Fuzzy-Clustered Mixture-of-Experts with Relational Regularization \\ for Interpretable Subgroup Modeling under Data Scarcity

Subgroup discovery in tabular domains frequently suffers from data scarcity, heterogeneous feature scales, and unstable cluster assignments. To address these issues, this study introduces \emph{Fuzzy-Clustered Mixture-of-Experts with Grey-Relational Regularization} (FC--MoE--GR), a unified framework combining grey-system theory with soft partitioning and local-expert modeling. Grey-relational grades serve as feature-level priors that guide both fuzzy membership formation and expert specialization. A variance-reduction perspective is established by deriving a tightened generalization bound induced by the grey regularizer, clarifying its effect on stability and calibration. Empirical evaluations on Telco Churn, Bank Marketing, and the Adult Income dataset show that the proposed design is best understood not only as a predictive model, but as a structured evaluation of calibration, assignment stability, and subgroup interpretability under data scarcity. More broadly, the study serves as a compact theory-linked benchmark for reliable subgroup modeling in limited-data tabular settings.