Fuzzy Rule Interpolation With $K$-Neighbors for TSK Models

Abstract

When a fuzzy system is presented with an incomplete (or sparse) rule base, fuzzy rule interpolation (FRI) offers a useful mechanism to infer conclusions for unmatched observations. However, most existing FRI methodologies are established for Mamdani inference models, but not for Takagi–Sugeno–Kang (TSK) ones. This article presents a novel approach for computing interpolated outcomes with TSK models, using only a small number of neighboring rules to an unmatched observation. Compared with existing methods, the new approach helps improve the computational efficiency of the overall interpolative reasoning process, while minimizing the adverse impact on accuracy induced by firing those rules of low similarities with the new observation. For problems that involve a rule base of a large size, where closest neighboring rules may be rather alike to one another, a rule-clustering-based method is introduced. It derives an interpolated conclusion by first clustering rules into different groups with a clustering algorithm and then, by utilizing only those rules that are each selected from one of a given, small number of closest rule clusters. Systematic experimental examinations are carried out to verify the efficacy of the introduced techniques, in comparison with state-of-the-art methods, over a range of benchmark regression problems, while employing different clustering algorithms (which also shows the flexibility in ways of implementing the novel approach).