From c072d085dadd511701e43cf43840993c70da6958 Mon Sep 17 00:00:00 2001 From: Shreya123714 <yadavshreya400@gmail.com> Date: Wed, 30 Oct 2024 16:46:13 +0530 Subject: [PATCH] Add guassian fuzzy set and its operations --- fuzzy_logic/gaussian_fuzzyset.py | 93 ++++++++++++++++++++++++++++++++ 1 file changed, 93 insertions(+) create mode 100644 fuzzy_logic/gaussian_fuzzyset.py diff --git a/fuzzy_logic/gaussian_fuzzyset.py b/fuzzy_logic/gaussian_fuzzyset.py new file mode 100644 index 000000000..8ca8947d9 --- /dev/null +++ b/fuzzy_logic/gaussian_fuzzyset.py @@ -0,0 +1,93 @@ +""" +By @Shreya123714 + +https://en.wikipedia.org/wiki/Fuzzy_set +https://en.wikipedia.org/wiki/Fuzzy_set_operations +https://en.wikipedia.org/wiki/Membership_function_(mathematics) +""" + +from __future__ import annotations +from dataclasses import dataclass +import numpy as np +import matplotlib.pyplot as plt + +@dataclass +class GaussianFuzzySet: + """ + A class for representing and manipulating Gaussian fuzzy sets. + + Attributes: + name: The name or label of the fuzzy set. + mean: The mean value (center) of the Gaussian fuzzy set. + std_dev: The standard deviation (controls the spread) of the Gaussian fuzzy set. + is_complement: Indicates whether this is the complement of the original fuzzy set. + + Methods: + membership(x): Calculate the membership value of an input 'x' in the fuzzy set. + complement(): Create a new GaussianFuzzySet instance representing the complement. + plot(): Plot the membership function of the fuzzy set. + + >>> fuzzy_set = GaussianFuzzySet("Medium Temperature", mean=25, std_dev=5) + >>> fuzzy_set.membership(25) + 1.0 + >>> fuzzy_set.membership(30) + 0.6065306597126334 + >>> fuzzy_set.complement().membership(25) + 0.0 + """ + + name: str + mean: float + std_dev: float + is_complement: bool = False # This flag indicates if it's the complement set + + def membership(self, x: float) -> float: + """ + Calculate the membership value of an input 'x' in the Gaussian fuzzy set. + If it's a complement set, returns 1 - the Gaussian membership. + + >>> GaussianFuzzySet("Medium", 0, 1).membership(0) + 1.0 + >>> GaussianFuzzySet("Medium", 0, 1).membership(1) + 0.6065306597126334 + """ + membership_value = np.exp(-0.5 * ((x - self.mean) / self.std_dev) ** 2) + return 1 - membership_value if self.is_complement else membership_value + + def complement(self) -> GaussianFuzzySet: + """ + Create a new GaussianFuzzySet instance representing the complement. + + >>> GaussianFuzzySet("Medium", 0, 1).complement().membership(0) + 0.0 + """ + return GaussianFuzzySet(f"¬{self.name}", self.mean, self.std_dev, is_complement=not self.is_complement) + + def plot(self): + """ + Plot the membership function of the Gaussian fuzzy set. + """ + x = np.linspace(self.mean - 3 * self.std_dev, self.mean + 3 * self.std_dev, 1000) + y = [self.membership(xi) for xi in x] + plt.plot(x, y, label=self.name) + plt.xlabel("x") + plt.ylabel("Membership") + plt.legend() + +if __name__ == "__main__": + from doctest import testmod + testmod() + + # Create an instance of GaussianFuzzySet + fuzzy_set = GaussianFuzzySet("Medium Temperature", mean=25, std_dev=5) + + # Display some membership values + print(f"Membership at mean (25): {fuzzy_set.membership(25)}") + print(f"Membership at 30: {fuzzy_set.membership(30)}") + print(f"Complement Membership at mean (25): {fuzzy_set.complement().membership(25)}") + + # Plot the Gaussian Fuzzy Set and its complement + fuzzy_set.plot() + fuzzy_set.complement().plot() + plt.title("Gaussian Fuzzy Set and its Complement") + plt.show()