Fractal-Fuzzy Decision Framework for Feature Influence and Selection in Climate-Energy Models

Traditional feature selection methods often overlook complex feature interactions and fail to capture variability and uncertainty in feature contributions, leading to potentially misleading conclusions about their influence. The paper presents a framework that generates triangular fuzzy weights for each feature based on importance scores of PCA (Principal Component Analysis). This approach captures uncertainty and variability. It applies a Mandelbrot fractal transformation to the fuzzy decision matrix, modeling the complex interactions between climate features and peak demand while emphasizing critical influences. Additionally, it creates a fuzzy fractal matrix to adjust feature contributions according to fractal principles. We also established the Fuzzy Fractal Closeness Coefficient (FFCC), integrating PCA-explained variance and introducing an adaptive parameter for dynamic weighting, which recalibrates the fractal influence and FFCC to measure closeness to ideal solutions, resulting in an interpretable closeness score. To apply the method in a real-world setting, we used multivariate data from CEBECO and PAGASA to predict peak demand from weather features. After applying the approach, the temperature-related variables yield <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$F F C C \approx 0.99$</tex> to the most critical contributors to variability in peak energy demand. For instance, in energy demand forecasting, the paper demonstrates that temperaturerelated features (TMAX, TMIN, TMEAN) gain stronger influence as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> increases, while the relevance of rainfall and wind speed diminishes. The balance of the deterministic structure of fractal influence with the flexibility of fuzzy reasoning yields robust feature selection.