ex_fuzzy.fuzzy_sets.gaussianIVFS#

class ex_fuzzy.fuzzy_sets.gaussianIVFS(name, secondMF_lower, secondMF_upper, domain, lower_height=1.0)[source]#

Bases: IVFS

Gaussian Interval-Valued (Type-2) Fuzzy Set Implementation.

This class implements a Gaussian interval-valued fuzzy set with two Gaussian membership functions (upper and lower) representing the uncertainty boundaries. This allows for modeling higher-order uncertainty in fuzzy systems.

secondMF_lower#

Parameters [mean, std] for the lower membership function

Type:

list

secondMF_upper#

Parameters [mean, std] for the upper membership function

Type:

list

name#

Human-readable name for the fuzzy set

Type:

str

universe_size#

Size of the universe of discourse

Type:

int

Example

>>> lower_params = [5.0, 1.0]
>>> upper_params = [5.0, 1.5]
>>> iv_gauss = gaussianIVFS(lower_params, upper_params, "Medium", 10)
>>> membership = iv_gauss.membership(np.array([4.0, 5.0, 6.0]))
>>> print(membership.shape)  # (3, 2) - lower and upper bounds

Note

The interval-valued membership function provides both lower and upper bounds for each input, enabling Type-2 fuzzy reasoning.

__init__(name, secondMF_lower, secondMF_upper, domain, lower_height=1.0)#

Initialize an Interval-Valued Fuzzy Set.

Parameters:

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

  • secondMF_lower (list[float]) – Four parameters [a,b,c,d] for lower trapezoidal membership function (outer boundary)

  • secondMF_upper (list[float]) – Four parameters [a,b,c,d] for upper trapezoidal membership function (inner boundary)

  • domain (list[float]) – Two-element list [min, max] defining universe of discourse

  • lower_height (float, optional) – Maximum height of lower membership function. Defaults to 1.0.

Raises:

AssertionError – If membership function parameters are inconsistent or invalid

Example

>>> ivfs = IVFS("high", [6,7,9,10], [6.5,7.5,8.5,9.5], [0,10], 0.9)

Methods

__init__(name, secondMF_lower, ...[, ...])

Initialize an Interval-Valued Fuzzy Set.

membership(input)

Computes the Gaussian interval-valued membership values for input points.

shape()

Returns the shape of the fuzzy set.

type()

Returns the type of the fuzzy set.
membership(input)[source]#

Computes the Gaussian interval-valued membership values for input points.

Returns both lower and upper membership bounds for each input value, enabling Type-2 fuzzy set operations.

Parameters:

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

Returns:

Array of shape (n, 2) with [lower, upper] bounds for each input

Return type:

np.array

Example

>>> iv_gauss = gaussianIVFS([0, 1], [0, 1.5], "Zero", 5)
>>> values = iv_gauss.membership(np.array([0.0, 1.0]))
>>> print(values.shape)  # (2, 2) - 2 inputs, 2 bounds each
type()[source]#

Returns the type of the fuzzy set.

Returns:

Always returns FUZZY_SETS.t2 for Type-2 fuzzy sets

Return type:

FUZZY_SETS

shape()[source]#

Returns the shape of the fuzzy set.

Returns:

Always returns ‘gaussian’

Return type:

str