(c_{E_{4}}=\left(\frac{\lambda_{E}}{p_{E_{4}}}\right)\times gain_{c_{4}}\) & \(\sigma_{E_{4}}=707\pm\left(\frac{\lambda_{E}}{q_{E_{4}}}\right)\times gain_{c_ {4}}\) & Z \\ \(c_{E_{5}}=1667\pm\left(\frac{\lambda_{E}}{p_{E_{3}}}\right)\times gain_{c_{5}}\) & \(\sigma_{E_{5}}=707\pm\left(\frac{\lambda_{E}}{q_{E_{5}}}\right)\times gain_{c_ {5}}\) & PS \\ \(c_{E_{6}}=3333\pm\left(\frac{\lambda_{E}}{p_{E_{6}}}\right)\times gain_{c_{6}}\) & \(\sigma_{E_{6}}=707\pm\left(\frac{\lambda_{E}}{q_{E_{6}}}\right)\times gain_{c_ {6}}\) & PM \\ \(c_{E_{7}}=5000\pm\left(\frac{\lambda_{E}}{p_{E_{7}}}\right)\times gain_{c_{7}}\) & \(\sigma_{E_{7}}=707\pm\left(\frac{\lambda_{E}}{q_{E_{7}}}\right)\times gain_{c_ {7}}\) & PB \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The dynamically optimized \(c_{i}\) and \(\sigma_{i}\) factors for the membership functions of \(E_{k}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline \(C_{i}\) (Optimized Peak Value or the Center Value) & \(\mathbf{j}\) & \(\sigma_{i}\) (Optimized Standard Deviation) & \(\mathbf{j}\) \\ \hline \(gain_{c_{1}}=-\frac{1}{\alpha_{1}}G_{(Best)}\times 5000\) & 1 & \(gain_{\sigma_{1}}=\frac{1}{p_{1}}G_{(Best)_{j}}\times 707\) & 2 \\ \(gain_{c_{2}}=-\frac{1}{\alpha_{2}}G_{(Best)}\times 3333\) & 3 & \(gain_{\sigma_{2}}=\frac{1}{p_{2}}G_{(Best)_{1}}\times 707\) & 4 \\ \(gain_{c_{3}}=-\frac{1}{\alpha_{3}}G_{(Best)_{j}}\  
For example, Figure 7 shows that out of these seven linguistic variables, if the positive medium (PM) linguistic variable (PM membership function) is considered, the optimized state 1, state 2 and state 3 of the PM membership function can be obtained for the sampling instants \"\(k\)\", \"\(k+1\)\" and \"\(k+2\)\", respectively. When the membership function shape changes dynamically through this optimization mechanism, this causes the membership grade \(\mu_{A}(x)\) to become more dynamic for every sample instant \(k\). This enables one to capture the uncertainty behavior as the interval-valued membership function. Figure 8 shows the overall mechanism of the dynamic fuzzification process through the dynamic PSO mechanism. Figure 11 shows the optimized \(c_{i}\) and \(\sigma_{i}\) values obtained for all 21 linguistic variables. Moreover, according to Figure 11, this dynamic membership function optimization mechanism is mainly based on the dynamically optimized 14 common membership gain factors and the 3 dynamic I/O gain factors.