Methodology

Forecast definition

For each product category, the target is demand on date t. Inputs are sales on t-1, t-2, and t-3, plus weather known or forecast for t. This corrects the ambiguous alignment in the original prototype, which used current weather to forecast a different date.

Leakage controls

The primary protocol trains on 2016 and evaluates on 2017. Forward filling is performed within a year, and training medians are the only fallback. Min-Max parameters come exclusively from the training year. Test targets that were originally missing are excluded instead of imputed.

Every model is evaluated from the eighth valid test day onward so the weekly seasonal-naive baseline and three-lag models share exactly the same target dates.

Models

• Seasonal naive: demand from seven days earlier.
• ARIMA: (p,d,q) selected by training-set AIC; the full grid uses p,q=0..3, d=0..1. Evaluation is rolling one-step-ahead: each observed test-day sale becomes history only after that day's forecast has been made.
• LSTM: one 32-unit layer and linear output, Adam at 1e-3, temporal 80/20 training validation, maximum 300 epochs, patience 30.
• EFS sales-only: three normalized lag inputs.
• EFS target-weather: the same lags plus normalized average temperature, humidity, and rainfall for the target date.

EFS first learns a rule base with a genetic algorithm. It then performs Pattern Search parameter tuning, followed by a separate Pattern Search of type-2 lower-scale/lower-lag parameters while upper parameters remain fixed. Two input membership functions give at most 8 sales-only or 64 weather-model rules.

EFS backend identity

The MATLAB R2024b implementation is the reference implementation for thesis alignment. The optional python-it2 backend is an independent zero-order Sugeno implementation for environments without MATLAB. It uses product t-norm firing, interval firing bounds, center-of-sets type reduction, GA rule selection, Pattern Search of upper membership/consequent parameters, and a final Pattern Search of lower uncertainty while the upper parameters are locked. Its lower membership is explicitly defined as min(upper, LowerScale * gaussian(x; center + LowerLag, sigma)).

These backends share data, splits, seeds, metrics, and artifact fields but are not presumed numerically equivalent. The manifest, job, training summary, metrics, predictions, and ablation tables identify the selected backend.

Metrics and explanations

RMSE, MAE, MASE, and sMAPE are computed in original sales units. Normalized RMSE and MAE are reported only for thesis comparison. Three stochastic seeds are summarized as mean and standard deviation at both category and eight-category macro levels. Weather-ablation percentages compare the weather and sales-only EFS variants using the same metric and seed; positive values mean the weather variant reduced error.

Rules are exported with semantic antecedents/consequents, weights, empirical support, and mean and maximum activation on the test input window. They describe associations learned from the data and are not causal claims.