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FlFSetLR -- Fuzzy set with L and R functions

SYNOPSIS

TYPE

BASE CLASSES

FlFSet

DERIVED CLASSES

FlFSetTrapez

RELATED CLASSES

None

DESCRIPTION

FlFSetLR provides the LR-representation of fuzzy sets. At this representation, the interval [xm1, xm2] is considered to have the maximum membership value ( 1 if normalized ), the left (L) and right (R) approach is described by a shape function. Additionally, a left (alpha) and a right (beta) slope is defined, thus the whole membership function is:
L ( (xm1 - x) / alpha ) for x <= xm1
max (1 if normalized) for xm1 <= x <= xm2
R ( (x - xm2) / beta ) for x >= xm2

Constructors:

FlFSetLR();

FlFSetLR(FlParam *param);

FlFSetLR(double xm1, double xm2, double xalpha, double xbeta, FlFuncType fL, FlFuncType fR);

FlFSetLR(double min, double max, double xm1, double xm2, double xalpha, double xbeta,

FlFuncType fL, FlFuncType fR);

FlFSetLR(FlStringR xname, double min, double max, double xm1, double xm2

double xalpha, double xbeta, FlFuncType fL, FlFuncType fR);

FlFSetLR(FlStringR xname, double xm1, double xm2, double xalpha, double xbeta,

FlFuncType fL, FlFuncType fR);

Initializes FlFSetLR. The possible variables and their default values are:
left/right maximum (xm1,xm2) (0,0), the left/right slope (alpha,beta) (0,0), the left/right function (fL,fR) (FlFuncLin,FlFuncLin) and the values for the named FlFSet xname,min,max with the according default settings of that class.

typedef double (*FlFuncType)(double x);

Function pointer to the functions for L/R use. Implemented functions are:

double FlFuncExp (double x);

exp(-x)
double FlFuncExp2(double x);

exp(-x^2)
double FlFuncLin (double x);

1-x
double FlFuncSqr (double x);

1-x^2
double FlFuncHyp (double x);

1/(1+x)
double FlFuncHyp2(double x);

1/(1+x^2)

virtual double get_membership(double x) const;

Gets the membership values for x.

double get_m1() const;

Returns the value m1 (left maximum).

double get_m2() const;

Returns the value m2 (right maximum).

double get_alpha() const;

Returns the value alpha (left slope).

double get_beta() const;

Returns the value beta (right slope).

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