ex_fuzzy.fuzzy_sets.FS

class ex_fuzzy.fuzzy_sets.FS(name, membership_parameters, domain)

Bases: object

Base class for Type-1 fuzzy sets (Zadeh fuzzy sets).

This class implements the fundamental Type-1 fuzzy set with crisp membership functions. It serves as the base class for more specialized fuzzy set types like triangular, gaussian, and categorical fuzzy sets.

name

The linguistic name of the fuzzy set (e.g., “low”, “medium”, “high”)

Type:

str

membership_parameters

Parameters defining the membership function

Type:

list[float]

domain

Two-element list defining the universe of discourse [min, max]

Type:

list[float]

Example

>>> fs = FS("medium", [1, 2, 3, 4], [0, 5])  # Trapezoidal fuzzy set
>>> membership = fs.membership(2.5)
>>> print(membership)  # Should be 1.0 (fully in the set)

Note

This class uses trapezoidal membership functions by default. For other shapes, use specialized subclasses like gaussianFS or triangularFS.

__init__(name, membership_parameters, domain)

Initialize a Type-1 fuzzy set.

Parameters:

• name (str) – Linguistic name for the fuzzy set

• membership_parameters (list[float]) – Four parameters [a, b, c, d] defining the trapezoidal membership function where: - a: left foot (membership starts rising from 0) - b: left shoulder (membership reaches 1.0) - c: right shoulder (membership starts falling from 1.0) - d: right foot (membership reaches 0)

• domain (list[float]) – Two-element list [min, max] defining the universe of discourse for this fuzzy set

Example

>>> fs = FS("medium", [2, 3, 7, 8], [0, 10])
>>> # Creates a trapezoidal set: rises from 2-3, flat 3-7, falls 7-8

Methods

__init__(name, membership_parameters, domain)	Initialize a Type-1 fuzzy set.
membership(x)	Compute membership degrees for input values.
shape()	Returns the shape of the fuzzy set.
type()	Return the fuzzy set type identifier.

__init__(name, membership_parameters, domain)

Initialize a Type-1 fuzzy set.

Parameters:

• name (str) – Linguistic name for the fuzzy set

• membership_parameters (list[float]) – Four parameters [a, b, c, d] defining the trapezoidal membership function where: - a: left foot (membership starts rising from 0) - b: left shoulder (membership reaches 1.0) - c: right shoulder (membership starts falling from 1.0) - d: right foot (membership reaches 0)

• domain (list[float]) – Two-element list [min, max] defining the universe of discourse for this fuzzy set

Example

>>> fs = FS("medium", [2, 3, 7, 8], [0, 10])
>>> # Creates a trapezoidal set: rises from 2-3, flat 3-7, falls 7-8

membership(x)

Compute membership degrees for input values.

This method calculates the membership degree(s) for the given input value(s) using the trapezoidal membership function defined by this fuzzy set’s parameters.

Parameters:

x (np.array) – Input value(s) for which to compute membership degrees. Can be a single value, list, or numpy array.

Returns:

Membership degree(s) in the range [0, 1]. Shape matches input.

Return type:

np.array

Example

>>> fs = FS("medium", [2, 3, 7, 8], [0, 10])
>>> print(fs.membership(5))    # 1.0 (in flat region)
>>> print(fs.membership(2.5)) # 0.5 (on rising slope)
>>> print(fs.membership([1, 5, 9])) # [0.0, 1.0, 0.0]

type()

Return the fuzzy set type identifier.

Returns:

The type identifier (FUZZY_SETS.t1 for Type-1 fuzzy sets)

Return type:

FUZZY_SETS

__call__(x)

Calling the Fuzzy set returns its membership.

Parameters:

x (array) – input values in the fuzzy set referencial domain.

Returns:

membership of the fuzzy set.

Return type:

array

__str__()

Returns the name of the fuzzy set, its type and its parameters.

Returns:

string.

Return type:

str

shape()

Returns the shape of the fuzzy set.

Returns:

string.

Return type:

str