Membership Functions
- pyit2fls.zero_mf(x, params=[])
All zero membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list, optional
Additional parameters for the membership function, which are not needed for the zero membership function.
Returns
output : ndarray
Returns an array of membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = zero_mf(x)
- pyit2fls.singleton_mf(x, params)
Singleton membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. params[0] indicates the singleton center, and params[1] indicates the singleton height.
Returns
output : ndarray
Returns membership values corresponding to the input.
Notes
The singleton center, params[0], must be within the discretized universe of discourse.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = singleton_mf(x, [0.5, 1])
- pyit2fls.const_mf(x, params)
Constant membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. params[0] indicates the constant membership function’s height.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = const_mf(x, [0.5])
- pyit2fls.tri_mf(x, params)
Triangular membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The left end, center, right end, and height of the triangular membership function are indicated by params[0], params[1], params[2], and params[3], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = tri_mf(x, [0.1, 0.3, 0.5, 1])
- pyit2fls.rtri_mf(x, params)
Right triangular membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The right end, center, and height of the triangular membership function are indicated by params[0], params[1], and params[2], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = rtri_mf(x, [0.5, 0.2, 1])
- pyit2fls.ltri_mf(x, params)
Left triangular membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The left end, center, and height of the triangular membership function are indicated by params[0], params[1], and params[2], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = ltri_mf(x, [0.3, 0.5, 1])
- pyit2fls.trapezoid_mf(x, params)
Trapezoidal membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The left end, left center, right center, right end, and height of the trapezoidal membership function are indicated by params[0], params[1], params[2], params[3], and params[4], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = trapezoid_mf(x, [0.1, 0.3, 0.5, 0.7, 1])
- pyit2fls.gaussian_mf(x, params)
Gaussian membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The center, standard deviation, and height of the Gaussian membership function are indicated by params[0], params[1], and params[2], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = gaussian_mf(x, [0.5, 0.05, 1])
- pyit2fls.gauss_uncert_mean_umf(x, params)
Gaussian with uncertain mean UMF.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The lower limit of mean, upper limit of mean, standard deviation, and height of the Gaussian membership function are indicated by params[0], params[1], params[2], and params[3], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = gauss_uncert_mean_umf(x, [0.3, 0.7, 0.05, 1])
- pyit2fls.gauss_uncert_mean_lmf(x, params)
Gaussian with uncertain mean LMF.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The lower limit of mean, upper limit of mean, standard deviation, and height of the Gaussian membership function are indicated by params[0], params[1], params[2], and params[3], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = gauss_uncert_mean_lmf(x, [0.3, 0.7, 0.2, 1])
- pyit2fls.gauss_uncert_std_umf(x, params)
Gaussian with uncertain standard deviation UMF.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The center, lower limit of standard deviation, upper limit of standard deviation, and height of the Gaussian membership function are indicated by params[0], params[1], params[2], and params[3], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = gauss_uncert_std_umf(x, [0.5, 0.2, 0.5, 1])
- pyit2fls.gauss_uncert_std_lmf(x, params)
Gaussian with uncertain standard deviation LMF.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The center, lower limit of standard deviation, upper limit of standard deviation, and height of the Gaussian membership function are indicated by params[0], params[1], params[2], and params[3], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = gauss_uncert_std_lmf(x, [0.5, 0.2, 0.5, 1])
- pyit2fls.rgauss_uncert_std_umf(x, params)
Right Gaussian with uncertain standard deviation UMF.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The center, lower limit of standard deviation, upper limit of standard deviation, and height of the Gaussian membership function are indicated by params[0], params[1], params[2], and params[3], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = rgauss_uncert_std_umf(x, [0.5, 0.2, 0.5, 1])
- pyit2fls.rgauss_uncert_std_lmf(x, params)
Right Gaussian with uncertain standard deviation LMF.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The center, lower limit of standard deviation, upper limit of standard deviation, and height of the Gaussian membership function are indicated by params[0], params[1], params[2], and params[3], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = rgauss_uncert_std_lmf(x, [0.5, 0.2, 0.5, 1])
- pyit2fls.lgauss_uncert_std_umf(x, params)
Left Gaussian with uncertain standard deviation UMF.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The center, lower limit of standard deviation, upper limit of standard deviation, and height of the Gaussian membership function are indicated by params[0], params[1], params[2], and params[3], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = lgauss_uncert_std_umf(x, [0.5, 0.2, 0.5, 1])
- pyit2fls.lgauss_uncert_std_lmf(x, params)
Left Gaussian with uncertain standard deviation LMF.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse at which the membership function will be evaluated.
params : list
Additional parameters for the membership function. The center, lower limit of standard deviation, upper limit of standard deviation, and height of the Gaussian membership function are indicated by params[0], params[1], params[2], and params[3], respectively.
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = lgauss_uncert_std_lmf(x, [0.5, 0.2, 0.5, 1])
- pyit2fls.elliptic_mf(x, params)
Elliptic membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse in which the membership function will be evaluated.
params : list
Parameters of the elliptic membership function. The center, width, exponent, and height of the elliptic membership function are indicated by params[0], params[1], params[2], and params[3].
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = eliptic_mf(x, [0.5, 0.25, 1.3, 1.])
- pyit2fls.semi_elliptic_mf(x, params)
Semi-elliptic membership function.
Parameters
x : numpy (n,) shaped array
The array-like input x indicates the points from the universe of discourse in which the membership function will be evaluated.
params : list
Parameters of the semi-elliptic membership function. The center, width, and height of the semi-elliptic membership function are indicated by params[0], params[1], and params[2].
Returns
output : ndarray
Returns membership values corresponding to the input.
Examples
>>> x = linspace(0, 1, 201) >>> membership_value = eliptic_mf(x, [0.5, 0.25, 1.3, 1.])
- pyit2fls.gbell_mf(x, params)
Generalized bell shaped membership function.
Parameters
x : numpy (n,) shaped array
The array like input x indicates the points from universe of discourse in which the membership function would be evaluated.
params : list
Parameters of the generalized bell shaped membership function. The a, b, and c values and height of the generalized bell shaped membership function formula are indicated by params[0], params[1], params[2], and params[3].
Returns
output : ndarray
Returns membership values corresponding with the input.
Examples
>>> x = linspace(0., 1., 201) >>> membership_value = gbell_mf(x, [0.1, 1., 0.5, 1.])