Table 5 Membership functions and linguistic values of the fuzzy system

Input variable

BW_CH

\(\mu\left(x\right)=\left\{\begin{array}{cc}1&x<0.2\\{\frac{0.4-x}{0.2}} &x\in[0.2 . 0.4]\\0& x>0.4\end{array}\right.\)  

L

M

\(\mu \left(x\right)=\left\{\begin{array}{cc}0& x<0.62\\ \frac{0.9-x}{0.28}& x\in [0.62 . 0.9]\\ 1& x>0.9\end{array}\right.\)  

H

RT_CH

\(\mu \left(x\right)=\left\{\begin{array}{cc}\frac{0.4-x}{0.4}& x\in [0 . 0.4]\\ 0& x >0.4\end{array}\right.\)  

W

\(\mu \left(x\right)=\left\{\begin{array}{cc}0& x<0.1\\ \frac{x-0.1}{0.4}& x\in [0.1 . 0.5]\\ \frac{0.8-x}{0.3}& x\in [0.5 . 0.8]\\ 0& x>0.8\end{array}\right.\)  

M

\(\mu \left(x\right)=\left\{\begin{array}{cc}0& x<0.6\\ \frac{x-0.6}{0.4}& x\in [0.6 . 1]\end{array}\right.\)  

S

PP_CH

\(\mu \left(x\right)=\left\{\begin{array}{cc}\frac{0.35-x}{0.35}& x\in [0 . 0.35]\\ 0& x >0.35\end{array}\right.\)  

L

\(\mu \left(x\right)=\left\{\begin{array}{cc}0& x<0.15\\ \frac{x-0.15}{0.35}& x\in [0.15 . 0.5]\\ \frac{0.72-x}{0.22}& x\in [0.5 . 0.72]\\ 0& x>0.72\end{array}\right.\)  

M

\(\mu \left(x\right)=\left\{\begin{array}{cc}0& x\in [0 . 0.6]\\ \frac{x-0.6}{0.4}& x >0.6\end{array}\right.\)  

H

Output variable

SoCH

\(\mu \left(x\right)=\left\{\begin{array}{cc}1& x<0.15\\ \frac{0.22-x}{0.07}& x\in [0.15 . 0.22]\\ 0& x>0.22\end{array}\right.\)  

B

\(\mu \left(x\right)=\left\{\begin{array}{cc}0& x<0.18\\ \frac{x-0.18}{0.18}& x\in [0.18 . 0.27]\\ 1& x\in [0.27 . 0.4]\\ \frac{0.5-x}{0.1}& x\in [0.4 . 0.5]\\ 0& x>0.5\end{array}\right.\)  

M

\(\mu \left(x\right)=\left\{\begin{array}{cc}0& x<0.35\\ \frac{x-0.35}{0.15}& x\in [0.35 . 0.5]\\ 1& x\in [0.5 . 0.7]\\ \frac{0.78-x}{0.08}& x\in [0.7 . 0.78]\\ 0& x>0.78\end{array}\right.\)  

G

\(\mu \left(x\right)=\left\{\begin{array}{cc}0& x<0.58\\ \frac{0.8-x}{0.28}& x\in [0.58 . 0.8]\\ 1& x>0.8\end{array}\right.\)  

E