Gaussian fuzzy set

DIRECTORY.md

@@ -446,6 +446,7 @@
   * [Vicsek](fractals/vicsek.py)
 
 ## Fuzzy Logic
+  * [Gaussian Fuzzy Set](fuzzy_logic/Gaussian_fuzzy_set.py)
   * [Fuzzy Operations](fuzzy_logic/fuzzy_operations.py)
 
 ## Genetic Algorithm

fuzzy_logic/Gaussian_fuzzy_set.py

@@ -0,0 +1,105 @@
+"""
+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()