Bell

Bell

Bases: Term

Extended term that represents the generalized bell curve membership function.

Equation

\(\mu(x)=\dfrac{h}{1 + \left(\dfrac{|x-c|}{w}\right)^{2s}}\)

where

• \(h\): height of the Term
• \(c\): center of the Bell
• \(w\): width of the Bell
• \(s\): slope of the Bell

Attributes

center instance-attribute

center = center

slope instance-attribute

slope = slope

width instance-attribute

width = width

Functions

__init__

__init__(name: str = '', center: float = nan, width: float = nan, slope: float = nan, height: float = 1.0) -> None

Constructor.

Parameters:

Name	Type	Description	Default
name	str	name of the Term	''
center	float	center of the Bell	nan
width	float	width of the Bell	nan
slope	float	slope of the Bell	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	center width slope [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	\(\mu(x)=\dfrac{h}{1 + \left(\dfrac{|x-c|}{w}\right)^{2s}}\)

parameters

parameters() -> str

Return the space-separated parameters of the term.

Returns:

Type	Description
str	center width slope [height].