sgpp::optimization::TriangularFuzzyInterval Class Reference

Triangular fuzzy interval; its membership function linearly increases from 0 to 1, stays 1, and linearly decreases back to 0. More...

#include <TriangularFuzzyInterval.hpp>

Inheritance diagram for sgpp::optimization::TriangularFuzzyInterval:

Public Member Functions
double	evaluateConfidenceIntervalLowerBound (double alpha) const override
	Evaluate the lower bound of a confidence interval, which is always a closed interval \((\tilde{x})_\alpha = [a, b]\).
double	evaluateConfidenceIntervalUpperBound (double alpha) const override
	Evaluate the upper bound of a confidence interval, which is always a closed interval \((\tilde{x})_\alpha = [a, b]\).
double	evaluateMembershipFunction (double x) const override
	Evaluate the membership function.
double	getLeftMean () const
double	getLeftSpread () const
double	getRightMean () const
double	getRightSpread () const
	TriangularFuzzyInterval (const TriangularFuzzyInterval &other)
	Copy constructor.
	TriangularFuzzyInterval (double leftMean, double rightMean, double leftSpread, double rightSpread)
	Constructor.
	TriangularFuzzyInterval (double mean, double leftSpread, double rightSpread)
	Constructor.
	TriangularFuzzyInterval (double mean, double spread)
	Constructor.
	~TriangularFuzzyInterval () override
	Destructor.
Public Member Functions inherited from sgpp::optimization::FuzzyInterval
double	computeL1Error (const FuzzyInterval &other, NormMode normMode=NormMode::ViaMembershipFunction) const
	Compute absolute L1 error to other fuzzy interval.
double	computeL1Norm (NormMode normMode=NormMode::ViaMembershipFunction) const
	Compute L1 norm of fuzzy interval.
double	computeL2Error (const FuzzyInterval &other, NormMode normMode=NormMode::ViaMembershipFunction) const
	Compute absolute L2 error to other fuzzy interval.
double	computeL2Norm (NormMode normMode=NormMode::ViaMembershipFunction) const
	Compute L2 norm of fuzzy interval.
double	computeLinfError (const FuzzyInterval &other, NormMode normMode=NormMode::ViaMembershipFunction) const
	Compute absolute Linf error to other fuzzy interval.
double	computeLinfNorm (NormMode normMode=NormMode::ViaMembershipFunction) const
	Compute Linf norm of fuzzy interval.
double	computeRelativeL1Error (const FuzzyInterval &other, NormMode normMode=NormMode::ViaMembershipFunction) const
	Compute relative L1 error to other fuzzy interval.
double	computeRelativeL2Error (const FuzzyInterval &other, NormMode normMode=NormMode::ViaMembershipFunction) const
	Compute relative L2 error to other fuzzy interval.
double	computeRelativeLinfError (const FuzzyInterval &other, NormMode normMode=NormMode::ViaMembershipFunction) const
	Compute relative Linf error to other fuzzy interval.
	FuzzyInterval (const FuzzyInterval &other)
	Copy constructor.
	FuzzyInterval (double supportLowerBound, double supportUpperBound, size_t numberOfIntegralSamples=DEFAULT_NUMBER_OF_INTEGRAL_SAMPLES)
	Constructor.
size_t	getNumberOfIntegralSamples () const
double	getSupportLowerBound () const
double	getSupportUpperBound () const
void	setNumberOfIntegralSamples (size_t numberOfIntegralSamples)
virtual	~FuzzyInterval ()
	Destructor.

Protected Attributes
double	leftMean
	left mean
double	leftSpread
	left spread
double	rightMean
	right mean
double	rightSpread
	right spread
Protected Attributes inherited from sgpp::optimization::FuzzyInterval
size_t	numberOfIntegralSamples
	number of samples to compute norms
double	supportLowerBound
	lower bound of the support
double	supportUpperBound
	upper bound of the support

Additional Inherited Members
Public Types inherited from sgpp::optimization::FuzzyInterval
enum class	NormMode { ViaMembershipFunction , ViaConfidenceInterval }
	mode to determine norms of the fuzzy interval More...
Static Public Attributes inherited from sgpp::optimization::FuzzyInterval
static const size_t	DEFAULT_NUMBER_OF_INTEGRAL_SAMPLES = 10000
	default number of samples to compute norms

Detailed Description

Triangular fuzzy interval; its membership function linearly increases from 0 to 1, stays 1, and linearly decreases back to 0.

The core (i.e., the area where the membership function equals 1) is given by \([\mathrm{leftMean}, \mathrm{rightMean}]\). The support is given by \([\mathrm{leftMean} - \mathrm{leftSpread}, \mathrm{rightMean} + \mathrm{rightSpread}]\).

Constructor & Destructor Documentation

TriangularFuzzyInterval() [1/4]

sgpp::optimization::TriangularFuzzyInterval::TriangularFuzzyInterval	(	double	mean,
		double	spread
	)

Constructor.

Parameters

mean	left mean = right mean
spread	left spread = right spread

TriangularFuzzyInterval() [2/4]

sgpp::optimization::TriangularFuzzyInterval::TriangularFuzzyInterval	(	double	mean,
		double	leftSpread,
		double	rightSpread
	)

Constructor.

Parameters

mean	left mean = right mean
leftSpread	left spread
rightSpread	right spread

TriangularFuzzyInterval() [3/4]

sgpp::optimization::TriangularFuzzyInterval::TriangularFuzzyInterval	(	double	leftMean,
		double	rightMean,
		double	leftSpread,
		double	rightSpread
	)

Constructor.

Parameters

leftMean	left mean
rightMean	right mean
leftSpread	left spread
rightSpread	right spread

TriangularFuzzyInterval() [4/4]

sgpp::optimization::TriangularFuzzyInterval::TriangularFuzzyInterval

(

const TriangularFuzzyInterval &

other

)

Copy constructor.

Parameters

other

other triangular fuzzy interval

~TriangularFuzzyInterval()

sgpp::optimization::TriangularFuzzyInterval::~TriangularFuzzyInterval ( )

override

Destructor.

Member Function Documentation

evaluateConfidenceIntervalLowerBound()

double sgpp::optimization::TriangularFuzzyInterval::evaluateConfidenceIntervalLowerBound ( double  alpha ) const

overridevirtual

Evaluate the lower bound of a confidence interval, which is always a closed interval \((\tilde{x})_\alpha = [a, b]\).

Parameters

alpha

\(\alpha \in [0, 1]\)

Returns

\(a \in X\)

Implements sgpp::optimization::FuzzyInterval.

References alpha, leftMean, and leftSpread.

evaluateConfidenceIntervalUpperBound()

double sgpp::optimization::TriangularFuzzyInterval::evaluateConfidenceIntervalUpperBound ( double  alpha ) const

overridevirtual

Evaluate the upper bound of a confidence interval, which is always a closed interval \((\tilde{x})_\alpha = [a, b]\).

Parameters

alpha

\(\alpha \in [0, 1]\)

Returns

\(b \in X\)

Implements sgpp::optimization::FuzzyInterval.

References alpha, rightMean, and rightSpread.

evaluateMembershipFunction()

double sgpp::optimization::TriangularFuzzyInterval::evaluateMembershipFunction ( double  x ) const

overridevirtual

Evaluate the membership function.

Parameters

x	\(x \in X\)

Returns

\(\mu_{\tilde{x}}(x) \in [0, 1]\)

Implements sgpp::optimization::FuzzyInterval.

References leftMean, leftSpread, rightMean, and rightSpread.

getLeftMean()

double sgpp::optimization::TriangularFuzzyInterval::getLeftMean

(

)

const

Returns

left mean

References leftMean.

getLeftSpread()

double sgpp::optimization::TriangularFuzzyInterval::getLeftSpread

(

)

const

Returns

left spread

References leftSpread.

getRightMean()

double sgpp::optimization::TriangularFuzzyInterval::getRightMean

(

)

const

Returns

right mean

References rightMean.

getRightSpread()

double sgpp::optimization::TriangularFuzzyInterval::getRightSpread

(

)

const

Returns

right spread

References rightSpread.

Member Data Documentation

leftMean

double sgpp::optimization::TriangularFuzzyInterval::leftMean

protected

left mean

Referenced by evaluateConfidenceIntervalLowerBound(), evaluateMembershipFunction(), and getLeftMean().

leftSpread

double sgpp::optimization::TriangularFuzzyInterval::leftSpread

protected

left spread

Referenced by evaluateConfidenceIntervalLowerBound(), evaluateMembershipFunction(), and getLeftSpread().

rightMean

double sgpp::optimization::TriangularFuzzyInterval::rightMean

protected

right mean

Referenced by evaluateConfidenceIntervalUpperBound(), evaluateMembershipFunction(), and getRightMean().

rightSpread

double sgpp::optimization::TriangularFuzzyInterval::rightSpread

protected

right spread

Referenced by evaluateConfidenceIntervalUpperBound(), evaluateMembershipFunction(), and getRightSpread().

---

The documentation for this class was generated from the following files:

• optimization/src/sgpp/optimization/fuzzy/TriangularFuzzyInterval.hpp
• optimization/src/sgpp/optimization/fuzzy/TriangularFuzzyInterval.cpp