SigmoidProduct

SigmoidProduct

Bases: Term

Extended Term that represents the product of two sigmoid membership functions.

Equation

\(a = \mbox{Sigmoid}_\mbox{left}^\mbox{rise}(x)\)

\(b = \mbox{Sigmoid}_\mbox{right}^\mbox{fall}(x)\)

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

where

• \(h\): height of the Term
• \(\mbox{left}, \mbox{rise}\): inflection and slope of left Sigmoid
• \(\mbox{right}, \mbox{fall}\): inflection and slope of right Sigmoid

Attributes

falling instance-attribute

falling = falling

left instance-attribute

left = left

right instance-attribute

right = right

rising instance-attribute

rising = rising

Functions

__init__

__init__(
    name: str = "",
    left: float = nan,
    rising: float = nan,
    falling: float = nan,
    right: float = nan,
    height: float = 1.0,
) -> None

Constructor.

Parameters:

Name	Type	Description	Default
name	str	name of the Term	''
left	float	inflection of the left Sigmoid	nan
rising	float	slope of the left Sigmoid	nan
falling	float	slope of the right Sigmoid	nan
right	float	inflection of the right Sigmoid	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	left rising falling right [height].	required

membership

membership(x: Scalar) -> Scalar

Computes the membership function evaluated at \(x\).

Parameters:

Name	Type	Description	Default
x	Scalar	scalar	required

Returns:

Type	Description
Scalar	\(\mu(x) = h (a \times b)\)

parameters

parameters() -> str

Return the parameters of the term.

Returns:

Type	Description
str	left rising falling right [height].