Table 4.

Summary of ANFIS membership functions

Type	Membership function	Curve parameter	Curve shape
Trapezoidal	$\text{Trapmf}(x,a,b,c,d)=max\left(min,\left(\frac{x-a}{b-a},,,1,,,\frac{d-x}{d-c}\right),,,0\right)$	a, b defines feet and c, d defines curve shoulder	Just like trapezoid
Bell	$\text{Gbellmf}(x,a,b,c)=\frac{1}{1+{\left|\frac{x-c}{a}\right|}^{2b}}$	a determines the width, b is a positive integer and c sets the center of the curve	Bell shaped
Triangular	$\text{Trimf}(x,a,b,c)=max\left(min,\left(\frac{x-a}{b-a},,,1,,,\frac{c-x}{c-b}\right),,,0\right)$	a, c, and b specifies the feet and tip of the curve	Triangular shape
Gaussian	$\text{Gaussmf}(x,c,\sigma )=e^{-\frac{1}{2}{\left(\frac{x-c}{\sigma }\right)}^2}$	c specifies the center and $\sigma$ determines the width of curve	Smooth curve like bell