diff --git a/fuzzy_logic/fuzzy_operations.py b/fuzzy_logic/fuzzy_operations.py new file mode 100644 index 000000000000..e41cd2120049 --- /dev/null +++ b/fuzzy_logic/fuzzy_operations.py @@ -0,0 +1,195 @@ +""" +By @Shreya123714 + +https://en.wikipedia.org/wiki/Fuzzy_set +""" + +from __future__ import annotations + +from dataclasses import dataclass + +import matplotlib.pyplot as plt +import numpy as np + + +@dataclass +class FuzzySet: + """ + A class for representing and manipulating triangular fuzzy sets. + Attributes: + name: The name or label of the fuzzy set. + left_boundary: The left boundary of the fuzzy set. + peak: The peak (central) value of the fuzzy set. + right_boundary: 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. + complement(): Calculate the complement (negation) of this fuzzy set. + plot(): Plot the membership function of the fuzzy set. + + >>> sheru = FuzzySet("Sheru", 0.4, 1, 0.6) + >>> sheru + FuzzySet(name='Sheru', left_boundary=0.4, peak=1, right_boundary=0.6) + >>> str(sheru) + 'Sheru: [0.4, 1, 0.6]' + + >>> siya = FuzzySet("Siya", 0.5, 1, 0.7) + >>> siya + FuzzySet(name='Siya', left_boundary=0.5, peak=1, right_boundary=0.7) + + # Complement Operation + >>> sheru.complement() + FuzzySet(name='¬Sheru', left_boundary=0.4, peak=0.6, right_boundary=0) + >>> siya.complement() # doctest: +NORMALIZE_WHITESPACE + FuzzySet(name='¬Siya', left_boundary=0.30000000000000004, peak=0.5, + right_boundary=0) + + # Intersection Operation + >>> siya.intersection(sheru) + FuzzySet(name='Siya ∩ Sheru', left_boundary=0.5, peak=0.6, right_boundary=1.0) + + # Membership Operation + >>> sheru.membership(0.5) + 0.16666666666666663 + >>> sheru.membership(0.6) + 0.0 + + # Union Operations + >>> siya.union(sheru) + FuzzySet(name='Siya ∪ Sheru', left_boundary=0.4, peak=0.7, right_boundary=1.0) + """ + + name: str + left_boundary: float + peak: float + right_boundary: float + + def __str__(self) -> str: + """ + >>> FuzzySet("fuzzy_set", 0.1, 0.2, 0.3) + FuzzySet(name='fuzzy_set', left_boundary=0.1, peak=0.2, right_boundary=0.3) + """ + return ( + f"{self.name}: [{self.left_boundary}, {self.peak}, {self.right_boundary}]" + ) + + def complement(self) -> FuzzySet: + """ + Calculate the complement (negation) of this fuzzy set. + Returns: + FuzzySet: A new fuzzy set representing the complement. + + >>> FuzzySet("fuzzy_set", 0.1, 0.2, 0.3).complement() + FuzzySet(name='¬fuzzy_set', left_boundary=0.7, peak=0.9, right_boundary=0.8) + """ + return FuzzySet( + f"¬{self.name}", + 1 - self.right_boundary, + 1 - self.left_boundary, + 1 - self.peak, + ) + + def intersection(self, other) -> FuzzySet: + """ + Calculate the intersection of this fuzzy set + with another fuzzy set. + Args: + other: Another fuzzy set to intersect with. + Returns: + A new fuzzy set representing the intersection. + + >>> FuzzySet("a", 0.1, 0.2, 0.3).intersection(FuzzySet("b", 0.4, 0.5, 0.6)) + FuzzySet(name='a ∩ b', left_boundary=0.4, peak=0.3, right_boundary=0.35) + """ + return FuzzySet( + f"{self.name} ∩ {other.name}", + max(self.left_boundary, other.left_boundary), + min(self.right_boundary, other.right_boundary), + (self.peak + other.peak) / 2, + ) + + def membership(self, x: float) -> float: + """ + Calculate the membership value of an input 'x' in the fuzzy set. + Returns: + The membership value of 'x' in the fuzzy set. + + >>> a = FuzzySet("a", 0.1, 0.2, 0.3) + >>> a.membership(0.09) + 0.0 + >>> a.membership(0.1) + 0.0 + >>> a.membership(0.11) + 0.09999999999999995 + >>> a.membership(0.4) + 0.0 + >>> FuzzySet("A", 0, 0.5, 1).membership(0.1) + 0.2 + >>> FuzzySet("B", 0.2, 0.7, 1).membership(0.6) + 0.8 + """ + 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) + msg = f"Invalid value {x} for fuzzy set {self}" + raise ValueError(msg) + + 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. + + >>> FuzzySet("a", 0.1, 0.2, 0.3).union(FuzzySet("b", 0.4, 0.5, 0.6)) + FuzzySet(name='a ∪ b', left_boundary=0.1, peak=0.6, right_boundary=0.35) + """ + return FuzzySet( + f"{self.name} ∪ {other.name}", + min(self.left_boundary, other.left_boundary), + max(self.right_boundary, other.right_boundary), + (self.peak + other.peak) / 2, + ) + + 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) + + +if __name__ == "__main__": + from doctest import testmod + + testmod() + 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()