Gaussian

Gaussian

Bases: Term

Extended term that represents the gaussian curve membership function.

Equation

\(\mu(x) = h \exp\left(-\dfrac{(x-\mu)^2}{2\sigma^2}\right)\)

where

• \(h\): height of the Term
• \(\mu\): mean of the Gaussian
• \(\sigma\): standard deviation of the Gaussian

Attributes

mean instance-attribute

mean = mean

standard_deviation instance-attribute

standard_deviation = standard_deviation

Functions

__init__

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

Constructor.

Parameters:

Name	Type	Description	Default
name	str	name of the Term	''
mean	float	mean of the Gaussian	nan
standard_deviation	float	standard deviation of the Gaussian	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	mean standard_deviation [height].	required

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	\(\mu(x) = h \exp\left(-\dfrac{(x-\mu)^2}{2\sigma^2}\right)\)

parameters

parameters() -> str

Return the space-separated parameters of the term.

Returns:

Type	Description
str	mean standard_deviation [height].