PiShape

PiShape

Bases: Term

Extended term that represents the Pi-shaped membership function.

Equation

\(\mu(x) = h \left(\mbox{SShape}_{a}^{b}(x) \times \mbox{ZShape}_{c}^{d}(x)\right)\)

where

• \(h\): height of the Term
• \(a, b\): bottom left and top left parameters of the PiShape
• \(c, d\): top right and bottom right parameters of the PiShape

related

• fuzzylite.term.SShape
• fuzzylite.term.ZShape

Attributes

bottom_left instance-attribute

bottom_left = bottom_left

bottom_right instance-attribute

bottom_right = bottom_right

top_left instance-attribute

top_left = top_left

top_right instance-attribute

top_right = top_right

Functions

__init__

__init__(
    name: str = "",
    bottom_left: float = nan,
    top_left: float = nan,
    top_right: float = nan,
    bottom_right: float = nan,
    height: float = 1.0,
) -> None

Constructor.

Parameters:

Name	Type	Description	Default
name	str	name of the Term	''
bottom_left	float	bottom-left value of the PiShape	nan
top_left	float	top-left value of the PiShape	nan
top_right	float	top-right value of the PiShape	nan
bottom_right	float	bottom-right value of the PiShape	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	bottom_left top_left top_right bottom_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	\(\mu(x) = h \left(\mbox{SShape}_{a}^{b}(x) \times \mbox{ZShape}_{c}^{d}(x)\right)\)

parameters

parameters() -> str

Return the parameters of the term.

Returns:

Type	Description
str	bottom_left top_left top_right bottom_right [height].