Towards Dynamic Fuzzy Rule Interpolation via Density-Based Rule Promotion from Interpolated Outcomes

Abstract

Traditional fuzzy rule-based systems struggle with scenarios where knowledge gaps exist in the problem domain, due to limited data or experience. Fuzzy rule interpolation (FRI) effectively addresses the challenge of inference in fuzzy systems when faced with unmatched observations, due to the employment of an incomplete or sparse rule base. It generates temporary, interpolated rules for the unmatched observations, ensuring continued inference capability. However, the resultant valuable interpolated rules are conventionally discarded. This paper introduces a formal approach for dynamic fuzzy rule interpolation (D-FRI), based on the concept of density-based rule promotion and assisted by the use of the OPTICS clustering algorithm, through exploiting frequently appearing interpolated rules on the fly. This enhances the system’s knowledge coverage, efficiency, and robustness over time. An implementation of such a D-FRI system is presented, which combines transformation-based fuzzy rule interpolation (T-FRI) with OPTICS clustering. This offers an effective mechanism for evaluating and subsequently selecting potentially powerful interpolated rules for the system to dynamically enrich its knowledge base. The implemented system is verified by experimental investigations.