Welcome to phuzzy’s documentation!¶

phuzzy¶

https://travis-ci.org/lepy/phuzzy.svg?branch=master

Fuzzy calculation in Python.

Free software: MIT license
Documentation: https://phuzzy.readthedocs.io.

Features¶

TODO

Credits¶

This package was created with Cookiecutter and the audreyr/cookiecutter-pypackage project template.

Installation¶

Stable release¶

To install phuzzy, run this command in your terminal:

$ pip install phuzzy

This is the preferred method to install phuzzy, as it will always install the most recent stable release.

If you don’t have pip installed, this Python installation guide can guide you through the process.

From sources¶

The sources for phuzzy can be downloaded from the Github repo.

You can either clone the public repository:

$ git clone git://github.com/lepy/phuzzy

Or download the tarball:

$ curl  -OL https://github.com/lepy/phuzzy/tarball/master

Once you have a copy of the source, you can install it with:

$ python setup.py install

Usage¶

To use phuzzy in a project:

import phuzzy
tn = phuzzy.TruncNorm(alpha0=[2, 3], alpha1=[], number_of_alpha_levels=15, name="t")
tri = phuzzy.Triangle(alpha0=[1, 4], alpha1=[2], number_of_alpha_levels=5)
f = tn + tri
print(f.df)

available shapes¶

Uniform¶

import phuzzy.mpl as phm
uni = phm.Uniform(alpha0=[1, 4], number_of_alpha_levels=5, name="x")
uni.plot(show=True, filepath="/tmp/uniform.png", title=True)

Uniform fuzzy number (this is just an interval)

Triangle¶

import phuzzy.mpl as phm

tri = phm.Triangle(alpha0=[1, 4], alpha1=[2], number_of_alpha_levels=5)
tri.plot(show=False, filepath="/tmp/triangle.png", title=True)

Triangle fuzzy number

Trapezoid¶

import phuzzy.mpl as phm
trap = phm.Trapezoid(alpha0=[1, 5], alpha1=[2, 3], number_of_alpha_levels=5)
trap.plot(show=False, filepath="/tmp/trapezoid.png", title=True)

Trapezoid fuzzy number

TruncNorm¶

import phuzzy.mpl as phm
tn = phm.TruncNorm(alpha0=[1, 3], number_of_alpha_levels=15, name="x")
tn.plot(show=False, filepath="/tmp/truncnorm.png", title=True)

TruncNorm fuzzy number

TruncGenNorm¶

import phuzzy.mpl as phm
tgn = phm.TruncGenNorm(alpha0=[1, 4], alpha1=[2, 3], number_of_alpha_levels=15, beta=3.)
tgn.plot(show=False, filepath="/tmp/truncgennorm.png", title=True)

TruncGenNorm fuzzy number

Superellipse¶

import phuzzy.mpl as phm
se = phm.Superellipse(alpha0=[-1, 2.], alpha1=None, m=1.0, n=.5, number_of_alpha_levels=17)
se.plot(show=True, filepath="/tmp/superellipse.png", title=True)

Superellipse fuzzy number

basic operations¶

Addition¶

$z = x + y$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
y = phuzzy.TruncNorm(alpha0=[1, 3], number_of_alpha_levels=15, name="y")
z = x + y
z.name = "x+y"

Addition of fuzzy numbers

$z = 3 + x$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
z = 3 + x
z = x + 3

Substraction¶

$z = x - y$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
y = phuzzy.TruncNorm(alpha0=[1, 3], number_of_alpha_levels=15, name="y")
z = x - y
z.name = "x-y"

Substraction of fuzzy numbers

$y = 3 - x z = x - 3$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
y = 3 - x
z = x - 3

Multiplication¶

$z = x y$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
y = phuzzy.TruncNorm(alpha0=[1, 3], number_of_alpha_levels=15, name="y")
z = x * y
z.name = "x*y"

Multiplication of fuzzy numbers

$z = 3x$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
z = 3 * x
z = x * 3

Division¶

$z = \frac{x}{y}$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
y = phuzzy.TruncNorm(alpha0=[1, 3], number_of_alpha_levels=15, name="y")
z = x / y
z.name = "x/y"

Division of fuzzy numbers

$y = 3 / x z = x / 3$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
z = 3 / x
z = x / 3

Exponentiation¶

$z = x^y$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
y = phuzzy.TruncNorm(alpha0=[1, 3], number_of_alpha_levels=15, name="y")
z = x ** y
z.name = "x^y"

Power operation with fuzzy numbers

$z = x^3$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
z = x**3

Negation¶

$z = -x$

x = phuzzy.Trapezoid(alpha0=[0, 4], alpha1=[2, 3], number_of_alpha_levels=5)
z = -x

Absolute value¶

$z = |x|$

x = phuzzy.Trapezoid(alpha0=[-1, 4], alpha1=[2, 3], number_of_alpha_levels=5)
z = abs(x)
z = x.abs()

Shapes¶

Uniform¶

import phuzzy.mpl as phm
uni = phm.Uniform(alpha0=[1, 4], number_of_alpha_levels=5, name="x")
uni.plot(show=True, filepath="/tmp/uniform.png", title=True)

Uniform fuzzy number

Uniform fuzzy number operations

Triangle¶

import phuzzy.mpl as phm

tri = phm.Triangle(alpha0=[1, 4], alpha1=[2], number_of_alpha_levels=5)
tri.plot(show=False, filepath="/tmp/triangle.png", title=True)

Triangle fuzzy number

Triangle fuzzy number operations

Trapezoid¶

import phuzzy.mpl as phm
trap = phm.Trapezoid(alpha0=[1, 5], alpha1=[2, 3], number_of_alpha_levels=5)
trap.plot(show=False, filepath="/tmp/trapezoid.png", title=True)

Trapezoid fuzzy number

Trapezoid fuzzy number operations

TruncNorm¶

import phuzzy.mpl as phm
tn = phm.TruncNorm(alpha0=[1, 3], number_of_alpha_levels=15, name="x")
tn.plot(show=False, filepath="/tmp/truncnorm.png", title=True)

TruncNorm fuzzy number

TruncNorm fuzzy number operations

TruncGenNorm¶

import phuzzy.mpl as phm
tgn = phm.TruncGenNorm(alpha0=[1, 4], alpha1=[2, 3], number_of_alpha_levels=15, beta=3.)
tgn.plot(show=False, filepath="/tmp/truncgennorm.png", title=True)

TruncGenNorm fuzzy number

TruncGenNorm fuzzy number operations

Superellipse¶

import phuzzy.mpl as phm
se = phm.Superellipse(alpha0=[-1, 2.], alpha1=None, m=1.0, n=.5, number_of_alpha_levels=17)
se.plot(show=True, filepath="/tmp/superellipse.png", title=True)

Superellipse fuzzy number

Superellipse fuzzy number (variation m, n)

Superellipse fuzzy number operations

Plots¶

import phuzzy
from phuzzy.mpl import mix_mpl
import phuzzy.mpl.plots
x = phuzzy.TruncNorm(alpha0=[1, 2], name="x")
y = phuzzy.Triangle(alpha0=[3, 6], alpha1=[4], name="y")
mix_mpl(x)
x.plot(filepath="FuzzyNumber_plot.png")

x.plot()

fig, ax = phuzzy.mpl.plots.plot_xy(x, y)

fig, ax = phuzzy.mpl.plots.plot_xyz(x, y, x+y)

fig, ax = phuzzy.mpl.plots.plot_3d(x, y)

fig, ax = phuzzy.mpl.plots.plot_xy_3d(x, y)

Examples¶

Three-point bending¶

Simply supported beam with central load¶

What is the maximum deflection of a simple supported beam with central load, if there is an uncertainty of only 1% for all input parameter? The input parameter are load P, beam length L, beam width W, beam height H and young’s modulus E.

$P &= 5\, kN \pm 1\% L &= 2\, m \pm 1\% W &= 50\, mm \pm 1\% H &= 100\, mm \pm 1\% E &= 30000\, N/mm^2 \pm 1\%$

Three point bending test [wikipedia.org]

$w(x) &= {\begin{cases}-{\frac {Px(4x^{2}-3L^{2})}{48EI}},&{\mbox{for }}0\leq x\leq {\tfrac {L}{2}}\\{\frac {P(x-L)(L^{2}-8Lx+4x^{2})}{48EI}},&{\mbox{for }}{\tfrac {L}{2}}<x\leq L\end{cases}} w &= w_{L/2} = \tfrac {PL^{3}}{48EI} A &= WH I &= WH^3$

Code¶

import phuzzy as ph
number_of_alpha_levels = 31

# load P
P0 = 5000.  # N
dP = 0.01 * P0  # N
P = ph.Triangle(alpha0=[P0 - dP, P0 + dP], alpha1=[P0], name="P", number_of_alpha_levels=number_of_alpha_levels)

# dimensions L, W, H
W0 = 50  # mm
H0 = 100  # mm
L0 = 2000  # mm

dW = 0.01 * W0  # mm
dH = 0.01 * H0  # mm
dL = 0.01 * L0  # mm

L = ph.Triangle(alpha0=[L0 - dL, L0 + dL], alpha1=[L0], name="L", number_of_alpha_levels=number_of_alpha_levels)
W = ph.Triangle(alpha0=[W0 - dW, W0 + dW], alpha1=[W0], name="W", number_of_alpha_levels=number_of_alpha_levels)
H = ph.Triangle(alpha0=[H0 - dH, H0 + dH], alpha1=[H0], name="H", number_of_alpha_levels=number_of_alpha_levels)

# material

E0 = 30000.  # N/mm2
dE = 0.1 * E0  # N/mm2
E = ph.TruncNorm(alpha0=[E0 - dE, E0 + dE], alpha1=[E0], name="E", number_of_alpha_levels=number_of_alpha_levels)

I0 = W0 * H0 ** 3 / 12.
w0 = P0 * L0 ** 3 / (48 * E0 * I0)

print("I0 = {:.4g} mm^4".format(I0))
# I0 = 4.167e+06 mm^4
print("w0 = {:.4g} mm".format(w0))
# w0 = 6.667 mm

I = W * H** 3 / 12.
I.name = "I"
w = P * L ** 3 / (48 * E * I)
w.name = r"P L^3 / (48 EI)"

print("I = {} mm^4".format(I))
# I = FuzzyNumber(W*H^3/12.0:[[4002483.375, 4335850.041666667], [4166666.6666666665, 4166666.6666666665]]) mm^4

print("w = {} mm".format(w))
# w = FuzzyNumber(P*L^3/E*48*W*H^3/12.0:[[5.594629603627992, 8.024370049019725], [6.666666666666667, 6.666666666666667]]) mm

w_mean = w.mean()
dw_l = w_mean - w.min()
dw_r = w.max() - w_mean
print("w = {:.4g} mm (- {:.4g}|+ {:.4g})".format(w_mean, dw_l, dw_r))
# w = 6.703 mm (- 1.109|+ 1.321)
print("w = {:.4g} mm [{:.4g},{:.4g}]".format(w_mean, w.min(), w.max()))
# w = 6.703 mm [5.595,8.024]

Parameter¶

used Parameter

Results¶

results area moment of inertia I and deflections w

Source code ssb.py

phuzzy package¶

class phuzzy.Analysis(**kwargs)[source]¶

Bases: object

__dict__ = dict_proxy({'add_designvar': <function add_designvar>, '__module__': 'phuzzy', '__repr__': <function __str__>, '__dict__': <attribute '__dict__' of 'Analysis' objects>, '__weakref__': <attribute '__weakref__' of 'Analysis' objects>, 'designvars': <property object>, '__str__': <function __str__>, 'add_designvars': <function add_designvars>, '__init__': <function __init__>, '__doc__': None})¶

__init__(**kwargs)[source]¶: Analysis(kwargs)

__module__ = 'phuzzy'¶

__repr__()¶: x.__str__() <==> str(x)

__str__() <==> str(x)[source]¶

__weakref__¶: list of weak references to the object (if defined)

add_designvar(designvar)[source]¶

add design variable to doe

Parameters:	designvar – design variable
Returns:	None

add_designvars(designvars)[source]¶

add design variables to doe

Parameters:	designvars – list of design variables
Returns:	None

designvars¶

returns all design variables of doe

Returns:	dict of designvars

phuzzy.shapes package¶

class phuzzy.shapes.FuzzyNumber(**kwargs)[source]¶

Bases: object

convex fuzzy number

__abs__()[source]¶

apply abs operator to a fuzzy number

Parameters:	other – phuzzy.FuzzyNumber
Returns:	fuzzy number

__add__(other)[source]¶

adds a fuzzy number

Parameters:	other – phuzzy.FuzzyNumber
Returns:	fuzzy number

__contains__(other)[source]¶

operator in

Return type:	bool
Returns:	True or False

__dict__ = dict_proxy({'cdf': <function cdf>, 'ppf': <function ppf>, 'get_shape': <function get_shape>, '__str__': <function __str__>, 'export_csv': <function export_csv>, '__rsub__': <function __rsub__>, '__rdiv__': <function __rdiv__>, '__rmul__': <function __rmul__>, '__lt__': <function __lt__>, '__weakref__': <attribute '__weakref__' of 'FuzzyNumber' objects>, 'make_convex': <function make_convex>, '__rpow__': <function __rpow__>, 'convert_df': <function convert_df>, 'get_01': <property object>, '_get_df': <function _get_df>, '__abs__': <function __abs__>, 'defuzzification_centroid2': <function defuzzification_centroid2>, 'from_data': <classmethod object>, '__doc__': 'convex fuzzy number', '__sub__': <function __sub__>, 'df': <property object>, '_set_df': <function _set_df>, 'defuzzification': <function defuzzification>, 'defuzzification_centroid': <function defuzzification_centroid>, 'from_results': <classmethod object>, '__pow__': <function __pow__>, '__gt__': <function __gt__>, 'copy': <function copy>, '__eq__': <function __eq__>, 'from_str': <classmethod object>, 'has_zero': <function has_zero>, 'defuzzification_alpha_one': <function defuzzification_alpha_one>, '__hash__': None, '_get_cls': <staticmethod object>, 'mean': <function mean>, 'discretize': <function discretize>, '__module__': 'phuzzy.shapes', '__radd__': <function __radd__>, 'rvs': <function rvs>, '__dict__': <attribute '__dict__' of 'FuzzyNumber' objects>, '__truediv__': <function __truediv__>, 'defuzzification_mean': <function defuzzification_mean>, '_get_number_of_alpha_levels': <function _get_number_of_alpha_levels>, '__init__': <function __init__>, 'alpha0': <property object>, 'alpha1': <property object>, '__contains__': <function __contains__>, '_disretize_range': <function _disretize_range>, 'defuzzification_p50': <function defuzzification_p50>, 'abs': <function abs>, '__neg__': <function __neg__>, '__ne__': <function __ne__>, 'get_alpha_from_value': <function get_alpha_from_value>, 'import_csv': <function import_csv>, 'max': <function max>, '_unify': <function _unify>, 'update': <function update>, '__add__': <function __add__>, 'pdf': <function pdf>, 'alpha': <function alpha>, 'min': <function min>, 'number_of_alpha_levels': <property object>, 'to_str': <function to_str>, '__div__': <function __truediv__>, '__mul__': <function __mul__>, 'get_01_str': <property object>, '__repr__': <function __repr__>, '_set_number_of_alpha_levels': <function _set_number_of_alpha_levels>})¶

__div__(other)¶

divide by a fuzzy number

Parameters:	other – phuzzy.FuzzyNumber
Returns:	fuzzy number

__eq__(other)[source]¶

operation ==

Return type:	bool
Returns:	True or False

__gt__(other)[source]¶

operation >

Return type:	bool
Returns:	True or False

__hash__ = None¶

__init__(**kwargs)[source]¶

base fuzzy number

Parameters:	kwargs –

__lt__(other)[source]¶

operation <

Returns:	True or False

__module__ = 'phuzzy.shapes'¶

__mul__(other)[source]¶

multiply with a fuzzy number

Parameters:	other – phuzzy.FuzzyNumber
Returns:	fuzzy number

__ne__(other)[source]¶

operation !=

Return type:	bool
Returns:	True or False

__neg__()[source]¶

apply unary neg operator to a fuzzy number

Parameters:	other – phuzzy.FuzzyNumber
Returns:	fuzzy number

__pow__(other)[source]¶

apply power of a fuzzy number

Parameters:	other – phuzzy.FuzzyNumber
Returns:	fuzzy number

__radd__(other)[source]¶

__rdiv__(other)[source]¶

__repr__() <==> repr(x)[source]¶

__rmul__(other)[source]¶

__rpow__(other)[source]¶

apply exponent of a fuzzy number

Parameters:	other – phuzzy.FuzzyNumber
Returns:	fuzzy number

__rsub__(other)[source]¶

__str__() <==> str(x)[source]¶

__sub__(other)[source]¶

substract a fuzzy number

Parameters:	other – phuzzy.FuzzyNumber
Returns:	fuzzy number

__truediv__(other)[source]¶

divide by a fuzzy number

Parameters:	other – phuzzy.FuzzyNumber
Returns:	fuzzy number

__weakref__¶: list of weak references to the object (if defined)

abs()[source]¶

calculate absolute value

Returns:	FuzzyNumber

alpha(x)[source]¶: get alpha from x

alpha0¶: row for alpha=0

alpha1¶: row for alpha=1

cdf(x, **kwargs)[source]¶

Cumulative distribution function

Parameters:	x – x values n – number of integration points
Returns:	y

convert_df(alpha_levels=None, zero=0)[source]¶

copy()[source]¶

return a copy

Returns:	copy of fuzzy number

defuzzification(method='centroid')[source]¶

defuzzification_alpha_one()[source]¶: defuzzification

$(alpha1_r + alpha1_l) / 2$

defuzzification_centroid()[source]¶: defuzzification center of gravity

defuzzification_centroid2()[source]¶: defuzzification center of gravity

defuzzification_mean()[source]¶: defuzzification mean with discrete values

defuzzification_p50()[source]¶: defuzzification mean my means of ppf(0.5)

df¶: number of alpha levels

discretize(alpha0, alpha1, alpha_levels)[source]¶

discretize shape function

Parameters:	alpha0 – range at alpha=0 alpha1 – range at alpha=1 alpha_levels – number of alpha levels
Returns:	None

export_csv(filepath=None)[source]¶

export alpha levels to csv

Parameters:	filepath – csv file path
Returns:

classmethod from_data(**kwargs)[source]¶

instantiate fuzzy number from attributes

Parameters:	kwargs –
Return type:	phuzzy.FuzzyNumber or derived object
Returns:	fuzzy number

classmethod from_results(df_res, name=None, number_of_alpha_levels=11)[source]¶

create FuzzyNumber from DataFrame(“alpha”, “res”)

Parameters:	df – DataFrame with columns=[“alpha”, “res”]
Returns:	FuzzyNumber

classmethod from_str(s)[source]¶

deserialize fuzzy number to string

Returns:	fuzzy number string

get_01¶

get alpha=0 and alpha=1 values

Returns:	[[a0_l, a0_r], [a1_l, a1_r]]

get_01_str¶

get alpha=0 and alpha=1 values

Returns:	[[a0_l, a0_r], [a1_l, a1_r]]

get_alpha_from_value(x)[source]¶

get alpha values from given x values

Parameters:	x – x values
Returns:	alpha values

get_shape()[source]¶

get shape dataframe

Returns:	pandas.DataFrame(columns=[“alpha”, “x”])

has_zero()[source]¶

is zero in range

Return type:	bool
Returns:	True od False

import_csv(fh)[source]¶

load alpha levels from csv

Parameters:	fh – csv file path or file handle
Returns:	alpha level dataframe

make_convex()[source]¶

make fuzzy number convex

Returns:	None

max()[source]¶

maximal

Return type:	float
Returns:	max value of df

mean()[source]¶

mean value

Return type:	float
Returns:	mean value

min()[source]¶

minimum

Return type:	float
Returns:	min value of df

number_of_alpha_levels¶: number of alpha levels

pdf(x)[source]¶

Probability density function

Parameters:	x – x values
Returns:

ppf(x, **kwargs)[source]¶

Percent point function (inverse of cdf-percentiles).

Parameters:	x – x values n – number of integration points
Returns:	y

rvs(size, seed=None)[source]¶

Sample points according membership function

Parameters:	size – number of sample points
Returns:	sample points

to_str()[source]¶

serialize fuzzy number to string

Returns:	fuzzy number string

update(alpha0=None, alpha1=None, alpha_levels=None)[source]¶

class phuzzy.shapes.Trapezoid(**kwargs)[source]¶

Bases: phuzzy.shapes.FuzzyNumber

triange fuzzy number

__init__(**kwargs)[source]¶

base fuzzy number

Parameters:	kwargs –

__module__ = 'phuzzy.shapes'¶

cdf(x, **kwargs)[source]¶

Cumulative distribution function

Parameters:	x – x values n – number of integration points
Returns:	y

discretize(alpha0, alpha1, alpha_levels)[source]¶

discretize shape function

Parameters:	alpha0 – range at alpha=0 alpha1 – range at alpha=1 alpha_levels – number of alpha levels
Returns:	None

pdf(x)[source]¶

Parameters:	x –
Returns:

to_str()[source]¶

serialize fuzzy number to string

Returns:	fuzzy number string

class phuzzy.shapes.Triangle(**kwargs)[source]¶

Bases: phuzzy.shapes.FuzzyNumber

triange fuzzy number

__init__(**kwargs)[source]¶

base fuzzy number

Parameters:	kwargs –

__module__ = 'phuzzy.shapes'¶

cdf(x, **kwargs)[source]¶

Cumulative distribution function

Parameters:	x – x values n – number of integration points
Returns:	y

discretize(alpha0, alpha1, alpha_levels)[source]¶

discretize shape function

Parameters:	alpha0 – range at alpha=0 alpha1 – range at alpha=1 alpha_levels – number of alpha levels
Returns:	None

classmethod from_data(**kwargs)[source]¶

instantiate fuzzy number from attributes

Parameters:	kwargs –
Return type:	phuzzy.FuzzyNumber or derived object
Returns:	fuzzy number

pdf(x)[source]¶: https://en.wikipedia.org/wiki/Triangular_distribution

to_str()[source]¶

serialize fuzzy number to string

Returns:	fuzzy number string

class phuzzy.shapes.Uniform(**kwargs)[source]¶

Bases: phuzzy.shapes.FuzzyNumber

triange fuzzy number

__init__(**kwargs)[source]¶

base fuzzy number

Parameters:	kwargs –

__module__ = 'phuzzy.shapes'¶

cdf(x, **kwargs)[source]¶

Cumulative distribution function

Parameters:	x – x values n – number of integration points
Returns:	y

discretize(alpha0, alpha1, alpha_levels)[source]¶

discretize shape function

Parameters:	alpha0 – range at alpha=0 alpha1 – range at alpha=1 alpha_levels – number of alpha levels
Returns:	None

pdf(x)[source]¶: https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)

to_str()[source]¶

serialize fuzzy number to string

Returns:	fuzzy number string

phuzzy.shapes.superellipse module¶

superelliptic fuzzy number

Superellipse(alpha0=[-1, 2], alpha1=None, m=1, n=.5, number_of_alpha_levels=15)

Superellipse fuzzy number

class phuzzy.shapes.superellipse.Superellipse(**kwargs)[source]¶

Bases: phuzzy.shapes.FuzzyNumber

superelliptic fuzzy number

__init__(**kwargs)[source]¶

superelliptic fuzzy number

Parameters:	kwargs –

Superellipse(alpha0=[1, 2], alpha1=None, m=2, n=None, number_of_alpha_levels=17)

__module__ = 'phuzzy.shapes.superellipse'¶

discretize(alpha0, alpha1, alpha_levels)[source]¶

discretize shape function

Parameters:	alpha0 – range at alpha=0 alpha1 – range at alpha=1 alpha_levels – number of alpha levels
Returns:	None

classmethod from_str(s)[source]¶

instantiate a fuzzy number from string

Parameters:	s –
Return type:	phuzzy.FuzzyNumber
Returns:	fuzzy number

shape(x)[source]¶

shape function

Parameters:	x (array or float) – x values
Returns:	y values

to_str()[source]¶

serialize fuzzy number to string

Return type:	str
Returns:	fuzzy string

phuzzy.shapes.truncnorm module¶

Normal distibuted membership function

TruncNorm(alpha0=[1, 3], alpha1=None, number_of_alpha_levels=15)

TruncNorm fuzzy number

TruncGenNorm(alpha0=[1, 4], alpha1=None, number_of_alpha_levels=15, beta=5)

TruncGenNorm fuzzy number

class phuzzy.shapes.truncnorm.TruncGenNorm(**kwargs)[source]¶

Bases: phuzzy.shapes.FuzzyNumber

Truncated generalized normal distibuted membership function

__init__(**kwargs)[source]¶

create a TruncNorm object

Parameters:	kwargs –

TruncGenNorm(alpha0=[1, 3], alpha1=None, number_of_alpha_levels=17, beta=3)

__module__ = 'phuzzy.shapes.truncnorm'¶

discretize(alpha0, alpha1, alpha_levels)[source]¶

discretize shape function

Parameters:	alpha0 – range at alpha=0 alpha1 – range at alpha=1 alpha_levels – number of alpha levels
Returns:	None

distr¶

loc¶

mean¶

scale¶

std¶

class phuzzy.shapes.truncnorm.TruncNorm(**kwargs)[source]¶

Bases: phuzzy.shapes.FuzzyNumber

Normal distibuted membership function

__init__(**kwargs)[source]¶

create a TruncNorm object

Parameters:	kwargs –

TruncNorm(alpha0=[1, 3], alpha1=None, number_of_alpha_levels=17)

__module__ = 'phuzzy.shapes.truncnorm'¶

discretize(alpha0, alpha1, alpha_levels)[source]¶

discretize shape function

Parameters:	alpha0 – range at alpha=0 alpha1 – range at alpha=1 alpha_levels – number of alpha levels
Returns:	None

distr¶

calculate truncated normal distribution

Returns:	distribution object

loc¶

mean value

Return type:	float
Returns:	mean value aka location

mean¶

mean value

Return type:	float
Returns:	mean value aka location

scale¶

standard deviation

Return type:	float
Returns:	standard deviation

std¶

standard deviation

Return type:	float
Returns:	standard deviation

phuzzy.mpl module¶

class phuzzy.mpl.FuzzyNumber(**kwargs)[source]¶

Bases: phuzzy.shapes.FuzzyNumber, phuzzy.mpl.MPL_Mixin

Uniform fuzzy number with matplotlib mixin

__init__(**kwargs)[source]¶

base fuzzy number

Parameters:	kwargs –

__module__ = 'phuzzy.mpl'¶

class phuzzy.mpl.MPL_Mixin[source]¶

__module__ = 'phuzzy.mpl'¶

plot(ax=None, filepath=None, show=False, xlim=None, labels=True, title=False, ppf=None)[source]¶: plots fuzzy number with mpl

vplot(ax=None, filepath=None, show=False, xlim=None, labels=True, title=False, ppf=None)[source]¶: plots fuzzy number with mpl

class phuzzy.mpl.Superellipse(**kwargs)[source]¶

Bases: phuzzy.shapes.superellipse.Superellipse, phuzzy.mpl.MPL_Mixin

Superellipse fuzzy number with matplotlib mixin

__init__(**kwargs)[source]¶

superelliptic fuzzy number

Parameters:	kwargs –

Superellipse(alpha0=[1, 2], alpha1=None, m=2, n=None, number_of_alpha_levels=17)

__module__ = 'phuzzy.mpl'¶

class phuzzy.mpl.Trapezoid(**kwargs)[source]¶

Bases: phuzzy.shapes.Trapezoid, phuzzy.mpl.MPL_Mixin

Trapezoid fuzzy number with matplotlib mixin

__init__(**kwargs)[source]¶

base fuzzy number

Parameters:	kwargs –

__module__ = 'phuzzy.mpl'¶

class phuzzy.mpl.Triangle(**kwargs)[source]¶

Bases: phuzzy.shapes.Triangle, phuzzy.mpl.MPL_Mixin

Triangle fuzzy number with matplotlib mixin

__init__(**kwargs)[source]¶

base fuzzy number

Parameters:	kwargs –

__module__ = 'phuzzy.mpl'¶

class phuzzy.mpl.TruncGenNorm(**kwargs)[source]¶

Bases: phuzzy.shapes.truncnorm.TruncGenNorm, phuzzy.mpl.MPL_Mixin

Truncates general normal fuzzy number with matplotlib mixin

__init__(**kwargs)[source]¶

create a TruncNorm object

Parameters:	kwargs –

TruncGenNorm(alpha0=[1, 3], alpha1=None, number_of_alpha_levels=17, beta=3)

__module__ = 'phuzzy.mpl'¶

class phuzzy.mpl.TruncNorm(**kwargs)[source]¶

Bases: phuzzy.shapes.truncnorm.TruncNorm, phuzzy.mpl.MPL_Mixin

TruncNorm fuzzy number with matplotlib mixin

__init__(**kwargs)[source]¶

create a TruncNorm object

Parameters:	kwargs –

TruncNorm(alpha0=[1, 3], alpha1=None, number_of_alpha_levels=17)

__module__ = 'phuzzy.mpl'¶

class phuzzy.mpl.Uniform(**kwargs)[source]¶

Bases: phuzzy.shapes.Uniform, phuzzy.mpl.MPL_Mixin

Uniform fuzzy number with matplotlib mixin

__init__(**kwargs)[source]¶

base fuzzy number

Parameters:	kwargs –

__module__ = 'phuzzy.mpl'¶

phuzzy.mpl.extend_instance(obj, cls)[source]¶: Apply mixins to a class instance after creation

phuzzy.mpl.mix_mpl(obj)[source]¶

Contributing¶

Contributions are welcome, and they are greatly appreciated! Every little bit helps, and credit will always be given.

You can contribute in many ways:

Types of Contributions¶

Report Bugs¶

Report bugs at https://github.com/lepy/phuzzy/issues.

If you are reporting a bug, please include:

Your operating system name and version.
Any details about your local setup that might be helpful in troubleshooting.
Detailed steps to reproduce the bug.

Fix Bugs¶

Look through the GitHub issues for bugs. Anything tagged with “bug” and “help wanted” is open to whoever wants to implement it.

Implement Features¶

Look through the GitHub issues for features. Anything tagged with “enhancement” and “help wanted” is open to whoever wants to implement it.

Write Documentation¶

phuzzy could always use more documentation, whether as part of the official phuzzy docs, in docstrings, or even on the web in blog posts, articles, and such.

Submit Feedback¶

The best way to send feedback is to file an issue at https://github.com/lepy/phuzzy/issues.

If you are proposing a feature:

Explain in detail how it would work.
Keep the scope as narrow as possible, to make it easier to implement.
Remember that this is a volunteer-driven project, and that contributions are welcome :)

Get Started!¶

Ready to contribute? Here’s how to set up phuzzy for local development.

Fork the phuzzy repo on GitHub.

Clone your fork locally:

$ git clone git@github.com:your_name_here/phuzzy.git

Install your local copy into a virtualenv. Assuming you have virtualenvwrapper installed, this is how you set up your fork for local development:
```
$ mkvirtualenv phuzzy
$ cd phuzzy/
$ python setup.py develop
```
Create a branch for local development:
```
$ git checkout -b name-of-your-bugfix-or-feature
```
Now you can make your changes locally.
When you’re done making changes, check that your changes pass flake8 and the tests, including testing other Python versions with tox:
```
$ flake8 phuzzy tests
$ python setup.py test or py.test
$ tox
```
To get flake8 and tox, just pip install them into your virtualenv.

Commit your changes and push your branch to GitHub:

$ git add .
$ git commit -m "Your detailed description of your changes."
$ git push origin name-of-your-bugfix-or-feature

Submit a pull request through the GitHub website.

Pull Request Guidelines¶

Before you submit a pull request, check that it meets these guidelines:

The pull request should include tests.
If the pull request adds functionality, the docs should be updated. Put your new functionality into a function with a docstring, and add the feature to the list in README.rst.
The pull request should work for Python 2.7, 3.4, 3.5 and 3.6, and for PyPy. Check https://travis-ci.org/lepy/phuzzy/pull_requests and make sure that the tests pass for all supported Python versions.

Tips¶

To run a subset of tests:

$ py.test tests.test_phuzzy

Deploying¶

A reminder for the maintainers on how to deploy. Make sure all your changes are committed (including an entry in HISTORY.rst). Then run:

$ git push
$ git push --tags

Travis will then deploy to PyPI if tests pass.

Credits¶

Development Lead¶

Lepy <lepy@mailbox.org>

Contributors¶

None yet. Why not be the first?

History¶

0.4.0 (2018-04-13)¶

First release on PyPI.

0.5.0 (2018-04-16)¶

rename FuzzyNumber.df.columns = [“alpha”, “l”, “r”]
add operators __add__
add operators __sub__
add operators __mul__
add operators __div__

0.6.0 (2018-04-19)¶

add operators __radd__, __rsub__, __rmul__, __rdiv__, __truediv__
add operators __neg__, __abs__, __min__, __max__, __mean__
add operators __lt__, __gt__, __eq__, __contain__

0.7.0 (2018-04-24)¶

add plots
add approximated function evaluation

lsdyna

Welcome to phuzzy’s documentation!¶

phuzzy¶

Features¶

Credits¶

Installation¶

Stable release¶

From sources¶

Usage¶

available shapes¶

Uniform¶

Triangle¶

Trapezoid¶

TruncNorm¶

TruncGenNorm¶

Superellipse¶

basic operations¶

Addition¶

Substraction¶

Multiplication¶

Division¶

Exponentiation¶

Negation¶

Absolute value¶

Shapes¶

Uniform¶

Triangle¶

Trapezoid¶

TruncNorm¶

TruncGenNorm¶

Superellipse¶

Plots¶

Examples¶

Three-point bending¶

Simply supported beam with central load¶

Code¶

Parameter¶

Results¶

phuzzy package¶

phuzzy.shapes package¶

phuzzy.shapes.superellipse module¶

phuzzy.shapes.truncnorm module¶

phuzzy.mpl module¶

Contributing¶

Types of Contributions¶

Report Bugs¶

Fix Bugs¶

Implement Features¶

Write Documentation¶

Submit Feedback¶

Get Started!¶

Pull Request Guidelines¶

Tips¶

Deploying¶

Credits¶

Development Lead¶

Contributors¶

History¶

0.4.0 (2018-04-13)¶

0.5.0 (2018-04-16)¶

0.6.0 (2018-04-19)¶

0.7.0 (2018-04-24)¶

Indices and tables¶