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132 lines
3.9 KiB
Python
132 lines
3.9 KiB
Python
import matplotlib.pyplot as plt
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import numpy as np
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""""
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FuzzySet class for triangular fuzzy sets
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Author: Shreya123714
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Source: https://en.wikipedia.org/wiki/Fuzzy_set
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"""
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class FuzzySet:
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"""
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A class for representing and
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manipulating triangular fuzzy sets.
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Attributes:
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name (str): The name or label of the fuzzy set.
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a (float): The left boundary of the fuzzy set.
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b (float): The peak (central) value of the fuzzy set.
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c (float): The right boundary of the fuzzy set.
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Methods:
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membership(x): Calculate the membership value
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of an input 'x' in the fuzzy set.
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union(other): Calculate the union of this fuzzy set
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with another fuzzy set.
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intersection(other): Calculate the intersection of this fuzzy set
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with another fuzzy set.
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complement(): Calculate the complement (negation)
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of this fuzzy set.
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plot(): Plot the membership function of the fuzzy set.
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"""
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def __init__(
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self, name: str, left_boundary: float, peak: float, right_boundary: float
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) -> None:
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"""
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Initializes a triangular fuzzy set
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with the given parameters.
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Args:
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name (str): The name or label of the fuzzy set.
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a (float): The left boundary of the fuzzy set.
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b (float): The peak (central) value of
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the fuzzy set.
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c (float): The right boundary of the fuzzy set.
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"""
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self.name = name # Fuzzy set name
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self.left_boundary = left_boundary # Left boundary
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self.peak = peak # Peak value
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self.right_boundary = right_boundary # Right boundary
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def membership(self, x):
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"""
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Calculate the membership value of
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an input 'x' in the fuzzy set.
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Args:
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x (float): The input value for
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which the membership is calculated.
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Returns:
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float: The membership value of 'x' in
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the fuzzy set.
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"""
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if x <= self.left_boundary or x >= self.right_boundary:
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return 0
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elif self.left_boundary < x <= self.peak:
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return (x - self.left_boundary) / (self.peak - self.left_boundary)
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elif self.peak < x < self.right_boundary:
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return (self.right_boundary - x) / (self.right_boundary - self.peak)
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def union(self, other):
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"""
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Calculate the union of this fuzzy set
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with another fuzzy set.
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Args:
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other (FuzzySet): Another fuzzy set
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to union with.
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Returns:
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FuzzySet: A new fuzzy
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set representing the union.
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"""
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union_name = f"{self.name} ∪ {other.name}"
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return FuzzySet(
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union_name,
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min(self.left_boundary, other.left_boundary),
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max(self.right_boundary, other.right_boundary),
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(self.peak + other.peak) / 2,
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)
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def intersection(self, other):
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"""
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Calculate the intersection of this
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fuzzy set with another fuzzy set.
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Args:
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other (FuzzySet): Another fuzzy set to intersect with.
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Returns:
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FuzzySet: A new fuzzy set representing the intersection.
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"""
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intersection_name = f"{self.name} ∩ {other.name}"
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return FuzzySet(
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intersection_name,
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max(self.left_boundary, other.left_boundary),
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min(self.right_boundary, other.right_boundary),
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(self.peak + other.peak) / 2,
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)
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def complement(self):
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"""
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Calculate the complement (negation) of this fuzzy set.
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Returns:
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FuzzySet: A new fuzzy set representing the complement.
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"""
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complement_name = f"¬{self.name}"
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return FuzzySet(complement_name, 1 - self.right_boundary, 1 - self.left_boundary, 1 - self.peak)
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def plot(self):
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"""
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Plot the membership function of the fuzzy set.
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"""
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x = np.linspace(0, 1, 1000)
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y = [self.membership(xi) for xi in x]
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plt.plot(x, y, label=self.name)
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def __str__(self):
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return f"{self.name}: [{self.left_boundary}, {self.peak}, {self.right_boundary}]"
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