Abstract class for Zadeh's fuzzy extension principle to propagate fuzzy input uncertainties through a function to obtain a fuzzy output uncertainty. More...

#include <FuzzyExtensionPrinciple.hpp>

Inheritance diagram for sgpp::optimization::FuzzyExtensionPrinciple:

Public Member Functions
FuzzyInterval *	apply (const std::vector< FuzzyInterval * > &xFuzzy)
	Apply the fuzzy extension principle to fuzzy input intervals.

virtual void	clone (std::unique_ptr< FuzzyExtensionPrinciple > &clone) const =0
	Pure virtual method for cloning the fuzzy extension principle.

	FuzzyExtensionPrinciple (const base::ScalarFunction &f, size_t numberOfAlphaSegments=DEFAULT_NUMBER_OF_ALPHA_SEGMENTS)
	Constructor.

	FuzzyExtensionPrinciple (const FuzzyExtensionPrinciple &other)
	Copy constructor.

const base::DataVector &	getAlphaLevels () const

const std::vector< base::DataVector > &	getMaximumPoints () const

const base::DataVector &	getMaximumValues () const

const std::vector< base::DataVector > &	getMinimumPoints () const

const base::DataVector &	getMinimumValues () const

size_t	getNumberOfAlphaSegments () const

const std::vector< base::DataVector > &	getOptimizationDomainsLowerBounds () const

const std::vector< base::DataVector > &	getOptimizationDomainsUpperBounds () const

void	setNumberOfAlphaSegments (size_t numberOfAlphaSegments)

virtual	~FuzzyExtensionPrinciple ()
	Destructor.

Static Public Attributes
static const size_t	DEFAULT_NUMBER_OF_ALPHA_SEGMENTS = 10
	default number of \(\alpha\) segments

Protected Member Functions
virtual void	optimizeForSingleAlphaLevel (size_t j, base::DataVector &minimumPoint, double &minimumValue, base::DataVector &maximumPoint, double &maximumValue)=0
	Pure virtual method for solving the minimization/maximization problem for a single \(\alpha\) level.

virtual void	prepareApply ()
	Custom preparation method that is called before the parallelized optimizeForSingleAlphaLevel calls.

Protected Attributes
base::DataVector	alphaLevels
	number of \(\alpha\) segments

std::unique_ptr< base::ScalarFunction >	f
	function through which to propagate the uncertainties

size_t	m
	number of \(\alpha\) segments

std::vector< base::DataVector >	maximumPoints
	vector of maximum points (after `apply` call)

base::DataVector	maximumValues
	vector of maximum function values (after `apply` call)

std::vector< base::DataVector >	minimumPoints
	vector of minimum points (after `apply` call)

base::DataVector	minimumValues
	vector of minimum function values (after `apply` call)

std::vector< base::DataVector >	optimizationDomainsLowerBounds
	vector of lower bounds of input confidence intervals (after `apply` call)

std::vector< base::DataVector >	optimizationDomainsUpperBounds
	vector of upper bounds of input confidence intervals (after `apply` call)

Detailed Description

Abstract class for Zadeh's fuzzy extension principle to propagate fuzzy input uncertainties through a function to obtain a fuzzy output uncertainty.

Subclasses have to specify how the output confidence intervals are determined.

Literature: W. Andreas Klimke. Uncertainty Modeling using Fuzzy Arithmetic and Sparse Grids. PhD thesis, University of Stuttgart, IANS, 2006.

Constructor & Destructor Documentation

◆ FuzzyExtensionPrinciple() [1/2]

sgpp::optimization::FuzzyExtensionPrinciple::FuzzyExtensionPrinciple	(	const base::ScalarFunction &	f,
		size_t	numberOfAlphaSegments = `DEFAULT_NUMBER_OF_ALPHA_SEGMENTS`
	)

explicit

Constructor.

Parameters

f	function through which to propagate the uncertainties
numberOfAlphaSegments	number of \(\alpha\) segments

References f.

◆ FuzzyExtensionPrinciple() [2/2]

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

Copy constructor.

Parameters

other other fuzzy extension principle

References f.

◆ ~FuzzyExtensionPrinciple()

sgpp::optimization::FuzzyExtensionPrinciple::~FuzzyExtensionPrinciple ( )

virtual

Destructor.

Member Function Documentation

◆ apply()

FuzzyInterval * sgpp::optimization::FuzzyExtensionPrinciple::apply ( const std::vector< FuzzyInterval * > & xFuzzy )

Apply the fuzzy extension principle to fuzzy input intervals.

Parameters

xFuzzy vector of fuzzy input intervals

Returns: fuzzy output interval; plain pointer due to the Python interface; wrap return value with smart pointer

References alphaLevels, clone(), sgpp::base::Printer::disableStatusPrinting(), sgpp::base::Printer::enableStatusPrinting(), f, sgpp::base::Printer::getInstance(), sgpp::base::Printer::getMutex(), sgpp::base::Printer::isStatusPrintingEnabled(), sgpp::base::MutexType::lock(), m, maximumPoints, maximumValues, minimumPoints, minimumValues, optimizationDomainsLowerBounds, optimizationDomainsUpperBounds, sgpp::base::Printer::printStatusBegin(), sgpp::base::Printer::printStatusEnd(), sgpp::base::Printer::printStatusNewLine(), sgpp::base::Printer::printStatusUpdate(), and sgpp::base::MutexType::unlock().

◆ clone()

virtual void sgpp::optimization::FuzzyExtensionPrinciple::clone ( std::unique_ptr< FuzzyExtensionPrinciple > & clone ) const

pure virtual

Pure virtual method for cloning the fuzzy extension principle.

It should generate a pointer to the cloned object and it's used for parallel computations (the optimizeForSingleAlphaLevel() method might not be thread-safe).

Parameters

[out] clone pointer to cloned object

Implemented in sgpp::optimization::FuzzyExtensionPrincipleViaOptimization, sgpp::optimization::FuzzyExtensionPrincipleViaTransformation, and sgpp::optimization::FuzzyExtensionPrincipleViaVertexMethod.

Referenced by apply(), and sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::FuzzyExtensionPrincipleViaOptimization().

◆ getAlphaLevels()

const base::DataVector & sgpp::optimization::FuzzyExtensionPrinciple::getAlphaLevels ( ) const

Returns: vector of \(\alpha\) levels (after apply call)

References alphaLevels.

◆ getMaximumPoints()

const std::vector< base::DataVector > & sgpp::optimization::FuzzyExtensionPrinciple::getMaximumPoints ( ) const

Returns: vector of maximum points (after apply call)

References maximumPoints.

◆ getMaximumValues()

const base::DataVector & sgpp::optimization::FuzzyExtensionPrinciple::getMaximumValues ( ) const

Returns: vector of maximum function values (after apply call)

References maximumValues.

◆ getMinimumPoints()

const std::vector< base::DataVector > & sgpp::optimization::FuzzyExtensionPrinciple::getMinimumPoints ( ) const

Returns: vector of minimum points (after apply call)

References minimumPoints.

◆ getMinimumValues()

const base::DataVector & sgpp::optimization::FuzzyExtensionPrinciple::getMinimumValues ( ) const

Returns: vector of minimum function values (after apply call)

References minimumValues.

◆ getNumberOfAlphaSegments()

size_t sgpp::optimization::FuzzyExtensionPrinciple::getNumberOfAlphaSegments ( ) const

Returns: number of \(\alpha\) segments

References m.

◆ getOptimizationDomainsLowerBounds()

const std::vector< base::DataVector > & sgpp::optimization::FuzzyExtensionPrinciple::getOptimizationDomainsLowerBounds ( ) const

Returns: vector of lower bounds of input confidence intervals (after apply call)

References optimizationDomainsLowerBounds.

◆ getOptimizationDomainsUpperBounds()

const std::vector< base::DataVector > & sgpp::optimization::FuzzyExtensionPrinciple::getOptimizationDomainsUpperBounds ( ) const

Returns: vector of upper bounds of input confidence intervals (after apply call)

References optimizationDomainsUpperBounds.

◆ optimizeForSingleAlphaLevel()

virtual void sgpp::optimization::FuzzyExtensionPrinciple::optimizeForSingleAlphaLevel	(	size_t	j,
		base::DataVector &	minimumPoint,
		double &	minimumValue,
		base::DataVector &	maximumPoint,
		double &	maximumValue
	)

protectedpure virtual

Pure virtual method for solving the minimization/maximization problem for a single \(\alpha\) level.

Parameters

[in]	j	index of \(\alpha\) level
[out]	minimumPoint	minimum point
[out]	minimumValue	minimum function value
[out]	maximumPoint	maximum point
[out]	maximumValue	maximum function value

Implemented in sgpp::optimization::FuzzyExtensionPrincipleViaOptimization, sgpp::optimization::FuzzyExtensionPrincipleViaTransformation, and sgpp::optimization::FuzzyExtensionPrincipleViaVertexMethod.

◆ prepareApply()

void sgpp::optimization::FuzzyExtensionPrinciple::prepareApply ( )

protectedvirtual

Custom preparation method that is called before the parallelized optimizeForSingleAlphaLevel calls.

Here empty, but can be overridden by subclasses.

Reimplemented in sgpp::optimization::FuzzyExtensionPrincipleViaOptimization, sgpp::optimization::FuzzyExtensionPrincipleViaTransformation, and sgpp::optimization::FuzzyExtensionPrincipleViaVertexMethod.

◆ setNumberOfAlphaSegments()

void sgpp::optimization::FuzzyExtensionPrinciple::setNumberOfAlphaSegments ( size_t numberOfAlphaSegments )

Parameters

numberOfAlphaSegments number of \(\alpha\) segments

References m.

Member Data Documentation

◆ alphaLevels

base::DataVector sgpp::optimization::FuzzyExtensionPrinciple::alphaLevels

protected

number of \(\alpha\) segments

Referenced by apply(), and getAlphaLevels().

◆ DEFAULT_NUMBER_OF_ALPHA_SEGMENTS

const size_t sgpp::optimization::FuzzyExtensionPrinciple::DEFAULT_NUMBER_OF_ALPHA_SEGMENTS = 10

static

default number of \(\alpha\) segments

◆ f

std::unique_ptr<base::ScalarFunction> sgpp::optimization::FuzzyExtensionPrinciple::f

protected

function through which to propagate the uncertainties

◆ m

size_t sgpp::optimization::FuzzyExtensionPrinciple::m

protected

number of \(\alpha\) segments

Referenced by apply(), getNumberOfAlphaSegments(), sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::optimizeForSingleAlphaLevel(), sgpp::optimization::FuzzyExtensionPrincipleViaTransformation::optimizeForSingleAlphaLevel(), sgpp::optimization::FuzzyExtensionPrincipleViaTransformation::prepareApply(), and setNumberOfAlphaSegments().

◆ maximumPoints

std::vector<base::DataVector> sgpp::optimization::FuzzyExtensionPrinciple::maximumPoints

protected

vector of maximum points (after apply call)

Referenced by apply(), getMaximumPoints(), and sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::optimizeForSingleAlphaLevel().

◆ maximumValues

base::DataVector sgpp::optimization::FuzzyExtensionPrinciple::maximumValues

protected

vector of maximum function values (after apply call)

Referenced by apply(), and getMaximumValues().

◆ minimumPoints

std::vector<base::DataVector> sgpp::optimization::FuzzyExtensionPrinciple::minimumPoints

protected

vector of minimum points (after apply call)

Referenced by apply(), getMinimumPoints(), and sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::optimizeForSingleAlphaLevel().

◆ minimumValues

base::DataVector sgpp::optimization::FuzzyExtensionPrinciple::minimumValues

protected

vector of minimum function values (after apply call)

Referenced by apply(), and getMinimumValues().

◆ optimizationDomainsLowerBounds

std::vector<base::DataVector> sgpp::optimization::FuzzyExtensionPrinciple::optimizationDomainsLowerBounds

protected

vector of lower bounds of input confidence intervals (after apply call)

Referenced by apply(), getOptimizationDomainsLowerBounds(), sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::optimizeForSingleAlphaLevel(), sgpp::optimization::FuzzyExtensionPrincipleViaVertexMethod::optimizeForSingleAlphaLevel(), and sgpp::optimization::FuzzyExtensionPrincipleViaTransformation::prepareApply().

◆ optimizationDomainsUpperBounds

std::vector<base::DataVector> sgpp::optimization::FuzzyExtensionPrinciple::optimizationDomainsUpperBounds

protected

vector of upper bounds of input confidence intervals (after apply call)

Referenced by apply(), getOptimizationDomainsUpperBounds(), sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::optimizeForSingleAlphaLevel(), sgpp::optimization::FuzzyExtensionPrincipleViaVertexMethod::optimizeForSingleAlphaLevel(), and sgpp::optimization::FuzzyExtensionPrincipleViaTransformation::prepareApply().

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

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

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ FuzzyExtensionPrinciple() [1/2]

◆ FuzzyExtensionPrinciple() [2/2]

◆ ~FuzzyExtensionPrinciple()

Member Function Documentation

◆ apply()

◆ clone()

◆ getAlphaLevels()

◆ getMaximumPoints()

◆ getMaximumValues()

◆ getMinimumPoints()

◆ getMinimumValues()

◆ getNumberOfAlphaSegments()

◆ getOptimizationDomainsLowerBounds()

◆ getOptimizationDomainsUpperBounds()

◆ optimizeForSingleAlphaLevel()

◆ prepareApply()

◆ setNumberOfAlphaSegments()

Member Data Documentation

◆ alphaLevels

◆ DEFAULT_NUMBER_OF_ALPHA_SEGMENTS

◆ f

◆ m

◆ maximumPoints

◆ maximumValues

◆ minimumPoints

◆ minimumValues

◆ optimizationDomainsLowerBounds

◆ optimizationDomainsUpperBounds