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Add FuzzySet Class for Triangular Fuzzy Sets (#11036)
* Added Opertation for triangular fuzzy sets * Added Sources * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix the bug , for which test were failing * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Add type hints and improve parameter names * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Add Test For fuzzy_operations.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix the bug in fuzzy_operations.py * Add test_fuzzy_logic.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix the bug in fuzzy_operations.py & deleted test * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * fixed the typo error * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Again done * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * corrected wrong intendation due to which test fail * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * bug fixed * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Add test_fuzzy_logic * Modified fuzzy_operations.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fixed the bug, made a FuzzySet dataclass * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Replaced assertEqual of unittest to assert python * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * lets see * Changed test * orderd the import statements * Add docstring and dataclass the FuzzySet * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update fuzzy_operations.py * Delete fuzzy_logic/test_fuzzy_logic.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * https://en.wikipedia.org/wiki/Fuzzy_set --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
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Shreya123714
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fuzzy_logic/fuzzy_operations.py
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fuzzy_logic/fuzzy_operations.py
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"""
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By @Shreya123714
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https://en.wikipedia.org/wiki/Fuzzy_set
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"""
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from __future__ import annotations
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from dataclasses import dataclass
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import matplotlib.pyplot as plt
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import numpy as np
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@dataclass
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class FuzzySet:
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"""
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A class for representing and manipulating triangular fuzzy sets.
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Attributes:
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name: The name or label of the fuzzy set.
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left_boundary: The left boundary of the fuzzy set.
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peak: The peak (central) value of the fuzzy set.
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right_boundary: The right boundary of the fuzzy set.
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Methods:
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membership(x): Calculate the membership value of an input 'x' in the fuzzy set.
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union(other): Calculate the union of this fuzzy set with another fuzzy set.
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intersection(other): Calculate the intersection of this fuzzy set with another.
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complement(): Calculate the complement (negation) of this fuzzy set.
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plot(): Plot the membership function of the fuzzy set.
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>>> sheru = FuzzySet("Sheru", 0.4, 1, 0.6)
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>>> sheru
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FuzzySet(name='Sheru', left_boundary=0.4, peak=1, right_boundary=0.6)
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>>> str(sheru)
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'Sheru: [0.4, 1, 0.6]'
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>>> siya = FuzzySet("Siya", 0.5, 1, 0.7)
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>>> siya
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FuzzySet(name='Siya', left_boundary=0.5, peak=1, right_boundary=0.7)
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# Complement Operation
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>>> sheru.complement()
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FuzzySet(name='¬Sheru', left_boundary=0.4, peak=0.6, right_boundary=0)
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>>> siya.complement() # doctest: +NORMALIZE_WHITESPACE
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FuzzySet(name='¬Siya', left_boundary=0.30000000000000004, peak=0.5,
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right_boundary=0)
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# Intersection Operation
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>>> siya.intersection(sheru)
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FuzzySet(name='Siya ∩ Sheru', left_boundary=0.5, peak=0.6, right_boundary=1.0)
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# Membership Operation
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>>> sheru.membership(0.5)
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0.16666666666666663
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>>> sheru.membership(0.6)
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0.0
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# Union Operations
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>>> siya.union(sheru)
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FuzzySet(name='Siya ∪ Sheru', left_boundary=0.4, peak=0.7, right_boundary=1.0)
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"""
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name: str
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left_boundary: float
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peak: float
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right_boundary: float
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def __str__(self) -> str:
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"""
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>>> FuzzySet("fuzzy_set", 0.1, 0.2, 0.3)
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FuzzySet(name='fuzzy_set', left_boundary=0.1, peak=0.2, right_boundary=0.3)
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"""
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return (
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f"{self.name}: [{self.left_boundary}, {self.peak}, {self.right_boundary}]"
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)
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def complement(self) -> FuzzySet:
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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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>>> FuzzySet("fuzzy_set", 0.1, 0.2, 0.3).complement()
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FuzzySet(name='¬fuzzy_set', left_boundary=0.7, peak=0.9, right_boundary=0.8)
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"""
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return FuzzySet(
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f"¬{self.name}",
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1 - self.right_boundary,
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1 - self.left_boundary,
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1 - self.peak,
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)
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def intersection(self, other) -> FuzzySet:
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"""
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Calculate the intersection of this fuzzy set
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with another fuzzy set.
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Args:
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other: Another fuzzy set to intersect with.
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Returns:
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A new fuzzy set representing the intersection.
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>>> FuzzySet("a", 0.1, 0.2, 0.3).intersection(FuzzySet("b", 0.4, 0.5, 0.6))
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FuzzySet(name='a ∩ b', left_boundary=0.4, peak=0.3, right_boundary=0.35)
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"""
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return FuzzySet(
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f"{self.name} ∩ {other.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 membership(self, x: float) -> float:
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"""
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Calculate the membership value of an input 'x' in the fuzzy set.
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Returns:
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The membership value of 'x' in the fuzzy set.
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>>> a = FuzzySet("a", 0.1, 0.2, 0.3)
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>>> a.membership(0.09)
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0.0
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>>> a.membership(0.1)
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0.0
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>>> a.membership(0.11)
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0.09999999999999995
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>>> a.membership(0.4)
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0.0
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>>> FuzzySet("A", 0, 0.5, 1).membership(0.1)
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0.2
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>>> FuzzySet("B", 0.2, 0.7, 1).membership(0.6)
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0.8
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"""
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if x <= self.left_boundary or x >= self.right_boundary:
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return 0.0
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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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msg = f"Invalid value {x} for fuzzy set {self}"
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raise ValueError(msg)
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def union(self, other) -> FuzzySet:
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"""
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Calculate the union of this fuzzy set with another fuzzy set.
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Args:
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other (FuzzySet): Another fuzzy set to union with.
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Returns:
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FuzzySet: A new fuzzy set representing the union.
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>>> FuzzySet("a", 0.1, 0.2, 0.3).union(FuzzySet("b", 0.4, 0.5, 0.6))
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FuzzySet(name='a ∪ b', left_boundary=0.1, peak=0.6, right_boundary=0.35)
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"""
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return FuzzySet(
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f"{self.name} ∪ {other.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 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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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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a = FuzzySet("A", 0, 0.5, 1)
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b = FuzzySet("B", 0.2, 0.7, 1)
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a.plot()
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b.plot()
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plt.xlabel("x")
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plt.ylabel("Membership")
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plt.legend()
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plt.show()
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union_ab = a.union(b)
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intersection_ab = a.intersection(b)
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complement_a = a.complement()
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union_ab.plot()
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intersection_ab.plot()
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complement_a.plot()
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plt.xlabel("x")
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plt.ylabel("Membership")
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plt.legend()
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plt.show()
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