|
| 1 | +""" |
| 2 | +By @Shreya123714 |
| 3 | +
|
| 4 | +https://en.wikipedia.org/wiki/Fuzzy_set |
| 5 | +""" |
| 6 | + |
| 7 | +from __future__ import annotations |
| 8 | + |
| 9 | +from dataclasses import dataclass |
| 10 | + |
| 11 | +import matplotlib.pyplot as plt |
| 12 | +import numpy as np |
| 13 | + |
| 14 | + |
| 15 | +@dataclass |
| 16 | +class FuzzySet: |
| 17 | + """ |
| 18 | + A class for representing and manipulating triangular fuzzy sets. |
| 19 | + Attributes: |
| 20 | + name: The name or label of the fuzzy set. |
| 21 | + left_boundary: The left boundary of the fuzzy set. |
| 22 | + peak: The peak (central) value of the fuzzy set. |
| 23 | + right_boundary: The right boundary of the fuzzy set. |
| 24 | + Methods: |
| 25 | + membership(x): Calculate the membership value of an input 'x' in the fuzzy set. |
| 26 | + union(other): Calculate the union of this fuzzy set with another fuzzy set. |
| 27 | + intersection(other): Calculate the intersection of this fuzzy set with another. |
| 28 | + complement(): Calculate the complement (negation) of this fuzzy set. |
| 29 | + plot(): Plot the membership function of the fuzzy set. |
| 30 | +
|
| 31 | + >>> sheru = FuzzySet("Sheru", 0.4, 1, 0.6) |
| 32 | + >>> sheru |
| 33 | + FuzzySet(name='Sheru', left_boundary=0.4, peak=1, right_boundary=0.6) |
| 34 | + >>> str(sheru) |
| 35 | + 'Sheru: [0.4, 1, 0.6]' |
| 36 | +
|
| 37 | + >>> siya = FuzzySet("Siya", 0.5, 1, 0.7) |
| 38 | + >>> siya |
| 39 | + FuzzySet(name='Siya', left_boundary=0.5, peak=1, right_boundary=0.7) |
| 40 | +
|
| 41 | + # Complement Operation |
| 42 | + >>> sheru.complement() |
| 43 | + FuzzySet(name='¬Sheru', left_boundary=0.4, peak=0.6, right_boundary=0) |
| 44 | + >>> siya.complement() # doctest: +NORMALIZE_WHITESPACE |
| 45 | + FuzzySet(name='¬Siya', left_boundary=0.30000000000000004, peak=0.5, |
| 46 | + right_boundary=0) |
| 47 | +
|
| 48 | + # Intersection Operation |
| 49 | + >>> siya.intersection(sheru) |
| 50 | + FuzzySet(name='Siya ∩ Sheru', left_boundary=0.5, peak=0.6, right_boundary=1.0) |
| 51 | +
|
| 52 | + # Membership Operation |
| 53 | + >>> sheru.membership(0.5) |
| 54 | + 0.16666666666666663 |
| 55 | + >>> sheru.membership(0.6) |
| 56 | + 0.0 |
| 57 | +
|
| 58 | + # Union Operations |
| 59 | + >>> siya.union(sheru) |
| 60 | + FuzzySet(name='Siya ∪ Sheru', left_boundary=0.4, peak=0.7, right_boundary=1.0) |
| 61 | + """ |
| 62 | + |
| 63 | + name: str |
| 64 | + left_boundary: float |
| 65 | + peak: float |
| 66 | + right_boundary: float |
| 67 | + |
| 68 | + def __str__(self) -> str: |
| 69 | + """ |
| 70 | + >>> FuzzySet("fuzzy_set", 0.1, 0.2, 0.3) |
| 71 | + FuzzySet(name='fuzzy_set', left_boundary=0.1, peak=0.2, right_boundary=0.3) |
| 72 | + """ |
| 73 | + return ( |
| 74 | + f"{self.name}: [{self.left_boundary}, {self.peak}, {self.right_boundary}]" |
| 75 | + ) |
| 76 | + |
| 77 | + def complement(self) -> FuzzySet: |
| 78 | + """ |
| 79 | + Calculate the complement (negation) of this fuzzy set. |
| 80 | + Returns: |
| 81 | + FuzzySet: A new fuzzy set representing the complement. |
| 82 | +
|
| 83 | + >>> FuzzySet("fuzzy_set", 0.1, 0.2, 0.3).complement() |
| 84 | + FuzzySet(name='¬fuzzy_set', left_boundary=0.7, peak=0.9, right_boundary=0.8) |
| 85 | + """ |
| 86 | + return FuzzySet( |
| 87 | + f"¬{self.name}", |
| 88 | + 1 - self.right_boundary, |
| 89 | + 1 - self.left_boundary, |
| 90 | + 1 - self.peak, |
| 91 | + ) |
| 92 | + |
| 93 | + def intersection(self, other) -> FuzzySet: |
| 94 | + """ |
| 95 | + Calculate the intersection of this fuzzy set |
| 96 | + with another fuzzy set. |
| 97 | + Args: |
| 98 | + other: Another fuzzy set to intersect with. |
| 99 | + Returns: |
| 100 | + A new fuzzy set representing the intersection. |
| 101 | +
|
| 102 | + >>> FuzzySet("a", 0.1, 0.2, 0.3).intersection(FuzzySet("b", 0.4, 0.5, 0.6)) |
| 103 | + FuzzySet(name='a ∩ b', left_boundary=0.4, peak=0.3, right_boundary=0.35) |
| 104 | + """ |
| 105 | + return FuzzySet( |
| 106 | + f"{self.name} ∩ {other.name}", |
| 107 | + max(self.left_boundary, other.left_boundary), |
| 108 | + min(self.right_boundary, other.right_boundary), |
| 109 | + (self.peak + other.peak) / 2, |
| 110 | + ) |
| 111 | + |
| 112 | + def membership(self, x: float) -> float: |
| 113 | + """ |
| 114 | + Calculate the membership value of an input 'x' in the fuzzy set. |
| 115 | + Returns: |
| 116 | + The membership value of 'x' in the fuzzy set. |
| 117 | +
|
| 118 | + >>> a = FuzzySet("a", 0.1, 0.2, 0.3) |
| 119 | + >>> a.membership(0.09) |
| 120 | + 0.0 |
| 121 | + >>> a.membership(0.1) |
| 122 | + 0.0 |
| 123 | + >>> a.membership(0.11) |
| 124 | + 0.09999999999999995 |
| 125 | + >>> a.membership(0.4) |
| 126 | + 0.0 |
| 127 | + >>> FuzzySet("A", 0, 0.5, 1).membership(0.1) |
| 128 | + 0.2 |
| 129 | + >>> FuzzySet("B", 0.2, 0.7, 1).membership(0.6) |
| 130 | + 0.8 |
| 131 | + """ |
| 132 | + if x <= self.left_boundary or x >= self.right_boundary: |
| 133 | + return 0.0 |
| 134 | + elif self.left_boundary < x <= self.peak: |
| 135 | + return (x - self.left_boundary) / (self.peak - self.left_boundary) |
| 136 | + elif self.peak < x < self.right_boundary: |
| 137 | + return (self.right_boundary - x) / (self.right_boundary - self.peak) |
| 138 | + msg = f"Invalid value {x} for fuzzy set {self}" |
| 139 | + raise ValueError(msg) |
| 140 | + |
| 141 | + def union(self, other) -> FuzzySet: |
| 142 | + """ |
| 143 | + Calculate the union of this fuzzy set with another fuzzy set. |
| 144 | + Args: |
| 145 | + other (FuzzySet): Another fuzzy set to union with. |
| 146 | + Returns: |
| 147 | + FuzzySet: A new fuzzy set representing the union. |
| 148 | +
|
| 149 | + >>> FuzzySet("a", 0.1, 0.2, 0.3).union(FuzzySet("b", 0.4, 0.5, 0.6)) |
| 150 | + FuzzySet(name='a ∪ b', left_boundary=0.1, peak=0.6, right_boundary=0.35) |
| 151 | + """ |
| 152 | + return FuzzySet( |
| 153 | + f"{self.name} ∪ {other.name}", |
| 154 | + min(self.left_boundary, other.left_boundary), |
| 155 | + max(self.right_boundary, other.right_boundary), |
| 156 | + (self.peak + other.peak) / 2, |
| 157 | + ) |
| 158 | + |
| 159 | + def plot(self): |
| 160 | + """ |
| 161 | + Plot the membership function of the fuzzy set. |
| 162 | + """ |
| 163 | + x = np.linspace(0, 1, 1000) |
| 164 | + y = [self.membership(xi) for xi in x] |
| 165 | + |
| 166 | + plt.plot(x, y, label=self.name) |
| 167 | + |
| 168 | + |
| 169 | +if __name__ == "__main__": |
| 170 | + from doctest import testmod |
| 171 | + |
| 172 | + testmod() |
| 173 | + a = FuzzySet("A", 0, 0.5, 1) |
| 174 | + b = FuzzySet("B", 0.2, 0.7, 1) |
| 175 | + |
| 176 | + a.plot() |
| 177 | + b.plot() |
| 178 | + |
| 179 | + plt.xlabel("x") |
| 180 | + plt.ylabel("Membership") |
| 181 | + plt.legend() |
| 182 | + plt.show() |
| 183 | + |
| 184 | + union_ab = a.union(b) |
| 185 | + intersection_ab = a.intersection(b) |
| 186 | + complement_a = a.complement() |
| 187 | + |
| 188 | + union_ab.plot() |
| 189 | + intersection_ab.plot() |
| 190 | + complement_a.plot() |
| 191 | + |
| 192 | + plt.xlabel("x") |
| 193 | + plt.ylabel("Membership") |
| 194 | + plt.legend() |
| 195 | + plt.show() |
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