LR

class floulib.LR(*args, label='', color=None)

Bases: Multilinear

Contains various methods to perform operations on LR (Left-Right) fuzzy intervals, with L(x) = R(x) = max(0, 1-x).

Note

LR is a subclass of Multilinear, therefore all methods in Multilinear may be used.

Multilinear is a subclass of Plot, therefore all methods in Plot may also be used.

__init__(*args, label='', color=None)

Constructor

Parameters:

  • *args (float) –

    With four positional arguments, the LR fuzzy interval is trapezoidal

    • args[0] is m

    • args[1] is m_prime

    • args[2] is a

    • args[3] is b

    With three positional arguments, the LR fuzzy interal is triangular

    • args[0] is m

    • args[1] is a

    • args[2] is b

  • label (str, optional) – Label associated with the LR fuzzy interval. The default is ‘’.

  • color (matplotlib.colors, optional) – Color associated with the LR fuzzy interval. The default is None.

Raises:

Exception – Raised if the number of positional arguments is not 3 or 4.

Return type:

None.

Example

>>> from floulib import LR
>>> A = LR(1,1,2, label='A')
>>> B = LR(3,4,1,3, label='B')
>>> A.plot(xlim=[0,8]).add_plot(B)
_images/LR.__init__.png
area()

Area of a LR fuzzy interval.

Returns:

Area of the LR fuzzy interval.

Return type:

float

Example

>>> from floulib import LR
>>> A = LR(1, 0.5, 1)
>>> B = Trapezoid (0.5, 1, 2, 4)
>>> print(f'Area: A = {A.area():.3f}, B = {B.area():.3f}')
Area: A = 0.750, B = 2.250
centroid()

Centroid of a LR fuzzy interval.

Returns:

Centroid of the LR fuzzy interval.

Return type:

float

Example

>>> from floulib import LR
>>> A = LR(1, 0.5, 1)
>>> B = Trapezoid (0.5, 1, 2, 4)
>>> print(f'Centroid: A = {A.centroid():.3f}, B = {B.centroid():.3f}')
Centroid: A = 1.167, B = 1.944
is_precise()

Returns True if the LR fuzzy interval is precise.

Return type:

boolean

Example

>>> from floulib import LR
>>> A = LR(1, 0.5, 1)
>>> B = LR(1, 0, 0)
>>> print(A.is_precise(), B.is_precise())
False True
membership(x)

Computes the grade of membership of a point x to the LR fuzzy interval.

Parameters:

x (float) – The point x.

Returns:

y – The grade of membership.

Return type:

float

Example

>>> from floulib import LR
>>> A = LR(1, 0.5, 1)
>>> print(f'Grade of membership for x = 1.2 is {A.membership(1.2):.2f}')
Grade of membership for x = 1.2 is 0.80
mode()

Mode of a LR fuzzy number.

Returns:

Mean of m and m_prime.

Return type:

float

Example

>>> from floulib import LR
>>> A = LR(1, 0.5, 1)
>>> B = Trapezoid (0.5, 1, 2, 4)
>>> print(f'Mode: A = {A.mode():.3f}, B = {B.mode():.3f}')
Mode: A = 1.000, B = 1.500
__add__(other)

Implements + operator between two LR fuzzy intervals.

Parameters:

other (LR) – LR fuzzy interval to add.

Raises:

TypeError – Raised if the RHS operand is not an instance of LR.

Returns:

Addition of the two LR fuzzy intervals.

Return type:

LR

Example

>>> from floulib import LR
>>> A = LR(1,1,2, label = 'A')
>>> B = LR(3,1,1, label = 'B')
>>> C = (A+B).label('C=A+B')
>>> A.plot(xlim=[0,8]).add_plot(B).add_plot(C)
_images/LR.__add__.png
__neg__()

Implements - unary operator of a LR fuzzy interval.

Returns:

Opposite of a LR fuzzy interval.

Return type:

LR

Example

>>> from floulib import LR
>>> A = LR(1,1,2, label = 'A')
>>> C = (-A).label('C=-A')
>>> A.plot(xlim=[-4,4]).add_plot(C)
_images/LR.__neg__.png
__sub__(other)

Implements - operator between two LR fuzzy intervals.

Parameters:

other (LR) – LR fuzzy interval to substract.

Raises:

TypeError – Raised if the RHS operand is not an instance of LR.

Returns:

Difference of the two LR fuzzy intervals.

Return type:

LR

Example

>>> from floulib import LR
>>> A = LR(1,1,2, label = 'A')
>>> B = LR(3,1,1, label = 'B')
>>> C = (A-B).label('C=A-B')
>>> A.plot(xlim=[-5,5]).add_plot(B).add_plot(C)
_images/LR.__sub__.png
__str__()

Special method for printable string representation.

Returns:

Printable string.

Return type:

str

Example

>>> from floulib import LR
>>> A = LR(1,1,2)
>>> B = LR(3,4,1,3)
>>> print(A+B)
LR(4.00, 5.00, 2.00, 5.00)