membership function

Collaboration diagram for membership function:

Enumerations
enum	{   A_MF_NUL , A_MF_GAUSS , A_MF_GAUSS2 , A_MF_GBELL ,   A_MF_SIG , A_MF_DSIG , A_MF_PSIG , A_MF_TRAP ,   A_MF_TRI , A_MF_LINS , A_MF_LINZ , A_MF_S ,   A_MF_Z , A_MF_PI }
	enumeration for membership function More...

Functions
double	a_mf_gauss (double x, double sigma, double c)
	gaussian membership function
double	a_mf_gauss2 (double x, double sigma1, double c1, double sigma2, double c2)
	gaussian combination membership function
double	a_mf_gbell (double x, double a, double b, double c)
	generalized bell-shaped membership function
double	a_mf_sig (double x, double a, double c)
	sigmoidal membership function
double	a_mf_dsig (double x, double a1, double c1, double a2, double c2)
	difference between two sigmoidal membership functions
double	a_mf_psig (double x, double a1, double c1, double a2, double c2)
	product of two sigmoidal membership functions
double	a_mf_trap (double x, double a, double b, double c, double d)
	trapezoidal membership function
double	a_mf_tri (double x, double a, double b, double c)
	triangular membership function
double	a_mf_lins (double x, double a, double b)
	linear s-shaped saturation membership function
double	a_mf_linz (double x, double a, double b)
	linear z-shaped saturation membership function
double	a_mf_s (double x, double a, double b)
	s-shaped membership function
double	a_mf_z (double x, double a, double b)
	z-shaped membership function
double	a_mf_pi (double x, double a, double b, double c, double d)
	pi-shaped membership function
double	a_mf (unsigned int e, double x, double const *a)
	membership function

Detailed Description

Enumeration Type Documentation

anonymous enum

anonymous enum

enumeration for membership function

Enumerator
A_MF_NUL	none
A_MF_GAUSS	gaussian membership function
A_MF_GAUSS2	gaussian combination membership function
A_MF_GBELL	generalized bell-shaped membership function
A_MF_SIG	sigmoidal membership function
A_MF_DSIG	difference between two sigmoidal membership functions
A_MF_PSIG	product of two sigmoidal membership functions
A_MF_TRAP	trapezoidal membership function
A_MF_TRI	triangular membership function
A_MF_LINS	linear s-shaped saturation membership function
A_MF_LINZ	linear z-shaped saturation membership function
A_MF_S	s-shaped membership function
A_MF_Z	z-shaped membership function
A_MF_PI	pi-shaped membership function

Function Documentation

a_mf()

double a_mf	(	unsigned int	e,
		double	x,
		double const *	a )

membership function

Parameters

[in]	e	enumeration for membership function A_MF_GAUSS a_mf_gauss(x, sigma, c) A_MF_GAUSS2 a_mf_gauss2(x, sigma1, c1, sigma2, c2) A_MF_GBELL a_mf_gbell(x, a, b, c) A_MF_SIG a_mf_sig(x, a, c) A_MF_DSIG a_mf_dsig(x, a1, c1, a2, c2) A_MF_PSIG a_mf_psig(x, a1, c1, a2, c2) A_MF_TRAP a_mf_trap(x, a, b, c, d) A_MF_TRI a_mf_tri(x, a, b, c) A_MF_LINS a_mf_lins(x, a, b) A_MF_LINZ a_mf_linz(x, a, b) A_MF_S a_mf_s(x, a, b) A_MF_Z a_mf_z(x, a, b) A_MF_PI a_mf_pi(x, a, b, c, d)
[in]	x	input value for which to compute membership value.
[in]	a	is an array that stores parameters. a[2] a_mf_gauss a_mf_sig a_mf_lins a_mf_linz a_mf_s a_mf_z a[3] a_mf_gbell a_mf_tri a[4] a_mf_gauss2 a_mf_dsig a_mf_psig a_mf_trap a_mf_pi

Returns

membership value.

a_mf_dsig()

double a_mf_dsig	(	double	x,
		double	a1,
		double	c1,
		double	a2,
		double	c2 )

difference between two sigmoidal membership functions

\[ f(x,a_1,c_1,a_2,c_2)=\frac{1}{1+e^{-a_1(x-c_1)}}-\frac{1}{1+e^{-a_2(x-c_2)}} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a1	defines the width of the first transition area.
[in]	c1	defines the center of the first transition area.
[in]	a2	defines the width of the second transition area.
[in]	c2	defines the center of the second transition area.

Returns

membership value.

a_mf_gauss()

double a_mf_gauss	(	double	x,
		double	sigma,
		double	c )

gaussian membership function

\[ f(x,\sigma,c)=e^{-\frac{(x-c)^2}{2\sigma^2}} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	sigma	is the standard deviation.
[in]	c	is the mean.

Returns

membership value.

a_mf_gauss2()

double a_mf_gauss2	(	double	x,
		double	sigma1,
		double	c1,
		double	sigma2,
		double	c2 )

gaussian combination membership function

\[ f(x,\sigma_1,c_1,\sigma_2,c_2)=\begin{cases} e^{-\frac{(x-c_1)^2}{2\sigma_1^2}} & x \lt c_1 \\ 1 & c_1 \le x \le c_2 \\ e^{-\frac{(x-c_2)^2}{2\sigma_2^2}} & x \gt c_2 \\ \end{cases} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	sigma1	is the standard deviation of the left gaussian function.
[in]	c1	is the mean of the left gaussian function.
[in]	sigma2	is the standard deviation of the right gaussian function.
[in]	c2	is the mean of the right gaussian function.

Returns

membership value.

a_mf_gbell()

double a_mf_gbell	(	double	x,
		double	a,
		double	b,
		double	c )

generalized bell-shaped membership function

\[ f(x,a,b,c)=\frac{1}{1+\left|\frac{x-c}{a}\right|^{2b}} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a	defines the width of the membership function, where a larger value creates a wider membership function.
[in]	b	defines the shape of the curve on either side of the central plateau, where a larger value creates a more steep transition.
[in]	c	defines the center of the membership function.

Returns

membership value.

a_mf_lins()

double a_mf_lins	(	double	x,
		double	a,
		double	b )

linear s-shaped saturation membership function

\[ f(x,a,b)=\begin{cases} 0 & x \lt a \\ \frac{x-a}{b-a} & a \le x \le b \\ 1 & x \gt b \\ \end{cases} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a	defines its foot.
[in]	b	defines its shoulder.

Returns

membership value.

a_mf_linz()

double a_mf_linz	(	double	x,
		double	a,
		double	b )

linear z-shaped saturation membership function

\[ f(x,a,b)=\begin{cases} 1 & x \lt a \\ \frac{b-x}{b-a} & a \le x \le b \\ 0 & x \gt b \\ \end{cases} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a	defines its shoulder.
[in]	b	defines its foot.

Returns

membership value.

a_mf_pi()

double a_mf_pi	(	double	x,
		double	a,
		double	b,
		double	c,
		double	d )

pi-shaped membership function

\[ f(x,a,b,c,d)=\begin{cases} 0 & x \le a \\ 2(\frac{x-a}{b-a})^2 & a \le x \le \frac{a+b}{2} \\ 1-2(\frac{b-x}{b-a})^2 & \frac{a+b}{2} \le x \le b \\ 1 & b \le x \le c \\ 1-2(\frac{x-c}{d-c})^2 & c \le x \le \frac{c+d}{2} \\ 2(\frac{d-x}{d-c})^2 & \frac{c+d}{2} \le x \le d \\ 1 & x \ge d \\ \end{cases} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a	defines its left foot.
[in]	b	defines its left shoulder.
[in]	c	defines its right shoulder.
[in]	d	defines its right foot.

Returns

membership value.

a_mf_psig()

double a_mf_psig	(	double	x,
		double	a1,
		double	c1,
		double	a2,
		double	c2 )

product of two sigmoidal membership functions

\[ f(x,a_1,c_1,a_2,c_2)=\frac{1}{1+e^{-a_1(x-c_1)}}\times\frac{1}{1+e^{-a_2(x-c_2)}} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a1	defines the width of the first transition area.
[in]	c1	defines the center of the first transition area.
[in]	a2	defines the width of the second transition area.
[in]	c2	defines the center of the second transition area.

Returns

membership value.

a_mf_s()

double a_mf_s	(	double	x,
		double	a,
		double	b )

s-shaped membership function

\[ f(x,a,b)=\begin{cases} 0 & x \le a \\ 2(\frac{x-a}{b-a})^2 & a \le x \le \frac{a+b}{2} \\ 1-2(\frac{b-x}{b-a})^2 & \frac{a+b}{2} \le x \le b \\ 1 & x \ge b \\ \end{cases} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a	defines its foot.
[in]	b	defines its shoulder.

Returns

membership value.

a_mf_sig()

double a_mf_sig	(	double	x,
		double	a,
		double	c )

sigmoidal membership function

\[ f(x,a,c)=\frac{1}{1+e^{-a(x-c)}} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a	defines the width of the transition area.
[in]	c	defines the center of the transition area.

Returns

membership value.

a_mf_trap()

double a_mf_trap	(	double	x,
		double	a,
		double	b,
		double	c,
		double	d )

trapezoidal membership function

\[ f(x,a,b,c,d)=\begin{cases} 0 & x \le a \\ \frac{x-a}{b-a} & a \le x \le b \\ 1 & b \le x \le c \\ \frac{d-x}{d-c} & c \le x \le d \\ 0 & x \ge d \\ \end{cases} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a	defines its left foot.
[in]	b	defines its left shoulder.
[in]	c	defines its right shoulder.
[in]	d	defines its right foot.

Returns

membership value.

a_mf_tri()

double a_mf_tri	(	double	x,
		double	a,
		double	b,
		double	c )

triangular membership function

\[ f(x,a,b)=\begin{cases} 0 & x \le a \\ \frac{x-a}{b-a} & a \le x \le b \\ \frac{c-x}{c-b} & b \le x \le c \\ 0 & x \ge c \\ \end{cases} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a	defines its left foot.
[in]	b	defines its peak.
[in]	c	defines its right foot.

Returns

membership value.

a_mf_z()

double a_mf_z	(	double	x,
		double	a,
		double	b )

z-shaped membership function

\[ f(x,a,b)=\begin{cases} 1 & x \le a \\ 1-2(\frac{x-a}{b-a})^2 & a \le x \le \frac{a+b}{2} \\ 2(\frac{b-x}{b-a})^2 & \frac{a+b}{2} \le x \le b \\ 0 & x \ge b \\ \end{cases} \]

Parameters

[in]	x	input value for which to compute membership value.
[in]	a	defines its shoulder.
[in]	b	defines its foot.

Returns

membership value.