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108 lines
3.3 KiB
Python
108 lines
3.3 KiB
Python
"""
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By @Shreya123714
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https://en.wikipedia.org/wiki/Fuzzy_set
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https://en.wikipedia.org/wiki/Fuzzy_set_operations
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https://en.wikipedia.org/wiki/Membership_function_(mathematics)
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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 numpy as np
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import matplotlib.pyplot as plt
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@dataclass
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class GaussianFuzzySet:
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"""
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A class for representing and manipulating Gaussian fuzzy sets.
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Attributes:
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name: The name or label of the fuzzy set.
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mean: The mean value (center) of the Gaussian fuzzy set.
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std_dev: The standard deviation (controls the spread) of the Gaussian fuzzy set.
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is_complement: Indicates whether this is the complement of the original 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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complement(): Create a new GaussianFuzzySet instance representing the complement.
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plot(): Plot the membership function of the fuzzy set.
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>>> fuzzy_set = GaussianFuzzySet("Medium Temperature", mean=25, std_dev=5)
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>>> fuzzy_set.membership(25)
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1.0
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>>> fuzzy_set.membership(30)
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0.6065306597126334
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>>> fuzzy_set.complement().membership(25)
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0.0
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"""
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name: str
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mean: float
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std_dev: float
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is_complement: bool = False # This flag indicates if it's the complement set
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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 Gaussian fuzzy set.
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If it's a complement set, returns 1 - the Gaussian membership.
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>>> GaussianFuzzySet("Medium", 0, 1).membership(0)
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1.0
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>>> GaussianFuzzySet("Medium", 0, 1).membership(1)
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0.6065306597126334
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"""
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membership_value = np.exp(-0.5 * ((x - self.mean) / self.std_dev) ** 2)
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# Directly return for non-complement or return 1 - membership for complement
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return membership_value if not self.is_complement else 1 - membership_value
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def complement(self) -> GaussianFuzzySet:
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"""
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Create a new GaussianFuzzySet instance representing the complement.
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>>> GaussianFuzzySet("Medium", 0, 1).complement().membership(0)
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0.0
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"""
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return GaussianFuzzySet(
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f"¬{self.name}",
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self.mean,
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self.std_dev,
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is_complement=not self.is_complement,
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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 Gaussian fuzzy set.
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"""
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x = np.linspace(
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self.mean - 3 * self.std_dev, self.mean + 3 * self.std_dev, 1000
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)
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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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plt.xlabel("x")
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plt.ylabel("Membership")
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plt.legend()
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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# Create an instance of GaussianFuzzySet
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fuzzy_set = GaussianFuzzySet("Medium Temperature", mean=25, std_dev=5)
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# Display some membership values
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print(f"Membership at mean (25): {fuzzy_set.membership(25)}")
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print(f"Membership at 30: {fuzzy_set.membership(30)}")
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print(
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f"Complement Membership at mean (25): {fuzzy_set.complement().membership(25)}"
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)
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# Plot the Gaussian Fuzzy Set and its complement
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fuzzy_set.plot()
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fuzzy_set.complement().plot()
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plt.title("Gaussian Fuzzy Set and its Complement")
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plt.show()
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