Quasi-Gaussian fuzzy number. More...

#include <QuasiGaussianFuzzyNumber.hpp>

Inheritance diagram for sgpp::optimization::QuasiGaussianFuzzyNumber:

Public Member Functions
double	evaluateMembershipFunction (double x) const override
	Evaluate the membership function.

double	getCutoff () const

double	getMean () const

double	getStdev () const

	QuasiGaussianFuzzyNumber (const QuasiGaussianFuzzyNumber &other)
	Copy constructor.

	QuasiGaussianFuzzyNumber (double mean, double stdev, double cutoff)
	Constructor.

	~QuasiGaussianFuzzyNumber () override
	Destructor.

Public Member Functions inherited from sgpp::optimization::FuzzyIntervalViaMembershipFunction
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 \((\tilde{x})_\alpha = [a, b]\).

	FuzzyIntervalViaMembershipFunction (const FuzzyIntervalViaMembershipFunction &other)
	Copy constructor.

	FuzzyIntervalViaMembershipFunction (double supportLowerBound, double supportUpperBound, double coreLowerBound, double coreUpperBound, size_t numberOfIntegralSamples=DEFAULT_NUMBER_OF_INTEGRAL_SAMPLES, double binarySearchTolerance=DEFAULT_BINARY_SEARCH_TOLERANCE)
	Constructor.

double	getBinarySearchTolerance () const

double	getCoreLowerBound () const

double	getCoreUpperBound () const

void	setBinarySearchTolerance (double binarySearchTolerance)

	~FuzzyIntervalViaMembershipFunction () 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	cutoff
	cut-off point (multiples of the standard deviation)

double	mean
	mean

double	stdev
	standard deviation

Protected Attributes inherited from sgpp::optimization::FuzzyIntervalViaMembershipFunction
double	binarySearchTolerance
	tolerance for the binary search

double	coreLowerBound
	lower bound of the core

double	coreUpperBound
	upper bound of the core

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::FuzzyIntervalViaMembershipFunction
static constexpr double	DEFAULT_BINARY_SEARCH_TOLERANCE = 1e-6
	default tolerance for the binary search

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

Quasi-Gaussian fuzzy number.

A fuzzy number is a fuzzy interval where \(\{x \in X \mid \mu_{\tilde{x}}(x) = 1\} = \{a\}\) for some \(a \in X\). Quasi-Gaussian fuzzy numbers have a cut-off Gaussian function as membership function, which is parametrized by its mean, the standard deviation, and the cut-off point.

Constructor & Destructor Documentation

◆ QuasiGaussianFuzzyNumber() [1/2]

sgpp::optimization::QuasiGaussianFuzzyNumber::QuasiGaussianFuzzyNumber	(	double	mean,
		double	stdev,
		double	cutoff
	)

Constructor.

Parameters

mean	mean
stdev	standard deviation
cutoff	cut-off point (multiples of the standard deviation)

◆ QuasiGaussianFuzzyNumber() [2/2]

sgpp::optimization::QuasiGaussianFuzzyNumber::QuasiGaussianFuzzyNumber ( const QuasiGaussianFuzzyNumber & other )

Copy constructor.

Parameters

other other quasi-Gaussian fuzzy number

◆ ~QuasiGaussianFuzzyNumber()

sgpp::optimization::QuasiGaussianFuzzyNumber::~QuasiGaussianFuzzyNumber ( )

override

Destructor.

Member Function Documentation

◆ evaluateMembershipFunction()

double sgpp::optimization::QuasiGaussianFuzzyNumber::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 mean, stdev, sgpp::optimization::FuzzyInterval::supportLowerBound, and sgpp::optimization::FuzzyInterval::supportUpperBound.

◆ getCutoff()

double sgpp::optimization::QuasiGaussianFuzzyNumber::getCutoff ( ) const

Returns: cut-off point (multiples of the standard deviation)

References cutoff.

◆ getMean()

double sgpp::optimization::QuasiGaussianFuzzyNumber::getMean ( ) const

Returns: mean

References mean.

◆ getStdev()

double sgpp::optimization::QuasiGaussianFuzzyNumber::getStdev ( ) const

Returns: standard deviation

References stdev.

Member Data Documentation

◆ cutoff

double sgpp::optimization::QuasiGaussianFuzzyNumber::cutoff

protected

cut-off point (multiples of the standard deviation)

Referenced by getCutoff().

◆ mean

double sgpp::optimization::QuasiGaussianFuzzyNumber::mean

protected

mean

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::computeMoments(), python.uq.analysis.mc.MCAnalysis.MCAnalysis::computeMoments(), evaluateMembershipFunction(), getMean(), python.uq.dists.LibAGFDist.LibAGFDist::var(), and python.uq.dists.SGDEdist.SGDEdist::var().

◆ stdev

double sgpp::optimization::QuasiGaussianFuzzyNumber::stdev

protected

standard deviation

Referenced by evaluateMembershipFunction(), and getStdev().

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

optimization/src/sgpp/optimization/fuzzy/QuasiGaussianFuzzyNumber.hpp
optimization/src/sgpp/optimization/fuzzy/QuasiGaussianFuzzyNumber.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ QuasiGaussianFuzzyNumber() [1/2]

◆ QuasiGaussianFuzzyNumber() [2/2]

◆ ~QuasiGaussianFuzzyNumber()

Member Function Documentation

◆ evaluateMembershipFunction()

◆ getCutoff()

◆ getMean()

◆ getStdev()

Member Data Documentation

◆ cutoff

◆ mean

◆ stdev