Concave

Concave

Bases: Term

Edge Term that represents the concave membership function.

Equation

\(\mu(x) = \begin{cases} h \dfrac{e - i} {2e - i - x} & \mbox{if } i \leq e \wedge x < e \mbox{ (increasing concave)} \cr h \dfrac{i - e} {-2e + i + x} & \mbox{if } i > e \wedge x > e \mbox{ (decreasing concave)} \cr h & \mbox{otherwise} \cr \end{cases}\)

where

• \(h\): height of the Term
• \(i\): inflection of the Concave
• \(e\): end of the Concave

Attributes

end instance-attribute

end = end

inflection instance-attribute

inflection = inflection

Functions

__init__

__init__(name: str = '', inflection: float = nan, end: float = nan, height: float = 1.0) -> None

Constructor.

Parameters:

Name	Type	Description	Default
name	str	name of the Term	''
inflection	float	inflection of the Concave	nan
end	float	end of the Concave	nan
height	float	height of the Term	1.0

configure

configure(parameters: str) -> None

Configure the term with the parameters.

Parameters:

Name	Type	Description	Default
parameters	str	inflection end [height].	required

is_monotonic

is_monotonic() -> bool

Return True because the term is monotonic.

Returns:

Type	Description
bool	True

membership

membership(x: Scalar) -> Scalar

Compute the membership function value of \(x\).

Parameters:

Name	Type	Description	Default
x	Scalar	scalar	required

Returns:

Type	Description
Scalar	\(\mu(x) = \begin{cases} h \dfrac{e - i} {2e - i - x} & \mbox{if } i \leq e \wedge x < e \mbox{ (increasing concave)} \cr h \dfrac{i - e} {-2e + i + x} & \mbox{if } i > e \wedge x > e \mbox{ (decreasing concave)} \cr h & \mbox{otherwise} \cr \end{cases}\)

parameters

parameters() -> str

Return the parameters of the term.

Returns:

Type	Description
str	inflection end [height].

tsukamoto

tsukamoto(y: Scalar) -> Scalar

Compute the tsukamoto value of the monotonic term for activation degree \(y\).

Equation

\(y = h \dfrac{e - i} {2e - i - x}\)

\(x = h \dfrac{e-i}{y} + 2e -i\)

Parameters:

Name	Type	Description	Default
y	Scalar	activation degree	required

Returns:

Type	Description
Scalar	\(x = h \dfrac{e-i}{y} + 2e -i\)