DistToPi

class floulib.DistToPi(dist)

Bases: object

This class contains methods to transform probability distributions into possibility distributions.

__init__(dist)

Constructor

Parameters:

dist – The probability distribution.

Return type:

None.

Example

>>> from floulib import DistToPi
>>> import numpy as np
>>> from scipy.stats import norm
>>> mean = 0
>>> sigma = 1
>>> normal_dist = norm(mean, sigma)
>>> x = np.linspace(mean - 4*sigma, mean + 4*sigma, 1000)
>>> pi_opt = DistToPi(normal_dist)
>>> pi_opt(x).plot(label='$\pi_{optimal}$')

dpi(x)

Computes the optimal transformation of a unimodal symmetric probability distribution.

This method can be used as an interface with other libraries.

Parameters:

x (numpy.ndarray) – The array of points.

Returns:

The optimal possinility distribution.

Return type:

numpy.ndarray

Example

>>> from floulib import DistToPi
>>> import numpy as np
>>> from scipy.stats import norm
>>> import matplotlib.pyplot as plt
>>> mean = 0
>>> sigma = 1
>>> normal_dist = norm(mean, sigma)
>>> x = np.linspace(mean - 4*sigma, mean + 4*sigma, 1000)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, DistToPi(normal_dist).dpi(x))

membership(x, m=None)

Computes the grade of membership for x.

Parameters:

• x (float) – Point where the grade of membership is computed.

• m (TYPE, optional) –

  The mode of the distrubution. The default is None.

  • If m is None, the optimal transform is applied (see DistToPi.dpi()).

  • otherwise the tsn transformation is applied (see DistToPi.tsn()).

Returns:

Grade of membership.

Return type:

float

Example

Membership is computed with the optimal transformation.

>>> from floulib import DistToPi
>>> from scipy.stats import norm
>>> mean = 0
>>> sigma = 1
>>> normal_dist = norm(mean, sigma)
>>> print(DistToPi(normal_dist).membership(1.0))
0.31731050786291415

Membership is computed with the tsn transformation since Weilbull is not symetric.

>>> from floulib import DistToPi
>>> from scipy.stats import weibull_min
>>> c = 1.5
>>> mode = ((c-1.0)/c)**(1/c)
>>> weibull_dist = weibull_min(c)
>>> print(DistToPi(weibull_dist).membership(1.0, mode))
0.513417119032592

tsn(x, m)

Computes the tsn (two-side normalized) transformation of a unimodal symmetric probability distribution.

This method can be used as an interface with other libraries.

Parameters:

• x (numpy.ndarray) – The array of points.

• m (float) – The mode used for the transformation.

Returns:

The tsn possibility distribution.

Return type:

numpy.ndarray

Example

>>> from floulib import DistToPi
>>> import numpy as np
>>> from scipy.stats import weibull_min
>>> import matplotlib.pyplot as plt
>>> c = 1.5
>>> mode = ((c-1.0)/c)**(1/c)
>>> weibull_dist = weibull_min(c)
>>> x = np.linspace(0, 4, 1000)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, DistToPi(weibull_dist).tsn(x, mode), label = '$\pi_{tsn}$')
>>> ax.plot(x, weibull_dist.pdf(x), label = '$Weibull(1.5)$', alpha = 0.3)
>>> ax.legend()

__call__(x, m=None)

Special method to transform the probabilty distribution possibility into a discrete possibility distribution. .

Parameters:

• x (numpy.ndarray) – The universe of discourse on which the transformation is performed..

• m (float, optional) –

  The mode of the distrubution. The default is None.

  • If m is None, the optimal transform is applied (see DistToPi.dpi()).

  • otherwise the tsn transformation is applied (see DistToPi.tsn()).

Raises:

TypeError – Raised if the parameter is not an instance of numpy.ndarray.

Returns:

The Discrete fuzzy subsets.

Return type:

Discrete