Regression Examples

Ex-Fuzzy learns interpretable Type-1 fuzzy rules for continuous targets with ex_fuzzy.BaseFuzzyRulesRegressor. The estimator provides the familiar fit, predict, and score methods; score returns \(R^2\).

Train/Test Workflow

This example uses crisp zero-order Takagi-Sugeno consequents, where each rule learns a numeric output:

from ex_fuzzy import BaseFuzzyRulesRegressor
from sklearn.datasets import make_friedman1
from sklearn.model_selection import train_test_split

X, y = make_friedman1(
    n_samples=500,
    n_features=5,
    noise=0.5,
    random_state=0,
)
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.25, random_state=0
)

regressor = BaseFuzzyRulesRegressor(
    nRules=20,
    nAnts=3,
    consequent_type="crisp",
    backend="pymoo",
)
regressor.fit(X_train, y_train, n_gen=50, pop_size=50)

predictions = regressor.predict(X_test)
print(f"Test R2: {regressor.score(X_test, y_test):.3f}")
regressor.print_rules()

Predictions are the firing-strength-weighted average of active rule consequents. If no rule clears the tolerance, the model returns the training target mean.

Mamdani Consequents

Use consequent_type="fuzzy" when rules should name linguistic output sets. The optimizer learns the trapezoidal output sets as part of the chromosome, and predictions are centroid-defuzzified values.

mamdani = BaseFuzzyRulesRegressor(
    nRules=20,
    nAnts=3,
    consequent_type="fuzzy",
    n_output_lvs=4,
    n_universe_points=101,
    backend="pymoo",
)
mamdani.fit(X_train, y_train, n_gen=50, pop_size=50)
mamdani.print_rules()
# Rule 1: IF x0 IS Low AND x2 IS High THEN output IS Output_3

GPU-Accelerated EvoX

Install the optional EvoX dependencies and select the backend on the same estimator:

python -m pip install "ex-fuzzy[evox]"

gpu_regressor = BaseFuzzyRulesRegressor(
    nRules=30,
    nAnts=4,
    consequent_type="crisp",  # "fuzzy" is accelerated too
    backend="evox",
    verbose=True,
)
gpu_regressor.fit(X_train, y_train, n_gen=50, pop_size=100)

print(gpu_regressor.optimization_device_)  # "cuda" or "cpu"
print(gpu_regressor.gpu_accelerated_)      # True only on CUDA

EvoX evolves the population while Ex-Fuzzy evaluates the complete regression objective in PyTorch. CUDA is selected automatically when available; otherwise the same implementation runs on CPU. Population and sample batching adapts to available memory.

Rule Modes

rule_mode="additive" lets every active rule contribute to the prediction. rule_mode="sufficient" keeps only the strongest rule for each sample:

winner_takes_all = BaseFuzzyRulesRegressor(
    nRules=20,
    nAnts=3,
    rule_mode="sufficient",
    tolerance=0.05,
    backend="evox",
)

See Fuzzy Regression for modeling guidance and Fuzzy Regression for the complete parameter reference.