A Novel Framework of Fuzzy Rule Interpolation for Takagi-Sugeno-Kang Inference Systems

Abstract

Fuzzy rule interpolation (FRI) technique has been proposed to infer conclusions for unmatched instances when a fuzzy rule-based system is presented with a sparse rule base. Most existing FRI methodologies are not developed for Takagi-Sugeno-Kang (TSK) inference models. TSK inference extension (TSK+) is one of the methodologies proposed for TSK models with sparse rule bases. It works by replacing matching degrees with similarity measures across all the given rules, instead of just the matched ones, to generate the final conclusion. However, those rules with low similarities bring bias to the final result, which is mainly determined by the closest rules. To significantly strengthen the efficacy of this, a novel framework is presented here through the use of just a small number of closest rules to derive the final outcome. Compared with TSK+, the proposed method reduces the computational overheads of the inference process while avoiding the adverse impact caused by the rules of low similarities with the new observation. More importantly, to deal with large sized sparse rule bases, where neighbourhood rules may be similar with each other, a rule-clustering approach is proposed. That is, a clustering algorithm (say, fuzzy c-means) is first employed to cluster rules into different groups and then, the final interpolated conclusion is computed by the use of the closest rules selected from a small number of closest rule clusters. This approach helps further decrease the time complexity. The efficacy of these two modified methods is demonstrated via systematic experimental comparisons against the performance of the original TSK+.