Triangle

Triangle

Bases: Term

Basic Term that represents the triangle membership function.

Equation

\(\mu(x)= \begin{cases} 0 & \mbox{if } x < a \vee x > c \cr h & \mbox{if } (x = b) \vee (a=-\infty \wedge x < b) \vee (c=\infty \wedge x > b) \cr h \dfrac{x - a}{b - a} & \mbox{if } a \le x < b \cr h \dfrac{c - x}{c - b} & \mbox{if } b < x \le c \end{cases}\)

where

• \(h\): height of the Term
• \(a\): left vertex of the Triangle
• \(b\): top vertex of the Triangle
• \(c\): right vertex of the Triangle

Attributes

left instance-attribute

left = left

right instance-attribute

right = right

top instance-attribute

top = top

Functions

__init__

__init__(name: str = '', left: float = nan, top: float = nan, right: float = nan, height: float = 1.0) -> None

Constructor.

Parameters:

Name	Type	Description	Default
name	str	name of the Term	''
left	float	first vertex of the Triangle	nan
top	float	second vertex of the Triangle	nan
right	float	third vertex of the Triangle	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 top 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	\(\mu(x)= \begin{cases} 0 & \mbox{if } x < a \vee x > c \cr h & \mbox{if } (x = b) \vee (a=-\infty \wedge x < b) \vee (c=\infty \wedge x > b) \cr h \dfrac{x - a}{b - a} & \mbox{if } a \le x < b \cr h \dfrac{c - x}{c - b} & \mbox{if } b < x \le c \end{cases}\)

parameters

parameters() -> str

Return the parameters of the term.

Returns:

Type	Description
str	left top right [height].