ex_fuzzy.fuzzy_sets.gaussianFS

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

Bases: FS

Gaussian Type-1 Fuzzy Set Implementation.

This class implements a Gaussian fuzzy set with bell-shaped membership function. Gaussian fuzzy sets are characterized by their mean and standard deviation, providing smooth membership transitions ideal for continuous variables.

membership_parameters

[mean, standard_deviation] defining the Gaussian curve

Type:

list

name

Human-readable name for the fuzzy set

Type:

str

universe_size

Size of the universe of discourse

Type:

int

Example

>>> params = [5.0, 1.5]  # mean=5, std=1.5
>>> gauss_fs = gaussianFS(params, "Medium", 10)
>>> membership = gauss_fs.membership(np.array([4.0, 5.0, 6.0]))
>>> print(membership)  # [0.606, 1.0, 0.606]

Note

The membership function follows the formula: μ(x) = exp(-0.5 * ((x - mean) / std)^2)

__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(input)	Computes the Gaussian membership values for input points.
shape()	Returns the shape of the fuzzy set.
type()	Returns the type of the fuzzy set.

membership(input)

Computes the Gaussian membership values for input points.

The membership function implements the Gaussian curve formula using the mean and standard deviation parameters.

Parameters:

input (np.array) – Input values in the fuzzy set domain

Returns:

Membership values in range [0, 1]

Return type:

np.array

Example

>>> gauss_fs = gaussianFS([0, 1], "Zero", 5)
>>> values = gauss_fs.membership(np.array([-1, 0, 1]))
>>> print(values)  # [0.606, 1.0, 0.606]

type()

Returns the type of the fuzzy set.

Returns:

Always returns FUZZY_SETS.t1 for Type-1 fuzzy sets

Return type:

FUZZY_SETS

shape()

Returns the shape of the fuzzy set.

Returns:

Always returns ‘gaussian’

Return type:

str