Towards Dynamic Fuzzy Rule Interpolation via Density-Based Spatial Clustering of Interpolated Outcomes

Fuzzy rule interpolation (FRI) provides an innovative approach to deducing conclusions for observations that do not match existing rules in a sparse fuzzy rule base. Conventional fuzzy rule-based systems that rely on sparse rule bases often encounter limitations due to the lack of sufficient data or the absence of adequate human expertise necessary to formulate rules encompassing the majority of a given problem domain.
Beginning with a sparse rule base, the Fuzzy Rule Interpolation (FRI) approach constructs interpolated rules, specifically when such observations fail to trigger any rule present in the sparse rule base. Once the inference results through interpolation are found, the interpolated rules that might involve valuable information about the knowledge space are discarded. The system's overall efficiency and robustness will never improve by only performing FRI. This raises the need for dynamic fuzzy rule interpolation (D-FRI). That is, after the FRI process, interpolated rules that cover certain domain regions can be adapted to match future observations directly. Thus, a dynamic fuzzy rule promotion approach that evaluates interpolated rules and promotes potential valuable ones to the sparse rule base for future inference can improve the overall coverage of the domain knowledge and inference efficiency. This paper proposes a dynamic fuzzy rule interpolation framework that joins the popular Transformation-based Fuzzy Rule Interpolation (T-FRI) and Density-Based Spatial Clustering of interpolated outcomes. Experimental results demonstrate that the approach works effectively.