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fuzzy_operations.py
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import matplotlib.pyplot as plt
import numpy as np
""""
FuzzySet class for triangular fuzzy sets
Author: Shreya123714
Source: https://en.wikipedia.org/wiki/Fuzzy_set
"""
class FuzzySet:
"""
A class for representing and
manipulating triangular fuzzy sets.
Attributes:
name (str): The name or label of the fuzzy set.
a (float): The left boundary of the fuzzy set.
b (float): The peak (central) value of the fuzzy set.
c (float): The right boundary of the fuzzy set.
Methods:
membership(x): Calculate the membership value
of an input 'x' in the fuzzy set.
union(other): Calculate the union of this fuzzy set
with another fuzzy set.
intersection(other): Calculate the intersection of this fuzzy set
with another fuzzy set.
complement(): Calculate the complement (negation)
of this fuzzy set.
plot(): Plot the membership function of the fuzzy set.
"""
def __init__(self, name, a, b, c):
"""
Initializes a triangular fuzzy set
with the given parameters.
Args:
name (str): The name or label of the fuzzy set.
a (float): The left boundary of the fuzzy set.
b (float): The peak (central) value of
the fuzzy set.
c (float): The right boundary of the fuzzy set.
"""
self.name = name # Fuzzy set name
self.a = a # Left boundary
self.b = b # Peak value
self.c = c # Right boundary
def membership(self, x):
"""
Calculate the membership value of
an input 'x' in the fuzzy set.
Args:
x (float): The input value for
which the membership is calculated.
Returns:
float: The membership value of 'x' in
the fuzzy set.
"""
if x <= self.a or x >= self.c:
return 0
elif self.a < x <= self.b:
return (x - self.a) / (self.b - self.a)
elif self.b < x < self.c:
return (self.c - x) / (self.c - self.b)
def union(self, other):
"""
Calculate the union of this fuzzy set
with another fuzzy set.
Args:
other (FuzzySet): Another fuzzy set
to union with.
Returns:
FuzzySet: A new fuzzy
set representing the union.
"""
union_name = f"{self.name} ∪ {other.name}"
return FuzzySet(
union_name,
min(self.a, other.a),
max(self.c, other.c),
(self.b + other.b) / 2,
)
def intersection(self, other):
"""
Calculate the intersection of this
fuzzy set with another fuzzy set.
Args:
other (FuzzySet): Another fuzzy set to intersect with.
Returns:
FuzzySet: A new fuzzy set representing the intersection.
"""
intersection_name = f"{self.name} ∩ {other.name}"
return FuzzySet(
intersection_name,
max(self.a, other.a),
min(self.c, other.c),
(self.b + other.b) / 2,
)
def complement(self):
"""
Calculate the complement (negation) of this fuzzy set.
Returns:
FuzzySet: A new fuzzy set representing the complement.
"""
complement_name = f"¬{self.name}"
return FuzzySet(complement_name, 1 - self.c, 1 - self.a, 1 - self.b)
def plot(self):
"""
Plot the membership function of the fuzzy set.
"""
x = np.linspace(0, 1, 1000)
y = [self.membership(xi) for xi in x]
plt.plot(x, y, label=self.name)
def __str__(self):
return f"{self.name}: [{self.a}, {self.b}, {self.c}]"
# Example usage:
if __name__ == "__main__":
A = FuzzySet("A", 0, 0.5, 1)
B = FuzzySet("B", 0.2, 0.7, 1)
A.plot()
B.plot()
plt.xlabel("x")
plt.ylabel("Membership")
plt.legend()
plt.show()
union_ab = A.union(B)
intersection_ab = A.intersection(B)
complement_a = A.complement()
union_ab.plot()
intersection_ab.plot()
complement_a.plot()
plt.xlabel("x")
plt.ylabel("Membership")
plt.legend()
plt.show()