Density-based approach for fuzzy rule interpolation

Abstract

Sparse rule base is one of the common problems in fuzzy rule-based systems, and fuzzy rule interpolation (FRI) could derive interpolated results for the input based on the neighbor fuzzy rules when the input is not matched by any of the fuzzy rules. The core idea of FRI is that similar inputs would lead to similar results, and several FRI methods that use a pre-defined number of closest rules to obtain the interpolated results have been presented. However, this could lead to the loss of some information as selecting a given number of rules without considering the exact distance between them and the input could lead to the selection of unwanted rules or the ignoring of similar rules. This paper presents a density-based fuzzy rule interpolation method that uses a density-based approach to search and select the closest rules for unmatched inputs. Instead of selecting a given number of rules, the proposed method adaptively selects the closest rules that are within a certain range of the unmatched inputs, thus assuring the selected rules are with high similarity to the inputs. The performance of the proposed method is verified through fifteen classification benchmarks, showing the effectiveness and efficiency of the proposed method.