Defuzzifier

Bisector

Bases: IntegralDefuzzifier

Integral defuzzifier that computes the bisector of a fuzzy set.

related

• fuzzylite.defuzzifier.Defuzzifier
• fuzzylite.defuzzifier.IntegralDefuzzifier
• fuzzylite.defuzzifier.Centroid

Functions

defuzzify

defuzzify(term: Term, minimum: float, maximum: float) -> Scalar

Compute the bisector of a fuzzy set, that is, the x-coordinate such that the area to its left is approximately equal to the area to its right.

The defuzzification process integrates over the fuzzy set using the given range. The integration algorithm is the midpoint rectangle method (https://en.wikipedia.org/wiki/Rectangle_method).

Parameters:

Name	Type	Description	Default
term	Term	fuzzy set to defuzzify	required
minimum	float	value to start defuzzification	required
maximum	float	value to end defuzzification	required

Returns:

Type	Description
Scalar	\(x\)-coordinate of the bisector of the fuzzy set

Centroid

Bases: IntegralDefuzzifier

Integral defuzzifier that computes the centroid of a fuzzy set.

related

• fuzzylite.defuzzifier.Defuzzifier
• fuzzylite.defuzzifier.IntegralDefuzzifier
• fuzzylite.defuzzifier.Bisector

Functions

defuzzify

defuzzify(term: Term, minimum: float, maximum: float) -> Scalar

Compute the centroid of a fuzzy set.

The defuzzification process integrates over the fuzzy set using the given range. The integration algorithm is the midpoint rectangle method (https://en.wikipedia.org/wiki/Rectangle_method).

Parameters:

Name	Type	Description	Default
term	Term	fuzzy set to defuzzify	required
minimum	float	value to start defuzzification	required
maximum	float	value to end defuzzification	required

Returns:

Type	Description
Scalar	\(x\)-coordinate of the centroid of the fuzzy set

Defuzzifier

Bases: ABC

Abstract class for defuzzifiers.

related

• fuzzylite.defuzzifier.IntegralDefuzzifier
  • fuzzylite.defuzzifier.Bisector
  • fuzzylite.defuzzifier.Centroid
  • fuzzylite.defuzzifier.LargestOfMaximum
  • fuzzylite.defuzzifier.MeanOfMaximum
  • fuzzylite.defuzzifier.SmallestOfMaximum
• fuzzylite.defuzzifier.WeightedDefuzzifier
  • fuzzylite.defuzzifier.WeightedAverage
  • fuzzylite.defuzzifier.WeightedSum
• fuzzylite.variable.OutputVariable
• fuzzylite.term.Aggregated
• fuzzylite.term.Activated

Functions

__repr__

__repr__() -> str

Return the code to construct the defuzzifier in Python.

Returns:

Type	Description
str	code to construct the defuzzifier in Python.

__str__

__str__() -> str

Return the code to construct the defuzzifier in the FuzzyLite Language.

Returns:

Type	Description
str	code to construct the defuzzifier in the FuzzyLite Language.

configure

configure(parameters: str) -> None

Configure the defuzzifier with the parameters.

Parameters:

Name	Type	Description	Default
parameters	str	space-separated parameter values	required

defuzzify abstractmethod

defuzzify(term: Term, minimum: float, maximum: float) -> Scalar

Defuzzify the term using the range [minimum,maximum].

Parameters:

Name	Type	Description	Default
term	Term	term to defuzzify, typically an Aggregated term	required
minimum	float	minimum value of the range	required
maximum	float	maximum value of the range	required

Returns:

Type	Description
Scalar	defuzzified value of the term.

parameters

parameters() -> str

Return the space-separated parameters of the defuzzifier.

Returns:

Type	Description
str	space-separated parameters of the defuzzifier.

IntegralDefuzzifier

Bases: Defuzzifier

Abstract class for defuzzifiers that integrate over the fuzzy set.

related

• fuzzylite.defuzzifier.Defuzzifier
• fuzzylite.defuzzifier.Bisector
• fuzzylite.defuzzifier.Centroid
• fuzzylite.defuzzifier.LargestOfMaximum
• fuzzylite.defuzzifier.MeanOfMaximum
• fuzzylite.defuzzifier.SmallestOfMaximum

Attributes

default_resolution class-attribute instance-attribute

default_resolution: Final[int] = 1000

resolution instance-attribute

resolution = resolution or default_resolution

Functions

__init__

__init__(resolution: int | None = None) -> None

Constructor.

Parameters:

Name	Type	Description	Default
resolution	int | None	number of divisions to discretize the range and compute the area under the curve.	None

__repr__

__repr__() -> str

Return the code to construct the defuzzifier in Python.

Returns:

Type	Description
str	code to construct the defuzzifier in Python.

configure

configure(parameters: str) -> None

Configure the defuzzifier with the parameters.

Parameters:

Name	Type	Description	Default
parameters	str	list of space-separated parameter values	required

defuzzify abstractmethod

defuzzify(term: Term, minimum: float, maximum: float) -> Scalar

Implement the defuzzification of the term using the given range.

Parameters:

Name	Type	Description	Default
term	Term	term to defuzzify	required
minimum	float	value to start defuzzification	required
maximum	float	value to end defuzzification	required

Returns:

Type	Description
Scalar	defuzzified value.

parameters

parameters() -> str

Return the parameters to configure the defuzzifier.

Returns:

Type	Description
str	parameters to configure the defuzzifier.

LargestOfMaximum

Bases: IntegralDefuzzifier

Integral defuzzifier that computes the largest value of the maximum membership function of a fuzzy set.

related

• fuzzylite.defuzzifier.Defuzzifier
• fuzzylite.defuzzifier.IntegralDefuzzifier
• fuzzylite.defuzzifier.MeanOfMaximum
• fuzzylite.defuzzifier.SmallestOfMaximum

Functions

defuzzify

defuzzify(term: Term, minimum: float, maximum: float) -> Scalar

Compute the largest value of the maximum membership function of a fuzzy set.

The defuzzification process integrates over the fuzzy set using the given range. The integration algorithm is the midpoint rectangle method (https://en.wikipedia.org/wiki/Rectangle_method).

Parameters:

Name	Type	Description	Default
term	Term	fuzzy set to defuzzify	required
minimum	float	value to start defuzzification	required
maximum	float	value to end defuzzification	required

Returns:

Type	Description
Scalar	largest \(x\)-coordinate of the maximum membership function value in the fuzzy set

MeanOfMaximum

Bases: IntegralDefuzzifier

Integral defuzzifier that computes the mean value of the maximum membership function of a fuzzy set.

related

• fuzzylite.defuzzifier.Defuzzifier
• fuzzylite.defuzzifier.IntegralDefuzzifier
• fuzzylite.defuzzifier.SmallestOfMaximum
• fuzzylite.defuzzifier.LargestOfMaximum

Functions

defuzzify

defuzzify(term: Term, minimum: float, maximum: float) -> Scalar

Compute the mean value of the maximum membership function of a fuzzy set.

The defuzzification process integrates over the fuzzy set using the given range. The integration algorithm is the midpoint rectangle method (https://en.wikipedia.org/wiki/Rectangle_method).

Parameters:

Name	Type	Description	Default
term	Term	fuzzy set to defuzzify	required
minimum	float	value to start defuzzification	required
maximum	float	value to end defuzzification	required

Returns:

Type	Description
Scalar	mean \(x\)-coordinate of the maximum membership function value in the fuzzy set

SmallestOfMaximum

Bases: IntegralDefuzzifier

Integral defuzzifier that computes the smallest value of the maximum membership function of a fuzzy set.

related

• fuzzylite.defuzzifier.Defuzzifier
• fuzzylite.defuzzifier.IntegralDefuzzifier
• fuzzylite.defuzzifier.MeanOfMaximum
• fuzzylite.defuzzifier.LargestOfMaximum

Functions

defuzzify

defuzzify(term: Term, minimum: float, maximum: float) -> Scalar

Compute the smallest value of the maximum membership function in the fuzzy set.

The defuzzification process integrates over the fuzzy set using the given range. The integration algorithm is the midpoint rectangle method (https://en.wikipedia.org/wiki/Rectangle_method).

Parameters:

Name	Type	Description	Default
term	Term	fuzzy set to defuzzify	required
minimum	float	value to start defuzzification	required
maximum	float	value to end defuzzification	required

Returns:

Type	Description
Scalar	smallest \(x\)-coordinate of the maximum membership function value in the fuzzy set

WeightedAverage

Bases: WeightedDefuzzifier

Weighted defuzzifier that computes the weighted average of a fuzzy set represented by an Aggregated term.

related

• fuzzylite.defuzzifier.Defuzzifier
• fuzzylite.defuzzifier.WeightedDefuzzifier
• fuzzylite.defuzzifier.WeightedSum
• fuzzylite.term.Aggregated

Functions

defuzzify

defuzzify(term: Term, minimum: float = nan, maximum: float = nan) -> Scalar

Computes the weighted average of the fuzzy set.

The fuzzy set is represented by an Aggregated Term as \(y = \sum_i{w_iz_i}\), where \(w_i\) is the activation degree of term \(i\), and \(z_i = \mu_i(w_i)\).

In Takagi-Sugeno controllers, the membership function \(\mu_i(w_i)\) is generally a Constant, Linear, or Function term, which typically disregards the \(w_i\) value.

Warning

From version 8, the aggregation operator is used to aggregate multiple activations of the same term.

In previous versions, the implication and aggregation operators are not used for weighted defuzzification.

Parameters:

Name	Type	Description	Default
term	Term	term to defuzzify	required
minimum	float	irrelevant	nan
maximum	float	irrelevant	nan

Returns:

Type	Description
Scalar	weighted average of the fuzzy set

WeightedDefuzzifier

Bases: Defuzzifier

Abstract class for defuzzifiers that compute a weighted function on the fuzzy set.

related

• fuzzylite.defuzzifier.Defuzzifier
• fuzzylite.defuzzifier.WeightedAverage
• fuzzylite.defuzzifier.WeightedSum

Attributes

type instance-attribute

type = Type[type]

Classes

Type

Bases: Enum

Type of the weighted defuzzifier based on the terms in the fuzzy set.

• Automatic: Automatically inferred from the terms
• TakagiSugeno: Manually set to TakagiSugeno (or Inverse Tsukamoto)
• Tsukamoto: Manually set to Tsukamoto

Attributes

Automatic class-attribute instance-attribute

Automatic = auto()

TakagiSugeno class-attribute instance-attribute

TakagiSugeno = auto()

Tsukamoto class-attribute instance-attribute

Tsukamoto = auto()

Functions

__repr__

__repr__() -> str

Return the code to identify the type of defuzzifier in Python.

Returns:

Type	Description
str	code to identify the type of defuzzifier in Python.

Functions

__init__

__init__(type: str | Type = Automatic) -> None

Constructor.

Parameters:

Name	Type	Description	Default
type	str | Type	name or type of the weighted defuzzifier.	Automatic

__repr__

__repr__() -> str

Return the code to construct the defuzzifier in Python.

Returns:

Type	Description
str	code to construct the defuzzifier in Python.

configure

configure(parameters: str) -> None

Configure the defuzzifier with the parameters.

Parameters:

Name	Type	Description	Default
parameters	str	list of space-separated parameter values	required

defuzzify abstractmethod

defuzzify(term: Term, minimum: float = nan, maximum: float = nan) -> Scalar

Implement the defuzzification of the term.

Warning

From version 8, the aggregation operator is used to aggregate multiple activations of the same term.

In previous versions, the implication and aggregation operators are not used for weighted defuzzification.

Parameters:

Name	Type	Description	Default
term	Term	term to defuzzify	required
minimum	float	irrelevant	nan
maximum	float	irrelevant	nan

Returns:

Type	Description
Scalar	defuzzified value

infer_type classmethod

infer_type(component: Term | Variable) -> Type

Infer the type of the defuzzifier based on the component.

Parameters:

Name	Type	Description	Default
component	Term | Variable	term or variable to infer the type for	required

Returns:

Type	Description
Type	inferred type of the defuzzifier based on the component.

parameters

parameters() -> str

Return the parameters to configure the defuzzifier.

Returns:

Type	Description
str	parameters to configure the defuzzifier.

WeightedSum

Bases: WeightedDefuzzifier

Weighted defuzzifier that computes the weighted sum of a fuzzy set represented by an Aggregated term.

related

• fuzzylite.defuzzifier.Defuzzifier
• fuzzylite.defuzzifier.WeightedDefuzzifier
• fuzzylite.defuzzifier.WeightedAverage
• fuzzylite.term.Aggregated

Functions

defuzzify

defuzzify(term: Term, minimum: float = nan, maximum: float = nan) -> Scalar

Computes the weighted sum of the fuzzy set.

The fuzzy set is represented by Aggregated term as \(y = \sum_i{w_iz_i}\), where \(w_i\) is the activation degree of term \(i\), and \(z_i = \mu_i(w_i)\).

In Takagi-Sugeno controllers, the membership function \(\mu_i(w_i)\) is generally a Constant, Linear, or Function term, which typically disregards the \(w_i\) value.

Warning

From version 8, the aggregation operator is used to aggregate multiple activations of the same term.

In previous versions, the implication and aggregation operators are not used for weighted defuzzification.

Parameters:

Name	Type	Description	Default
term	Term	term to defuzzify	required
minimum	float	irrelevant	nan
maximum	float	irrelevant	nan

Returns:

Type	Description
Scalar	weighted sum of the fuzzy set