trapezoidal fuzzy set

DIRECTORY.md

@@ -447,6 +447,7 @@
 
 ## Fuzzy Logic
   * [Fuzzy Operations](fuzzy_logic/fuzzy_operations.py)
+  * [Trapazoidal Fuzzyset](fuzzy_logic/trapazoidal_fuzzyset.py)
 
 ## Genetic Algorithm
   * [Basic String](genetic_algorithm/basic_string.py)

fuzzy_logic/trapazoidal_fuzzyset.py

@@ -0,0 +1,122 @@
+"""
+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 matplotlib.pyplot as plt
+import numpy as np
+
+
+@dataclass
+class TrapezoidalFuzzySet:
+    """
+    Represents and manipulates trapezoidal fuzzy sets.
+
+    Attributes:
+        name: The name or label of the fuzzy set.
+        left_base: The left base of the trapezoid.
+        left_peak: The top left vertex of the trapezoid.
+        right_peak: The top right vertex of the trapezoid.
+        right_base: The right base of the trapezoid.
+        is_complement: Indicates if this is the complement of the fuzzy set.
+
+    Methods:
+        membership(value): Calculates membership value for input 'value'.
+        complement(): Creates left_base TrapezoidalFuzzySet instance representing
+            the complement.
+        plot(): Plots the membership function of the fuzzy set.
+    """
+
+    name: str
+    left_base: float
+    left_peak: float
+    right_peak: float
+    right_base: float
+    is_complement: bool = False  # Flag for complement set
+
+    def membership(self, value: float) -> float:
+        """
+        Calculates membership value for input 'value'. For complement sets,
+        returns 1 - trapezoidal membership.
+
+        >>> TrapezoidalFuzzySet("Medium", 0, 1, 2, 3).membership(1)
+        1.0
+        >>> TrapezoidalFuzzySet("Medium", 0, 1, 2, 3).membership(0.5)
+        0.5
+        """
+        if value < self.left_base or value > self.right_base:
+            membership_value = 0.0
+        elif self.left_base <= value < self.left_peak:
+            membership_value = (value - self.left_base) / (
+                self.left_peak - self.left_base
+            )
+        elif self.left_peak <= value <= self.right_peak:
+            membership_value = 1.0
+        elif self.right_peak < value <= self.right_base:
+            membership_value = (self.right_base - value) / (
+                self.right_base - self.right_peak
+            )
+
+        # For complements, invert the membership value
+        return membership_value if not self.is_complement else 1 - membership_value
+
+    def complement(self) -> TrapezoidalFuzzySet:
+        """
+        Creates a new TrapezoidalFuzzySet instance representing the complement.
+
+        >>> TrapezoidalFuzzySet("Medium", 0, 1, 2, 3).complement().membership(1)
+        0.0
+        """
+        return TrapezoidalFuzzySet(
+            f"¬{self.name}",
+            self.left_base,
+            self.left_peak,
+            self.right_peak,
+            self.right_base,
+            is_complement=not self.is_complement,
+        )
+
+    def plot(self) -> None:
+        """
+        Plots the membership function of the trapezoidal fuzzy set.
+
+        >>> fuzzy_set = TrapezoidalFuzzySet("Medium", left_base=0,left_peak=1,
+        ...                                 right_peak=2, right_base=3)
+        >>> fuzzy_set.plot()
+        """
+        x = np.linspace(self.left_base - 1, self.right_base + 1, 1000)
+        y = [self.membership(xi) for xi in x]
+        plt.plot(x, y, label=self.name)
+        plt.xlabel("Value")
+        plt.ylabel("Membership")
+        plt.title(f"Membership Function for {self.name}")
+        plt.grid()
+        plt.legend()
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+
+    # Create an instance of TrapezoidalFuzzySet
+    fuzzy_set = TrapezoidalFuzzySet(
+        "Medium Temperature", left_base=20, left_peak=25, right_peak=30, right_base=35
+    )
+
+    # Display some membership values
+    print(f"Membership at 25: {fuzzy_set.membership(25)}")
+    print(f"Membership at 22: {fuzzy_set.membership(22)}")
+    print(f"Complement Membership at 25: {fuzzy_set.complement().membership(25)}")
+
+    # Plot of Trapezoidal Fuzzy Set and its complement
+    fuzzy_set.plot()
+    fuzzy_set.complement().plot()
+    plt.title("Trapezoidal Fuzzy Set and its Complement")
+    plt.show()