fuzzy_operations.py

import numpy as np

import matplotlib.pyplot as plt

from dataclasses import dataclass
"""
By @Shreya123714

#How fuzzy set is created using FuzzySet Class
>>>me = FuzzySet("Sheru",0.4,1,0.6)
>>>me.__str__()
'Sheru: [0.4, 1, 0.6]'
>>>me
FuzzySet(name='Sheru', left_boundary=0.4, peak=1, right_boundary=0.6)
>>>s = FuzzySet("Siya",0.5,1,0.7)

#Union Operations
>>>s.union(me)
FuzzySet(name='Siya ∪ Sheru', left_boundary=0.4, peak=0.7, right_boundary=1.0)

#Intersection Operation
>>>s.intersection(me)
FuzzySet(name='Siya ∩ Sheru', left_boundary=0.5, peak=0.6, right_boundary=1.0)

#Complement Operation
>>>s.complement()
FuzzySet(name='¬Siya', left_boundary=0.30000000000000004, peak=0.5, right_boundary=0)
"""


@dataclass
class FuzzySet:
    """
    A class for representing and manipulating triangular fuzzy sets.
    Attributes:
        name (str): The name or label of the fuzzy set.
        left_boundary (float): The left boundary of the fuzzy set.
        peak (float): The peak (central) value of the fuzzy set.
        right_boundary (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.
    """

    name: str
    left_boundary: float
    peak: float
    right_boundary: float

    def membership(self, x: float) -> float:
        """
        Calculate the membership value of an input 'x' in the fuzzy set.
        Returns:
            float: The membership value of 'x' in the fuzzy set.
        """
        if x <= self.left_boundary or x >= self.right_boundary:
            return 0.0
        elif self.left_boundary < x <= self.peak:
            return (x - self.left_boundary) / (self.peak - self.left_boundary)
        elif self.peak < x < self.right_boundary:
            return (self.right_boundary - x) / (self.right_boundary - self.peak)

    def union(self, other) -> "FuzzySet":
        """
        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.left_boundary, other.left_boundary),
            max(self.right_boundary, other.right_boundary),
            (self.peak + other.peak) / 2,
        )

    def intersection(self, other) -> "FuzzySet":
        """
        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.left_boundary, other.left_boundary),
            min(self.right_boundary, other.right_boundary),
            (self.peak + other.peak) / 2,
        )

    def complement(self) -> "FuzzySet":
        """
        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.right_boundary,
            1 - self.left_boundary,
            1 - self.peak,
        )

    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.left_boundary}, {self.peak}, {self.right_boundary}]"
        )


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()
else:
    import unittest
    
    from test_fuzzy_logic import TestFuzzySet

    suite = unittest.TestLoader().loadTestsFromTestCase(TestFuzzySet)
    unittest.TextTestRunner(verbosity=2).run(suite)