Discrete

Discrete

Bases: Term

Basic term that represents a discrete membership function.

Equation

\(\mu(x) = h\dfrac{(y_\max - y_\min)}{(x_\max - x_\min)} (x - x_\min) + y_\min\)

where

• \(h\): height of the Term
• \(x_{\min}, x_{\max}\): lower and upper bounds of \(x\), respectively
• \(y_{\min}, y_{\max}\): membership function values \(\mu(x_{\min})\) and \(\mu(x_{\max})\), respectively

related

• numpy.interp

Warning

The pairs of values in any Discrete term must be sorted in ascending order by the \(x\) coordinate because the membership function is computed using binary search to find the lower and upper bounds of \(x\).

Attributes

Floatable class-attribute instance-attribute

Floatable = Union[SupportsFloat, str]

values instance-attribute

values = values

Functions

__init__

__init__(name: str = '', values: ScalarArray | Sequence[Floatable] | None = None, height: float = 1.0) -> None

Constructor.

Parameters:

Name	Type	Description	Default
name	str	name of the term	''
values	ScalarArray | Sequence[Floatable] | None	2D array of \((x,y)\) pairs	None
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	x1 y1 ... xn yn [height].	required

create staticmethod

create(
    name: str,
    xy: str | Sequence[Floatable] | tuple[Sequence[Floatable], Sequence[Floatable]] | dict[Floatable, Floatable],
    height: float = 1.0,
) -> Discrete

Create a discrete term from the parameters.

Parameters:

Name	Type	Description	Default
name	str	name of the term	required
xy	str | Sequence[Floatable] | tuple[Sequence[Floatable], Sequence[Floatable]] | dict[Floatable, Floatable]	coordinates	required
height	float	height of the term	1.0

Returns:

Type	Description
Discrete	Discrete term.

membership

membership(x: Scalar) -> Scalar

Compute the membership function value of \(x\).

The function uses binary search to find the lower and upper bounds of \(x\) and then linearly interpolates the membership function value between the bounds.

Warning

The pairs of values in any Discrete term must be sorted in ascending order by the \(x\) coordinate because the membership function is computed using binary search to find the lower and upper bounds of \(x\).

Parameters:

Name	Type	Description	Default
x	Scalar	scalar	required

Returns:

Type	Description
Scalar	\(\mu(x) = h\dfrac{(y_\max - y_\min)}{(x_\max - x_\min)} (x - x_\min) + y_\min\)

parameters

parameters() -> str

Return the space-separated parameters of the term.

Returns:

Type	Description
str	x1 y1 ... xn yn [height].

sort

sort() -> None

Sort in ascending order the pairs of values by the \(x\)-coordinate.

to_dict

to_dict() -> dict[float, float]

Return a dictionary of values in the form {x: y}.

Returns:

Type	Description
dict[float, float]	dictionary of values in the form {x: y}.

to_list

to_list() -> list[float]

Return a list of values in the form [x1,y1, ..., xn, yn].

Returns:

Type	Description
list[float]	list of values in the form [x1,y1, ..., xn, yn].

to_xy staticmethod

to_xy(x: Any, y: Any) -> ScalarArray

Create list of values from the parameters.

Parameters:

Name	Type	Description	Default
x	Any	\(x\)-coordinate(s) that can be converted into scalar(s)	required
y	Any	\(y\)-coordinate(s) that can be converted into scalar(s)	required

Returns:

Type	Description
ScalarArray	array of \(n\)-rows and \(2\)-columns \((n,2)\).

Raises:

Type	Description
ValueError	when the shapes of \(x\) and \(y\) are different.

x

x() -> ScalarArray

Return \(x\) coordinates.

Returns:

Type	Description
ScalarArray	\(x\) coordinates.

y

y() -> ScalarArray

Return \(y\) coordinates.

Returns:

Type	Description
ScalarArray	\(y\) coordinates.