A Layered Entropy Model for Transparent Uncertainty Quantification in Medical AI: Advancing Trustworthy Decision Support in Small-Data Clinical Settings

Smaller data environments with expert systems are generally driven by the need for interpretable reasoning frameworks, such as fuzzy rule-based systems (FRBS), which cannot often quantify epistemic uncertainty during decision-making. This study proposes a novel Layered Entropy Model (LEM) comprising three semantic layers: Membership Function Entropy (MFE), Rule Activation Entropy (RAE), and System Output Entropy (SOE). Shannon entropy is applied at each layer to enable granular diagnostic transparency throughout the inference process. The approach was evaluated using both synthetic simulations and a real-world case study on the PIMA Indian Diabetes dataset. In the real data experiment, the system produced sharp, fully confident decisions with zero entropy at all layers, yielding an Epistemic Confidence Index (ECI) of 1.0. The proposed framework maintains full compatibility with conventional Type-1 FRBS design while introducing a computationally efficient and fully interpretable uncertainty quantification capability. The results demonstrate that LEM can serve as a powerful tool for validating expert knowledge, auditing system transparency, and deployment in high-stakes, small-data decision domains, such as healthcare, safety, and finance. The model contributes directly to the goals of explainable artificial intelligence (XAI) by embedding uncertainty traceability within the reasoning process itself.