Rule learning

Learning a rule base from data (Wang-Mendel)

wang_mendel generates a Mamdani rule base from data: each sample becomes one rule (picking the highest-membership term per variable), and antecedent conflicts are resolved by rule degree.

import numpy as np
import fuzzytool as fz

X = np.random.default_rng(0).uniform(0, 10, size=(300, 2))
y = (X[:, 0] + X[:, 1]) / 2

a = fz.Variable("a", (0, 10), terms=["lo", "mid", "hi"])
b = fz.Variable("b", (0, 10), terms=["lo", "mid", "hi"])
out = fz.Variable("out", (0, 10), terms=["lo", "mid", "hi"])

sys = fz.wang_mendel(X, y, [a, b], out)   # a ready-to-use Mamdani system
sys(a=8, b=7)    # -> 5.88  (learned system approximates the mean (a + b) / 2)

The input variables supply the partition; the learned system is a plain Mamdani, so it also supports batch predict and serialization.

Tsukamoto inference

Tsukamoto consequents are monotonic membership functions; a rule firing with strength w outputs the value where its consequent reaches w (its inverse), and the system returns the firing-weighted average — no defuzzification.

import fuzzytool as fz

x = fz.Variable("x", (0, 10), terms=["lo", "hi"])
sys = fz.Tsukamoto()
sys.rule(x["lo"], fz.ramp_down(0, 30))   # monotonic consequents only
sys.rule(x["hi"], fz.ramp_up(0, 30))
sys(x=7)    # -> 21.0

Use ramp_up, ramp_down, or sigmoid — each exposes the inverse Tsukamoto needs.