GaussianProduct

GaussianProduct ¶

Bases: Term

Extended term that represents the two-sided gaussian membership function.

Equation

\(a = \begin{cases} \mbox{Gaussian}^{\mu_a}_{\sigma_a}(x) & \mbox{if } x < \mu_a \cr 1.0 & \mbox{otherwise} \cr \end{cases}\)

\(b = \begin{cases} \mbox{Gaussian}^{\mu_b}_{\sigma_b}(x) & \mbox{if } x > \mu_b \cr 1.0 & \mbox{otherwise} \cr \end{cases}\)

\(\mu(x) = h (a \times b)\)

where

\(h\): height of the Term
\(\mu_a, \sigma_a\): mean and standard deviation of the first Gaussian
\(\mu_b, \sigma_b\): mean and standard deviation of the second Gaussian

Attributes¶

mean_a `instance-attribute` ¶

mean_a = mean_a

mean_b `instance-attribute` ¶

mean_b = mean_b

standard_deviation_a `instance-attribute` ¶

standard_deviation_a = standard_deviation_a

standard_deviation_b `instance-attribute` ¶

standard_deviation_b = standard_deviation_b

Functions¶

init ¶

__init__(
    name: str = "",
    mean_a: float = nan,
    standard_deviation_a: float = nan,
    mean_b: float = nan,
    standard_deviation_b: float = nan,
    height: float = 1.0,
) -> None

Constructor.

Parameters:

Name	Type	Description	Default
`name`	`str`	name of the Term	`''`
`mean_a`	`float`	mean of the first Gaussian	`nan`
`standard_deviation_a`	`float`	standard deviation of the first Gaussian	`nan`
`mean_b`	`float`	mean of the second Gaussian	`nan`
`standard_deviation_b`	`float`	standard deviation of the second 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_a standard_deviation_a mean_b standard_deviation_b [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`	\(\mu(x) = h (a \times b)\)

parameters ¶

parameters() -> str

Return the space-separated parameters of the term.

Returns:

Type	Description
`str`	`mean_a standard_deviation_a mean_b standard_deviation_b [height]`.

GaussianProduct