Fuzzy and Explainable AI for CMB Polarization Segmentation: Regional Stability Under Controlled Perturbations

The cosmic microwave background (CMB) contains key information about the early Universe, particularly through its polarization structure. This work proposes a Fuzzy and Explainable Artificial Intelligence framework (FAS-XAI) for the regional analysis of CMB polarization using Planck SMICA data. From the Stokes components Q and U, the polarization amplitude P and the scalar polarization modes E and B are derived. Regional features are then extracted over a HEALPix grid, considering only polarization-valid regions defined by the Planck polarization mask. Fuzzy C-Means identifies four interpretable polarization regimes: high-polarization structured regions, E-dominated medium-polarization regions, B-enhanced medium-polarization regions, and low-polarization regions. An XGBoost-SHAP layer is used to explain the resulting fuzzy memberships. XGBoost accurately reproduces the memberships, with R2 > 0.98 for all clusters, while SHAP confirms the physical relevance of amplitude-related features and the log(B/E) balance. Finally, controlled perturbations in P and log(B/E) reveal a globally robust fuzzy structure with localized sensitivity. The proposed framework provides an interpretable methodology for studying regional CMB polarization patterns and their stability under controlled perturbations.