Hedge

Any ¶

Bases: Hedge

Special hedge that always returns 1.0.

The antecedent of a rule considers Any to be a syntactically special hedge because it is not followed by a term (e.g., if Variable is any then... vs if Variable is very term then...)

The hedge is useful for better documenting rules.

hedge ¶

hedge(x: Scalar) -> Scalar

Return scalar of same shape of x filled with 1.0.

Parameters:

Name	Type	Description	Default
`x`	`Scalar`	irrelevant except for its shape	required

Returns:

Type	Description
`Scalar`	\(h(x)=1.0\)

Extremely ¶

Bases: Hedge

Hedge that modifies the membership function value of a term as follows.

Equation

\(h(x) = \begin{cases} 2x^2 & \mbox{if } x \le 0.5 \cr 1-2(1-x)^2 & \mbox{otherwise} \cr \end{cases}\)

hedge ¶

hedge(x: Scalar) -> Scalar

Compute \(\text{Extremely}(x)\).

Parameters:

Name	Type	Description	Default
`x`	`Scalar`	membership function value	required

Returns:

Type	Description
`Scalar`	\(h(x) = \begin{cases} 2x^2 & \mbox{if } x \le 0.5 \cr 1-2(1-x)^2 & \mbox{otherwise} \cr \end{cases}\)

Hedge ¶

Bases: ABC

Abstract class for hedges.

Hedges are used in the antecedent and consequent of a rule to modify the membership function of the term it precedes.

The hedges in the library can be ordered based on the difference between the membership function \(\mu(x)\) and its hedge \(h(\mu(x))\) as follows (from most similar to least): Seldom \(<\) Somewhat \(<\) Very \(<\) Extremely \(<\) Not \(<\) Any

`term`	Seldom	Somewhat	Very	Extremely	Not	Any
fuzzylite.term.Rectangle	fuzzylite.hedge.Seldom fuzzylite.term.Rectangle	fuzzylite.hedge.Somewhat fuzzylite.term.Rectangle	fuzzylite.hedge.Very fuzzylite.term.Rectangle	fuzzylite.hedge.Extremely fuzzylite.term.Rectangle	fuzzylite.hedge.Not fuzzylite.term.Rectangle	fuzzylite.hedge.Any fuzzylite.term.Rectangle

fuzzylite.term.SemiEllipse	fuzzylite.hedge.Seldom fuzzylite.term.SemiEllipse	fuzzylite.hedge.Somewhat fuzzylite.term.SemiEllipse	fuzzylite.hedge.Very fuzzylite.term.SemiEllipse	fuzzylite.hedge.Extremely fuzzylite.term.SemiEllipse	fuzzylite.hedge.Not fuzzylite.term.SemiEllipse	fuzzylite.hedge.Any fuzzylite.term.SemiEllipse

fuzzylite.term.Triangle	fuzzylite.hedge.Seldom fuzzylite.term.Triangle	fuzzylite.hedge.Somewhat fuzzylite.term.Triangle	fuzzylite.hedge.Very fuzzylite.term.Triangle	fuzzylite.hedge.Extremely fuzzylite.term.Triangle	fuzzylite.hedge.Not fuzzylite.term.Triangle	fuzzylite.hedge.Any fuzzylite.term.Triangle

fuzzylite.term.Trapezoid	fuzzylite.hedge.Seldom fuzzylite.term.Trapezoid	fuzzylite.hedge.Somewhat fuzzylite.term.Trapezoid	fuzzylite.hedge.Very fuzzylite.term.Trapezoid	fuzzylite.hedge.Extremely fuzzylite.term.Trapezoid	fuzzylite.hedge.Not fuzzylite.term.Trapezoid	fuzzylite.hedge.Any fuzzylite.term.Trapezoid

fuzzylite.term.Discrete	fuzzylite.hedge.Seldom fuzzylite.term.Discrete	fuzzylite.hedge.Somewhat fuzzylite.term.Discrete	fuzzylite.hedge.Very fuzzylite.term.Discrete	fuzzylite.hedge.Extremely fuzzylite.term.Discrete	fuzzylite.hedge.Not fuzzylite.term.Discrete	fuzzylite.hedge.Any fuzzylite.term.Discrete

fuzzylite.term.Bell	fuzzylite.hedge.Seldom fuzzylite.term.Bell	fuzzylite.hedge.Somewhat fuzzylite.term.Bell	fuzzylite.hedge.Very fuzzylite.term.Bell	fuzzylite.hedge.Extremely fuzzylite.term.Bell	fuzzylite.hedge.Not fuzzylite.term.Bell	fuzzylite.hedge.Any fuzzylite.term.Bell

fuzzylite.term.Cosine	fuzzylite.hedge.Seldom fuzzylite.term.Cosine	fuzzylite.hedge.Somewhat fuzzylite.term.Cosine	fuzzylite.hedge.Very fuzzylite.term.Cosine	fuzzylite.hedge.Extremely fuzzylite.term.Cosine	fuzzylite.hedge.Not fuzzylite.term.Cosine	fuzzylite.hedge.Any fuzzylite.term.Cosine

fuzzylite.term.Gaussian	fuzzylite.hedge.Seldom fuzzylite.term.Gaussian	fuzzylite.hedge.Somewhat fuzzylite.term.Gaussian	fuzzylite.hedge.Very fuzzylite.term.Gaussian	fuzzylite.hedge.Extremely fuzzylite.term.Gaussian	fuzzylite.hedge.Not fuzzylite.term.Gaussian	fuzzylite.hedge.Any fuzzylite.term.Gaussian

fuzzylite.term.GaussianProduct	fuzzylite.hedge.Seldom fuzzylite.term.GaussianProduct	fuzzylite.hedge.Somewhat fuzzylite.term.GaussianProduct	fuzzylite.hedge.Very fuzzylite.term.GaussianProduct	fuzzylite.hedge.Extremely fuzzylite.term.GaussianProduct	fuzzylite.hedge.Not fuzzylite.term.GaussianProduct	fuzzylite.hedge.Any fuzzylite.term.GaussianProduct

fuzzylite.term.PiShape	fuzzylite.hedge.Seldom fuzzylite.term.PiShape	fuzzylite.hedge.Somewhat fuzzylite.term.PiShape	fuzzylite.hedge.Very fuzzylite.term.PiShape	fuzzylite.hedge.Extremely fuzzylite.term.PiShape	fuzzylite.hedge.Not fuzzylite.term.PiShape	fuzzylite.hedge.Any fuzzylite.term.PiShape

fuzzylite.term.SigmoidDifference	fuzzylite.hedge.Seldom fuzzylite.term.SigmoidDifference	fuzzylite.hedge.Somewhat fuzzylite.term.SigmoidDifference	fuzzylite.hedge.Very fuzzylite.term.SigmoidDifference	fuzzylite.hedge.Extremely fuzzylite.term.SigmoidDifference	fuzzylite.hedge.Not fuzzylite.term.SigmoidDifference	fuzzylite.hedge.Any fuzzylite.term.SigmoidDifference

fuzzylite.term.SigmoidProduct	fuzzylite.hedge.Seldom fuzzylite.term.SigmoidProduct	fuzzylite.hedge.Somewhat fuzzylite.term.SigmoidProduct	fuzzylite.hedge.Very fuzzylite.term.SigmoidProduct	fuzzylite.hedge.Extremely fuzzylite.term.SigmoidProduct	fuzzylite.hedge.Not fuzzylite.term.SigmoidProduct	fuzzylite.hedge.Any fuzzylite.term.SigmoidProduct

fuzzylite.term.Spike	fuzzylite.hedge.Seldom fuzzylite.term.Spike	fuzzylite.hedge.Somewhat fuzzylite.term.Spike	fuzzylite.hedge.Very fuzzylite.term.Spike	fuzzylite.hedge.Extremely fuzzylite.term.Spike	fuzzylite.hedge.Not fuzzylite.term.Spike	fuzzylite.hedge.Any fuzzylite.term.Spike

fuzzylite.term.Arc	fuzzylite.hedge.Seldom fuzzylite.term.Arc	fuzzylite.hedge.Somewhat fuzzylite.term.Arc	fuzzylite.hedge.Very fuzzylite.term.Arc	fuzzylite.hedge.Extremely fuzzylite.term.Arc	fuzzylite.hedge.Not fuzzylite.term.Arc	fuzzylite.hedge.Any fuzzylite.term.Arc

fuzzylite.term.Binary	fuzzylite.hedge.Seldom fuzzylite.term.Binary	fuzzylite.hedge.Somewhat fuzzylite.term.Binary	fuzzylite.hedge.Very fuzzylite.term.Binary	fuzzylite.hedge.Extremely fuzzylite.term.Binary	fuzzylite.hedge.Not fuzzylite.term.Binary	fuzzylite.hedge.Any fuzzylite.term.Binary

fuzzylite.term.Concave	fuzzylite.hedge.Seldom fuzzylite.term.Concave	fuzzylite.hedge.Somewhat fuzzylite.term.Concave	fuzzylite.hedge.Very fuzzylite.term.Concave	fuzzylite.hedge.Extremely fuzzylite.term.Concave	fuzzylite.hedge.Not fuzzylite.term.Concave	fuzzylite.hedge.Any fuzzylite.term.Concave

fuzzylite.term.Ramp	fuzzylite.hedge.Seldom fuzzylite.term.Ramp	fuzzylite.hedge.Somewhat fuzzylite.term.Ramp	fuzzylite.hedge.Very fuzzylite.term.Ramp	fuzzylite.hedge.Extremely fuzzylite.term.Ramp	fuzzylite.hedge.Not fuzzylite.term.Ramp	fuzzylite.hedge.Any fuzzylite.term.Ramp

fuzzylite.term.Sigmoid	fuzzylite.hedge.Seldom fuzzylite.term.Sigmoid	fuzzylite.hedge.Somewhat fuzzylite.term.Sigmoid	fuzzylite.hedge.Very fuzzylite.term.Sigmoid	fuzzylite.hedge.Extremely fuzzylite.term.Sigmoid	fuzzylite.hedge.Not fuzzylite.term.Sigmoid	fuzzylite.hedge.Any fuzzylite.term.Sigmoid

fuzzylite.term.SShape - fuzzylite.term.ZShape	fuzzylite.hedge.Seldom fuzzylite.term.SShape - fuzzylite.hedge.Seldom fuzzylite.term.ZShape][]	fuzzylite.hedge.Somewhat fuzzylite.term.SShape - fuzzylite.hedge.Somewhat fuzzylite.term.ZShape	fuzzylite.hedge.Very fuzzylite.term.SShape - fuzzylite.hedge.Very fuzzylite.term.ZShape	fuzzylite.hedge.Extremely fuzzylite.term.SShape - fuzzylite.hedge.Extremely fuzzylite.term.ZShape	fuzzylite.hedge.Not fuzzylite.term.SShape - fuzzylite.hedge.Not fuzzylite.term.ZShape	fuzzylite.hedge.Any fuzzylite.term.SShape - fuzzylite.hedge.Any fuzzylite.term.ZShape

fuzzylite.term.SShape	fuzzylite.hedge.Seldom fuzzylite.term.SShape	fuzzylite.hedge.Somewhat fuzzylite.term.SShape	fuzzylite.hedge.Very fuzzylite.term.SShape	fuzzylite.hedge.Extremely fuzzylite.term.SShape	fuzzylite.hedge.Not fuzzylite.term.SShape	fuzzylite.hedge.Any fuzzylite.term.SShape

fuzzylite.term.ZShape	fuzzylite.hedge.Seldom fuzzylite.term.ZShape	fuzzylite.hedge.Somewhat fuzzylite.term.ZShape	fuzzylite.hedge.Very fuzzylite.term.ZShape	fuzzylite.hedge.Extremely fuzzylite.term.ZShape	fuzzylite.hedge.Not fuzzylite.term.ZShape	fuzzylite.hedge.Any fuzzylite.term.ZShape

name `property` ¶

name: str

Return the name of the hedge.

Returns:

Type	Description
`str`	name of the hedge.

Functions¶

repr ¶

__repr__() -> str

Return the Python code to construct the hedge.

Returns:

Type	Description
`str`	Python code to construct the hedge.

str ¶

__str__() -> str

Return the name of the hedge.

Returns:

Type	Description
`str`	name of the hedge.

hedge `abstractmethod` ¶

hedge(x: Scalar) -> Scalar

Implement the hedge for the membership function value \(x\).

Parameters:

Name	Type	Description	Default
`x`	`Scalar`	membership function value	required

Returns:

Type	Description
`Scalar`	hedge of \(x\).

HedgeFunction ¶

Bases: Hedge

Hedge that modifies the membership function value of a term according to the term Function.

This hedge is not registered with the HedgeFactory because the Function cannot be easily configured.

fuzzylite.hedge.Hedge
fuzzylite.hedge.HedgeLambda
fuzzylite.factory.HedgeFactory

Attributes¶

function `instance-attribute` ¶

function = function

name `property` ¶

name: str

Get the name of the hedge.

Returns:

Type	Description
`str`	name of the hedge

Functions¶

init ¶

__init__(function: Function) -> None

Constructor.

Parameters:

Name	Type	Description	Default
`function`	`Function`	function \(f\).	required

hedge ¶

hedge(x: Scalar) -> Scalar

Compute \(f(x)\).

Parameters:

Name	Type	Description	Default
`x`	`Scalar`	membership function value	required

Returns:

Type	Description
`Scalar`	\(h(x) = f(x)\)

HedgeLambda ¶

Bases: Hedge

Hedge that modifies the membership function value of a term according to a \(\lambda\) function.

This hedge is not registered with the HedgeFactory because the \(\lambda\) function cannot be easily configured.

fuzzylite.hedge.Hedge
fuzzylite.hedge.HedgeFunction
fuzzylite.factory.HedgeFactory

Attributes¶

_name `instance-attribute` ¶

_name = name

function `instance-attribute` ¶

function = function

name `property` ¶

name: str

Get the name of the hedge.

Returns:

Type	Description
`str`	name of the hedge

Functions¶

init ¶

__init__(name: str, function: Callable[[Scalar], Scalar]) -> None

Constructor.

Parameters:

Name	Type	Description	Default
`name`	`str`	name of the hedge	required
`function`	`Callable[[Scalar], Scalar]`	\(\lambda\) function.	required

hedge ¶

hedge(x: Scalar) -> Scalar

Compute \(\lambda(x)\).

Parameters:

Name	Type	Description	Default
`x`	`Scalar`	membership function value	required

Returns:

Type	Description
`Scalar`	\(h(x) = \lambda(x)\)

Not ¶

Bases: Hedge

Hedge that modifies the membership function value of a term by.

Equation

\(h(x) = 1-x\)

hedge ¶

hedge(x: Scalar) -> Scalar

Compute \(\text{Not}(x)\).

Parameters:

Name	Type	Description	Default
`x`	`Scalar`	membership function value	required

Returns:

Type	Description
`Scalar`	\(h(x) = 1-x\)

Seldom ¶

Bases: Hedge

Hedge that modifies the membership function value of a term as follows.

Equation

\(h(x) = \begin{cases} \sqrt{\dfrac{x}{2}} & \mbox{if } x \le 0.5 \cr 1-\sqrt{\dfrac{1-x}{2}} & \mbox{otherwise} \end{cases}\)

hedge ¶

hedge(x: Scalar) -> Scalar

Compute \(\text{Seldom(x)}\).

Parameters:

Name	Type	Description	Default
`x`	`Scalar`	membership function value	required

Returns:

Type	Description
`Scalar`	\(h(x) = \begin{cases} \sqrt{\dfrac{x}{2}} & \mbox{if \(x \le 0.5\)} \cr 1-\sqrt{\dfrac{(1-x)}{2}} & \mbox{otherwise}\cr \end{cases}\)

Somewhat ¶

Bases: Hedge

Hedge that modifies the membership function value of a term by.

Equation

\(h(x) = \sqrt{x}\)

hedge ¶

hedge(x: Scalar) -> Scalar

Compute \(\text{Somewhat}(x)\).

Parameters:

Name	Type	Description	Default
`x`	`Scalar`	membership function value	required

Returns:

Type	Description
`Scalar`	\(h(x) = \sqrt{x}\)

Very ¶

Bases: Hedge

Hedge that modifies the membership function value of a term by.

Equation

\(h(x) = x^2\)

hedge ¶

hedge(x: Scalar) -> Scalar

Compute \(\text{Very}(x)\).

Parameters:

Name	Type	Description	Default
`x`	`Scalar`	membership function value	required

Returns:

Type	Description
`Scalar`	\(h(x) = x^2\)

Hedge

Any ¶

Functions¶

hedge ¶

Extremely ¶

Functions¶

hedge ¶

Hedge ¶

Attributes¶

name property ¶

Functions¶

__repr__ ¶

__str__ ¶

hedge abstractmethod ¶

HedgeFunction ¶

Attributes¶

function instance-attribute ¶

name property ¶

Functions¶

__init__ ¶

hedge ¶

HedgeLambda ¶

Attributes¶

_name instance-attribute ¶

function instance-attribute ¶

name property ¶

Functions¶

__init__ ¶

hedge ¶

Not ¶

Functions¶

hedge ¶

Seldom ¶

Functions¶

hedge ¶

Somewhat ¶

Functions¶

hedge ¶

Very ¶

Functions¶

hedge ¶

name `property` ¶

repr ¶

str ¶

hedge `abstractmethod` ¶

function `instance-attribute` ¶

name `property` ¶

init ¶

_name `instance-attribute` ¶

function `instance-attribute` ¶

name `property` ¶

init ¶