Abstract class for a fuzzy interval which is defined by stating its confidence intervals \((\tilde{x})_\alpha\) for all \(\alpha \in [0, 1]\). More...

#include <FuzzyIntervalViaConfidenceInterval.hpp>

Inheritance diagram for sgpp::optimization::FuzzyIntervalViaConfidenceInterval:

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

	FuzzyIntervalViaConfidenceInterval (const FuzzyIntervalViaConfidenceInterval &other)
	Copy constructor.

	FuzzyIntervalViaConfidenceInterval (double supportLowerBound, double supportUpperBound, size_t numberOfIntegralSamples=DEFAULT_NUMBER_OF_INTEGRAL_SAMPLES, double binarySearchTolerance=DEFAULT_BINARY_SEARCH_TOLERANCE)
	Constructor.

double	getBinarySearchTolerance () const

void	setBinarySearchTolerance (double binarySearchTolerance)

	~FuzzyIntervalViaConfidenceInterval () 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.

virtual double	evaluateConfidenceIntervalLowerBound (double alpha) const =0
	Pure virtual method to evaluate the lower bound of a confidence interval, which is always a closed interval \((\tilde{x})_\alpha = [a, b]\).

virtual double	evaluateConfidenceIntervalUpperBound (double alpha) const =0
	Pure virtual method to evaluate the upper bound of a confidence interval, which is always a closed interval \((\tilde{x})_\alpha = [a, b]\).

	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.

Static Public Attributes
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

Protected Attributes
double	binarySearchTolerance
	tolerance for the binary search

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...

Detailed Description

Abstract class for a fuzzy interval which is defined by stating its confidence intervals \((\tilde{x})_\alpha\) for all \(\alpha \in [0, 1]\).

Constructor & Destructor Documentation

◆ FuzzyIntervalViaConfidenceInterval() [1/2]

sgpp::optimization::FuzzyIntervalViaConfidenceInterval::FuzzyIntervalViaConfidenceInterval	(	double	supportLowerBound,
		double	supportUpperBound,
		size_t	numberOfIntegralSamples = `DEFAULT_NUMBER_OF_INTEGRAL_SAMPLES`,
		double	binarySearchTolerance = `DEFAULT_BINARY_SEARCH_TOLERANCE`
	)

Constructor.

Needs the support of the fuzzy interval (which is always a closed interval, so it suffices to supply lower and upper bound).

Parameters

supportLowerBound	lower bound of the support
supportUpperBound	upper bound of the support
numberOfIntegralSamples	number of samples to compute norms
binarySearchTolerance	tolerance for the binary search

◆ FuzzyIntervalViaConfidenceInterval() [2/2]

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

Copy constructor.

Parameters

other other fuzzy interval

◆ ~FuzzyIntervalViaConfidenceInterval()

sgpp::optimization::FuzzyIntervalViaConfidenceInterval::~FuzzyIntervalViaConfidenceInterval ( )

override

Destructor.

Member Function Documentation

◆ evaluateMembershipFunction()

double sgpp::optimization::FuzzyIntervalViaConfidenceInterval::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 binarySearchTolerance, sgpp::optimization::FuzzyInterval::evaluateConfidenceIntervalLowerBound(), sgpp::optimization::FuzzyInterval::evaluateConfidenceIntervalUpperBound(), sgpp::optimization::FuzzyInterval::supportLowerBound, and sgpp::optimization::FuzzyInterval::supportUpperBound.

◆ getBinarySearchTolerance()

double sgpp::optimization::FuzzyIntervalViaConfidenceInterval::getBinarySearchTolerance ( ) const

Returns: tolerance for the binary search

References binarySearchTolerance.

◆ setBinarySearchTolerance()

void sgpp::optimization::FuzzyIntervalViaConfidenceInterval::setBinarySearchTolerance ( double binarySearchTolerance )

Parameters

binarySearchTolerance tolerance for the binary search

References binarySearchTolerance.

Member Data Documentation

◆ binarySearchTolerance

double sgpp::optimization::FuzzyIntervalViaConfidenceInterval::binarySearchTolerance

protected

tolerance for the binary search

Referenced by evaluateMembershipFunction(), getBinarySearchTolerance(), and setBinarySearchTolerance().

◆ DEFAULT_BINARY_SEARCH_TOLERANCE

constexpr double sgpp::optimization::FuzzyIntervalViaConfidenceInterval::DEFAULT_BINARY_SEARCH_TOLERANCE = 1e-6

staticconstexpr

default tolerance for the binary search

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

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

Public Member Functions

Static Public Attributes

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ FuzzyIntervalViaConfidenceInterval() [1/2]

◆ FuzzyIntervalViaConfidenceInterval() [2/2]

◆ ~FuzzyIntervalViaConfidenceInterval()

Member Function Documentation

◆ evaluateMembershipFunction()

◆ getBinarySearchTolerance()

◆ setBinarySearchTolerance()

Member Data Documentation

◆ binarySearchTolerance

◆ DEFAULT_BINARY_SEARCH_TOLERANCE