NFGA-LINEAR: An Explainable Neuro-Fuzzy Genetic Framework for Forecasting Anomaly-Affected Data-Scarce Time Series

Abstract

Reliable forecasting becomes particularly challenging when a time series is short, nonlinear, and contaminated by occasional, abnormal observations. We develop NFGA-LINEAR, an interpretable Takagi–Sugeno–Kang neurofuzzy framework in which a genetic algorithm jointly determines the number of rules and optimizes Gaussian antecedents and rule-specific linear consequents. A robust residual-based procedure was incorporated for anomaly detection. The framework was assessed using weekly data from the Cholera, ILINet, and household electricity series using a leakage-controlled, one-step-ahead walk-forward design. XGBoost, LSTM, NFGA Core, and NFGA-LINEAR were evaluated using ten matched random seeds, whereas deterministic methods were summarized through single-run descriptive comparisons. Performance was dataset-dependent: Persistence produced the lowest RMSE for Cholera, ARIMA ranked first for ILINet, and Prophet and XGBoost differed by only approximately 1.1 × 10−6 RMSE on Electricity. In the prespecified matched ablation, replacing the constant consequents of NFGA-Core with local linear consequents lowered the mean RMSE by 69.0%, 40.2%, and 4.5% for Cholera, ILINet, and Electricity, respectively. Exact Wilcoxon signed-rank tests, followed by Holm correction across the three primary comparisons, gave adjusted p values of 0.0059, 0.0059, and 0.0371. Under synthetic anomaly- injection rates of 5% and 10%, NFGA-LINEAR achieved the highest macro-F1 for Cholera and ILINet, whereas Prophet performed best on Electricity. Fixed-model NFGA-LINEAR inference required approximately 0.081–0.110 ms per observation, with an approximate stored parameter representation of 1.9 2.8 KB. These findings position NFGA-LINEAR as a compact and transparent accuracy–complexity compromise while confirming that neither its forecasting nor detection performance is uniformly superior across datasets.