Fuzzify

class floulib.Fuzzify(*args)

Bases: object

__init__(*args)

Constructor

Parameters:

*args (Terms | numpy.ndarray | Tuple[Term]) –

• numpy.ndarray for numeric fuzzification.

• Terms if only one parameter is given or several Term parameters for symbolic defuzzification.

Raises:

• TypeError – Raised if the argument is not an instance of Terms or numpy.ndarray when one parameter is given.

• TypeError – Raised if args are not instances of Term when several parameters are given.

Return type:

None.

numeric(*args)

Numeric fuzzification

Parameters:

x (numbers.Number | Multilinear | Discrete) – The parameter for the fuzzification.

Raises:

TypeError – Raised if the parameter is not an instance of numbers.Number, Multilinear or Discrete.

Return type:

LR | Multilinear | Discrete

Example

>>> from floulib import Fuzzify, LR
>>> x0 = 3
>>> X0 = Fuzzify().numeric(x0)
>>> X0.plot(xlim = [2, 4])
>>> print(X0.is_precise())
True

symbolic(x)

Symbolic fuzzification

Parameters:

x (numbers.Number) – The imput.

Raises:

Exception – Raised if the Terms are not given in the constructor.

Returns:

The symbolic fuzzy subset.

Return type:

Discrete

Example

>>> from floulib import Fuzzify, Term, Triangle
>>> small = Term('small', Triangle(0, 0, 20))
>>> big = Term('big', Triangle(0, 20, 20))
>>> x0 = 12
>>> X0 = Fuzzify(small, big).symbolic(x0)
>>> X0.plot()
>>> print(X0)
0.400/small + 0.600/big

Other solution using Terms

>>> from floulib import Fuzzify, Term, Terms, Triangle
>>> small = Term('small', Triangle(0, 0, 20))
>>> big = Term('big', Triangle(0, 20, 20))
>>> T_size = Terms(small, big)
>>> x0 = 12
>>> X0 = Fuzzify(T_size).symbolic(x0)
>>> X0.plot()
>>> print(X0)
0.400/small + 0.600/big

symbolic_upper(x)

Upper symbolic fuzzification

The upper symbolic fuzzification is obtained by computing, for each term, its possibiliy knowing the input.

Parameters:

x (Multilinear | Discrete) – The input.

Raises:

• Exception – Raised if terms are not provided to the constructor.

• TypeError – Raised if x is not an instance of Multilinear or Discrete.

Returns:

The symbolic fuzzy subset.

Return type:

Discrete

Example

>>> from floulib import Fuzzify, LR, Term, Terms, Triangle
>>> small = Term('small', Triangle(0, 0, 20, label = 'small'))
>>> big = Term('big', Triangle(0, 20, 20, label = 'big'))
>>> T_size = Terms(small, big)
>>> A = LR(12, 1, 1, label = 'A')
>>> X0 = Fuzzify(T_size).symbolic_upper(A)
>>> T_size.plot(nrows = 2).add_plot(A).add_plot(X0, index = 1)
>>> print(X0)
0.429/small + 0.619/big

symbolic_lower(x)

Lower symbolic fuzzification

The lower symbolic fuzzification is obtained by computing, for each term, its necessity knowing the input.

Parameters:

x (Multilinear | Discrete) – The input.

Raises:

• Exception – Raised if terms are not provided to the constructor.

• TypeError – Raised if x is not an instance of Multilinear.

Returns:

The symbolic fuzzy subset.

Return type:

Discrete

Example

>>> from floulib import Fuzzify, LR, Term, Terms, Triangle
>>> small = Term('small', Triangle(0, 0, 20, label = 'small'))
>>> big = Term('big', Triangle(0, 20, 20, label = 'big'))
>>> T_size = Terms(small, big)
>>> A = LR(12, 1, 1, label = 'A')
>>> X0 = Fuzzify(T_size).symbolic_lower(A)
>>> T_size.plot(nrows = 2).add_plot(A).add_plot(X0, index = 1)
>>> print(X0)
0.381/small + 0.571/big