fuzzy_logic

Fuzzy Logic

Fuzzy logic generalizes classical (crisp) set theory: instead of an element either belonging to a set or not, it belongs to a degree between 0 and 1. That degree is given by a membership function mu: X -> [0, 1] over a universe of discourse X. Fuzzy logic is widely used in control systems, decision making, and pattern recognition where boundaries are naturally vague ("young", "warm", "fast").

Learn more:

• Fuzzy logic
• Fuzzy set
• Membership function
• T-norm (the family of fuzzy AND/OR operators)

Contents

File	What it does
fuzzy_operations.py	A FuzzySet class modelling a triangular fuzzy number by its (left, peak, right) points, with membership, union, intersection, complement, and plotting. Best when your fuzzy sets are triangular and you want to keep working with the parameters.
fuzzy_set_operations.py	The classic Zadeh operators on sampled membership vectors: union, intersection, complement, difference, algebraic_sum/product, and bounded_sum/difference. Works on any membership shape (triangular, trapezoidal, Gaussian, ...) because it operates on the sampled values directly. Dependency-free (NumPy only).

The two files are complementary: fuzzy_operations.py stays in the parametric (left, peak, right) representation, while fuzzy_set_operations.py works on the discretized membership arrays and therefore supports the full set of Zadeh operators for arbitrary shapes.

Quick example

import numpy as np
from fuzzy_logic.fuzzy_set_operations import (
    triangular_membership,
    fuzzy_union,
    fuzzy_intersection,
)

universe = np.linspace(0, 75, 75)
young = triangular_membership(universe, 0, 25, 50)
middle_aged = triangular_membership(universe, 25, 50, 75)

young_or_middle_aged = fuzzy_union(young, middle_aged)
young_and_middle_aged = fuzzy_intersection(young, middle_aged)

Run the doctests for either module with:

python -m doctest -v fuzzy_logic/fuzzy_set_operations.py