Algebraic Rule Base Structure: A Cross-Model Analysis Tool by Involving Directional Parameter

Fuzzy Rule Interpolation (FRI) has become an important tool for enhancing reasoning accuracy in systems with sparse rule bases. However, many existing approaches are developed in an ad hoc manner. This paper introduces a formal framework, termed location view, which transforms traditional scalar-based rule representations into an isomorphic geometric space. Through mathematical formalisation, the framework provides a tool that focusses on the impact of an individual rule in a rule interpolation process. In addition, by integrating both distance and directional parameters, the proposed framework addresses limitations of conventional methods caused by their relying solely on scalar metrics, such as the Euclidean distance. The location view offers both enhanced interpretability and improved accuracy for performing fuzzy interpolative reasoning, by capturing the nuanced relationships between rules and observations. The results of the experimental investigations demonstrate the success of the improved FRI mechanism leveraging the direction parameters.