Fuzzy interval by piecewise linear interpolation of sample points \((x_i, \alpha_i)\) of the membership function \(\mu_{\tilde{x}}\), i.e., \(\mu_{\tilde{x}}(x_i) = \alpha_i\) ( \(i = 1, \dotsc, n\)). More...

#include <InterpolatedFuzzyInterval.hpp>

Inheritance diagram for sgpp::optimization::InterpolatedFuzzyInterval:

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

const base::DataVector &	getAlphaData () const

const base::DataVector &	getXData () const

	InterpolatedFuzzyInterval (const base::DataVector &xData, const base::DataVector &alphaData)
	Constructor.

	InterpolatedFuzzyInterval (const InterpolatedFuzzyInterval &other)
	Copy constructor.

	~InterpolatedFuzzyInterval () 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.

Static Public Member Functions
static double	getCoreLowerBound (const base::DataVector &xData, const base::DataVector &alphaData)
	Compute the lower bound of the core (i.e., the area where the membership function equals 1).

static double	getCoreUpperBound (const base::DataVector &xData, const base::DataVector &alphaData)
	Compute the upper bound of the core (i.e., the area where the membership function equals 1).

static InterpolatedFuzzyInterval *	tryDowncast (FuzzyInterval &fuzzyInterval)
	Try to cast a FuzzyInterval to an InterpolatedFuzzyInterval (`dynamic_cast`), needed for the Python interface.

Protected Attributes
base::DataVector	alphaData
	\(\alpha\) data of sample points

base::DataVector	xData
	\(x\) data of sample points

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

Fuzzy interval by piecewise linear interpolation of sample points \((x_i, \alpha_i)\) of the membership function \(\mu_{\tilde{x}}\), i.e., \(\mu_{\tilde{x}}(x_i) = \alpha_i\) ( \(i = 1, \dotsc, n\)).

The data must fulfill the following:

\(x_i < x_{i+1}\) for \(i = 1, \dotsc, n-1\)
\(\alpha_1 = 0 = \alpha_n\)
There are some \(1 < j \le k < n\) such that:
- \(\alpha_i = 1\) for \(i = j, \dotsc, k\)
- \(\alpha_i < \alpha_{i+1}\) for \(i = 1, \dotsc, j-1\)
- \(\alpha_i > \alpha_{i+1}\) for \(i = k, \dotsc, n-1\)

Constructor & Destructor Documentation

◆ InterpolatedFuzzyInterval() [1/2]

sgpp::optimization::InterpolatedFuzzyInterval::InterpolatedFuzzyInterval	(	const base::DataVector &	xData,
		const base::DataVector &	alphaData
	)

Constructor.

Parameters

xData	\(x\) data of sample points
alphaData	\(\alpha\) data of sample points

◆ InterpolatedFuzzyInterval() [2/2]

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

Copy constructor.

Parameters

other other interpolated fuzzy interval

◆ ~InterpolatedFuzzyInterval()

sgpp::optimization::InterpolatedFuzzyInterval::~InterpolatedFuzzyInterval ( )

override

Destructor.

Member Function Documentation

◆ evaluateMembershipFunction()

double sgpp::optimization::InterpolatedFuzzyInterval::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 alphaData, sgpp::base::DataVector::getSize(), sgpp::optimization::FuzzyInterval::supportLowerBound, sgpp::optimization::FuzzyInterval::supportUpperBound, and xData.

◆ getAlphaData()

const base::DataVector & sgpp::optimization::InterpolatedFuzzyInterval::getAlphaData ( ) const

Returns: \(\alpha\) data of sample points

References alphaData.

◆ getCoreLowerBound()

double sgpp::optimization::InterpolatedFuzzyInterval::getCoreLowerBound	(	const base::DataVector &	xData,
		const base::DataVector &	alphaData
	)

static

Compute the lower bound of the core (i.e., the area where the membership function equals 1).

Parameters

xData	\(x\) data of sample points
alphaData	\(\alpha\) data of sample points

References alphaData, sgpp::base::DataVector::getSize(), and xData.

◆ getCoreUpperBound()

double sgpp::optimization::InterpolatedFuzzyInterval::getCoreUpperBound	(	const base::DataVector &	xData,
		const base::DataVector &	alphaData
	)

static

Compute the upper bound of the core (i.e., the area where the membership function equals 1).

Parameters

xData	\(x\) data of sample points
alphaData	\(\alpha\) data of sample points

References alphaData, sgpp::base::DataVector::getSize(), and xData.

◆ getXData()

const base::DataVector & sgpp::optimization::InterpolatedFuzzyInterval::getXData ( ) const

Returns: \(x\) data of sample points

References xData.

◆ tryDowncast()

InterpolatedFuzzyInterval * sgpp::optimization::InterpolatedFuzzyInterval::tryDowncast ( FuzzyInterval & fuzzyInterval )

static

Try to cast a FuzzyInterval to an InterpolatedFuzzyInterval (dynamic_cast), needed for the Python interface.

Parameters

fuzzyInterval FuzzyInterval to cast

Returns: pointer to InterpolatedFuzzyInterval if succesful, nullptr otherwise

Member Data Documentation

◆ alphaData

base::DataVector sgpp::optimization::InterpolatedFuzzyInterval::alphaData

protected

\(\alpha\) data of sample points

Referenced by evaluateMembershipFunction(), getAlphaData(), getCoreLowerBound(), and getCoreUpperBound().

◆ xData

base::DataVector sgpp::optimization::InterpolatedFuzzyInterval::xData

protected

\(x\) data of sample points

Referenced by evaluateMembershipFunction(), getCoreLowerBound(), getCoreUpperBound(), and getXData().

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

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

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ InterpolatedFuzzyInterval() [1/2]

◆ InterpolatedFuzzyInterval() [2/2]

◆ ~InterpolatedFuzzyInterval()

Member Function Documentation

◆ evaluateMembershipFunction()

◆ getAlphaData()

◆ getCoreLowerBound()

◆ getCoreUpperBound()

◆ getXData()

◆ tryDowncast()

Member Data Documentation

◆ alphaData

◆ xData