Rule-Ranking-Based Approximate Knowledge Interpolation With Directional Monotonicity

Fuzzy rule interpolation (FRI) empowers fuzzy rule-based systems (FRBSs) with the ability to infer, even when presented with a sparse rule base where no direct rules are applicable to a given observation. The core principle lies in creating an intermediate fuzzy rule—either interpolated or extrapolated—derived from rules neighboring the observation. Conventionally, the selection of these rules hinges upon distance metrics. While this approach is easy to grasp and has been instrumental in the evolution of various FRI methods, it is burdened by the necessity of extensive distance calculations. This becomes particularly cumbersome when swift responses are imperative or when dealing with large datasets. This article introduces a groundbreaking rule-ranking-based FRI method, termed RT-FRI, which overcomes the constraints of the longstanding distance-centric FRI approach. Instead of relying on distances, RT-FRI harnesses ranking scores for rules and unmatched observation. These scores are produced by amalgamating the antecedent attributes using aggregation functions, thus streamlining the rule selection procedure. Recognizing the rigid monotonicity demands of aggregation functions, a variant—DMRT-FRI—has been introduced to ensure directional monotonicity. Experimental results indicate that RT-FRI emerges as a highly efficient technique, with DMRT-FRI exemplifying a notable balance of accuracy and efficiency.