zadeh package

Subpackages

• zadeh.compile package
  • Module contents

Submodules

zadeh.domains module

class zadeh.domains.CategoricalDomain(name, values)

Bases: zadeh.domains.Domain

centroid(set)

get_ipywidget(**kwargs)

Get a widget representing the domain

get_mesh()

Get a mesh representing the domain

class zadeh.domains.Domain(name)

Bases: object

A domain where diffuse sets are defined

defuzzify(set)

Calculate a crisp number from the fuzzy set

evaluate_set(set)

Get a pair of list with a mesh representing the domain and the evaluation of a membership function on it

get_ipywidget(**kwargs)

Get a widget representing the domain

get_mesh()

Get a mesh representing the domain

plot_set(set, **kwargs)

Plot a fuzzy set

class zadeh.domains.FloatDomain(name, min, max, steps)

Bases: zadeh.domains.Domain

bisector(set)

Defuzzify with the bisector (value separating two portions of equal area under the membership function)

centroid(set)

Defuzzify with the centroid (center of mass)

defuzzify(set)

Calculate a crisp number from the fuzzy set

get_ipywidget(**kwargs)

Get a widget representing the domain

get_mesh()

Get a mesh representing the domain

lom(set)

Defuzzify with the largest of maximum

mom(set)

Defuzzify with the middle of maximum

som(set)

Defuzzify with the smaller of maximum

zadeh.fis module

class zadeh.fis.FIS(variables, rules, target, defuzzification='centroid', aggregation='max', implication='min', AND='min', OR='max')

Bases: object

A fuzzy inference system

batch_predict(X)

Get the crisp output for a batch of inputs

Parameters

X (pd.DataFrame or np.array or list of list) – Input values. If pandas dataframe, must have a column for each of the variables with the same name. If array-like, order must be consistent with the variables.

Returns

An array with the predictions.

Return type

np.array

compile()

Get a compiled version of the model

dict_to_ordered(values)

Transform a dict of inputs into an array in the FIS order

static from_matlab(path)

Import a MATLAB® model from a .fis file

get_1d_interactive(variable, continuous_update=False)

Produce an interactive plot with the output as a function of a variable when the rest are fixed.

Parameters

• variable (FuzzyVariable) – The independent variable.

• continuous_update (bool) – Whether to continuously update with the widgets value.

get_2d_interactive(variable1, variable2, continuous_update=False)

Produce an interactive plot with the output as a function of two variables when the rest are fixed.

Parameters

• variable1 (FuzzyVariable) – The first independent variable.

• variable2 (FuzzyVariable) – The second independent variable.

• continuous_update (bool) – Whether to continuously update with the widgets value.

get_crisp_output(values)

Get the output of the system as a crisp value

Parameters

values (dict of str) – A mapping from variables to their fuzzy values.

Returns

Centroid of the output of the system

get_interactive(continuous_update=False)

Display an interactive plot with the fuzzy output of the FIS

Parameters

continuous_update (bool) – Whether to continuously update with the widgets value.

get_output(values)

Get the output of the system as a fuzzy set

Parameters

values (dict of str) – A mapping from variables to their fuzzy values.

Returns

The fuzzy set

Return type

FuzzySet

static load(path)

Load a FIS from the given path

plot_1d(variable, fixed_variables=None, axes=None)

Produce a plot with the output as a function of a variable when the rest are fixed.

Parameters

• variable (FuzzyVariable) – The independent variable.

• fixed_variables (dict of str) – A mapping with fuzzy values of the rest of the variables.

• axes (plt.Axes) – An existing axes instance to plot. If None, a new figure is created.

Returns

Axes for further tweaking

Return type

plt.Axes

plot_2d(variable1, variable2, fixed_variables=None, axes=None)

Produce a plot with the output as a function of two variables when the rest are fixed.

Parameters

• variable1 (FuzzyVariable) – The first independent variable.

• variable2 (FuzzyVariable) – The second independent variable.

• fixed_variables (dict of str) – A mapping with fuzzy values of the rest of the variables.

• axes (plt.Axes) – An existing axes instance to plot. An 3D projection must have been set on it. If None, a new figure is created.

Returns

Axes for further tweaking

Return type

plt.Axes

plot_rules(values, color='k')

Produce a plot which can be used to explain the behaviour of the system for the given set of values

Parameters

• values (dict of str) – A mapping from variables to their values.

• color (str) – Color used to plot rule activation

Returns

2-tuple of (fig, axes) for further tweaking

plot_rules_interactive(continuous_update=False)

Create an interactive explorer for the plot_rules method

Parameters

continuous_update (bool) – Whether to continuously update with the widgets value.

save(path)

Save the FIS definition to a path

zadeh.mparser module

Matlab .fis-like parser

zadeh.mparser.parse_mf(description)

Parse a membership function

Parameters

description (str) – A line defining the membership function.

Returns

A fuzzy set defined by the membership function

Return type

FuzzySet

zadeh.mparser.parse_rule(rule, operation, inputs, output)

Parse a line defining a fuzzy rule

Parameters

• rule (str) – Line defining the rule

• operation (str) – “1” for “and”, “2” for “or” (file format meaning).

• inputs (list of FuzzyVariable) – The ordered list of inputs.

• output (FuzzyVariable) – The output of the system

Returns

The description of the fuzzy rule

Return type

FuzzyRule

zadeh.mparser.parse_variable(variable, steps=100)

Parse a section defining a fuzzy variable

Parameters

• variable – Section of the file defining the variable.

• steps (int) – The number of steps for FloatDomain.

Returns

A representation of the variable

Return type

FuzzyVariable

zadeh.mparser.read_mfis(path, steps=100)

Parse a MATLAB® Fuzzy Inference System-like file

zadeh.rules module

class zadeh.rules.FuzzyAnd(proposition_list)

Bases: zadeh.rules.FuzzyProposition

A fuzzy proposition of the form <p1> and <p2>

class zadeh.rules.FuzzyNot(proposition)

Bases: zadeh.rules.FuzzyProposition

A fuzzy proposition of the form ‘not <p>’

class zadeh.rules.FuzzyNotValuation(variable, value)

Bases: zadeh.rules.FuzzyProposition

An ‘elemental’ fuzzy proposition of the form <variable> is not <value>

While this could be described using the unitary negation operator, the class is provided for convenience

class zadeh.rules.FuzzyOr(proposition_list)

Bases: zadeh.rules.FuzzyProposition

A fuzzy proposition of the form <p1> or <p2>

class zadeh.rules.FuzzyProposition

Bases: object

A fuzzy-logic proposition

class zadeh.rules.FuzzyRule(antecedent, consequent, weight=1.0)

Bases: object

A fuzzy rule of the form ‘if <antecedent> then <consequent>’, possibly with a weight in (0, 1]

class zadeh.rules.FuzzyRuleSet(rule_list)

Bases: object

A set of fuzzy rules

static automatic(antecedent_var, consequent_var, weight=1.0, reverse=False)

class zadeh.rules.FuzzyValuation(variable, value)

Bases: zadeh.rules.FuzzyProposition

An elemental fuzzy proposition of the form ‘<variable> is <value>’

zadeh.rules.prod(xx)

zadeh.server module

zadeh.sets module

class zadeh.sets.BellFuzzySet(a, b, c)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by a generalized Bell MF

:math:`mu_{a,b,c}(x)= frac{1}{1+left|

rac{x-c}{a}right|^{2b}}`

class zadeh.sets.DiscreteFuzzySet(d)

Bases: zadeh.sets.FuzzySet

A discrete fuzzy set (non-null in a discrete set of points)

class zadeh.sets.FuzzySet(mu=None)

Bases: object

A fuzzy set

class zadeh.sets.FuzzySetAnd(sets, method=None)

Bases: zadeh.sets.FuzzySet

An AND operation between Fuzzy sets

class zadeh.sets.FuzzySetNeg(set)

Bases: zadeh.sets.FuzzySet

A negation operation on a Fuzzy set

class zadeh.sets.FuzzySetOr(sets, method=None)

Bases: zadeh.sets.FuzzySet

An OR operation between Fuzzy sets

class zadeh.sets.FuzzySetScaled(set, scale)

Bases: zadeh.sets.FuzzySet

A scaled Fuzzy sets

class zadeh.sets.Gaussian2FuzzySet(s1, a1, s2, a2)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by two Gaussian functions

\[\begin{split}G^2_{s_1,a_1,s_2,a_2}(x) = \begin{cases} G_{s_1, a_1}(x), &\quad\text{if } x\leq a_1\\ 1, &\quad\text{if } a_1 \leq x \leq a_2\\ G_{s_2, a_2}(x), &\quad\text{if } x\geq a_2\\ \end{cases}\end{split}\]

Parameters

• s1 – Width of the first Gaussian.

• a1 – Start of the membership=1.0 plateau.

• s2 – Width of the second Gaussian.

• a2 – End of the membership=1.0 plateau.

class zadeh.sets.GaussianFuzzySet(s, a)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by a Gaussian function

\[G_{s,a}(x) = \mathrm{e}^{-\frac{{(x - a)}^2}{2 s^2}}\]

Parameters

• s – Width of the Gaussian.

• a – Position of the peak of the Gaussian.

class zadeh.sets.PiFuzzySet(a, b, c, d)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by a Pi-shaped function (a combination of S-shaped MF followed by a Z-shaped MF)

\[Z_{a,b,c,d}(x) = S_{a,b}(x)\cdot Z_{c,d}(x)\]

class zadeh.sets.SFuzzySet(a, b)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by an S-shaped function.

\[\begin{split}S_{a,b}(x) = \begin{cases} 0, &\quad\text{if } x\leq a\\ 2\left(\frac{x-a}{b-a}\right)^2, &\quad\text{if } a \leq x\leq \frac{a+b}{2}\\ 1-2\left(\frac{x-b}{b-a}\right)^2, &\quad\text{if } \frac{a+b}{2} \leq x \leq b\\ 1, &\quad\text{if } x\geq b\\ \end{cases}\end{split}\]

class zadeh.sets.SigmoidalDifferenceFuzzySet(a1, c1, a2, c2)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by the difference of two sigmoid functions clipped to [0, 1]

\(\sigma_{a_1,c_1,a_2,c_2}^\mathrm{d}(x)=\mathrm{clip}_{0,1}(\sigma_{a_1,c_1}(x) - \sigma_{a_2,c_2}(x))\)

Typical unimodal membership functions are defined setting the same sign for (a1, a2), and choosing (c1, c2) enough apart for both sigmoids reach ~1 in a common subset.

class zadeh.sets.SigmoidalFuzzySet(a, c)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by a sigmoid function

\(\sigma_{a,c}(x)= \frac{1}{1+e^{\left(-a (x-c)\right)}}\)

If a>0, the sigmoid is increasing, otherwise decreasing. The magnitude of “a” defines the width of the transition, “c” defines its location.

class zadeh.sets.SigmoidalProductFuzzySet(a1, c1, a2, c2)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by the product of two sigmoid functions

\(\sigma_{a_1,c_1,a_2,c_2}^\mathrm{p}(x)=\sigma_{a_1,c_1}(x)\cdot \sigma_{a_2,c_2}(x)\)

Typical unimodal membership functions are defined setting the opposite sign for (a1, a2), and choosing (c1, c2) enough apart for both sigmoids reach ~1 in a common subset.

class zadeh.sets.SingletonSet(x)

Bases: zadeh.sets.FuzzySet

A singleton fuzzy set (Kronecker delta)

class zadeh.sets.TrapezoidalFuzzySet(a, b, c, d)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by a trapezoidal function

class zadeh.sets.TriangularFuzzySet(a, b, c)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by a triangular function

class zadeh.sets.ZFuzzySet(a, b)

Bases: zadeh.sets.FuzzySet

A fuzzy set defined by a Z-shaped function

\[\begin{split}Z_{a,b}(x) = \begin{cases} 0, &\quad\text{if } x\leq a\\ 1-2\left(\frac{x-a}{b-a}\right)^2, &\quad\text{if } a \leq x\leq \frac{a+b}{2}\\ 2\left(\frac{x-b}{b-a}\right)^2, &\quad\text{if } \frac{a+b}{2} \leq x \leq b\\ 1, &\quad\text{if } x\geq b\\ \end{cases}\end{split}\]

zadeh.sets.prod(xx)

zadeh.variables module

class zadeh.variables.FuzzyVariable(domain, values, name=None)

Bases: object

A fuzzy variable

static automatic(name, min, max, steps, values, endpoints=True, value_names=None, width_factor=1.0, shape='gaussian')

Automatically create a fuzzy variable with the number of values provided.

Parameters

• name (str) – Name of the variable and of its domain.

• min (float) – Minimum value of the domain

• max (float) – Maximum value of the domain

• steps (int or float) – Number of steps if int or step size if float.

• values (int) – Number of values.

• endpoints (bool) – Whether the start and ending points are considered.

• value_names (list of str) – Names of values. If not provided or if length does not match, they will be automatically guessed when possible.

• width_factor (float) – A scale factor for the width of the membership function defining the values.

• shape (str) – Kind of sets used to define the values. Available options are: - gaussian: Gaussian sets. - triangular: Triangular sets. - trapezoidal: Trapezoidal sets. - spline: order-2 spline-based sets (S, Pi, Z). - sigmoidald: Sigmoidal functions, using the sigmoidal difference for non-endpoints. - sigmoidalp: Sigmoidal functions, using the sigmoidal product for non-endpoints.

Returns

The automatically generated fuzzy variable.

Return type

FuzzyVariable

plot(value=None)

Plot the membership function for each of the values

Parameters

value (str) – A value to highlight. If so, the other values are shown dimmed and not in the legend

Module contents

zadeh - Python package to build fuzzy inference systems