FAME: Introducing Fuzzy Additive Models for Explainable AI

In this study, we introduce the Fuzzy Additive Model (FAM) and FAM with Explainability (FAME) as a solution for Explainable Artificial Intelligence (XAI). The family consists of three layers: (1) a Projection Layer that compresses the input space, (2) a Fuzzy Layer built upon Single Input-Single Output Fuzzy Logic Systems (SFLS), where SFLS functions as subnetworks within an additive index model, and (3) an Aggregation Layer. This architecture integrates the interpretability of SFLS, which uses human-understandable if-then rules, with the explainability of input-output relationships, leveraging the additive model structure. Furthermore, using SFLS inherently addresses issues such as the curse of dimensionality and rule explosion. To further improve interpretability, we propose a method for sculpting antecedent space within FAM, transforming it into FAME. We show that FAME captures the input-output relationships with fewer active rules, thus improving clarity. To learn the FAM family, we present a deep learning framework. Through the presented comparative results, we demonstrate the promising potential of FAME in reducing model complexity while retaining interpretability, positioning it as a valuable tool for XAI.