Towards hierarchical fuzzy rule interpolation

Abstract

Fuzzy rule interpolation offers a useful means for enhancing the robustness of fuzzy models by making inference possible in systems of only a sparse rule base. However in practical applications, as the application domain of fuzzy systems expand to more complex ones, the “curse of dimensionality” problem of the conventional fuzzy systems became apparent, which makes the already challenging tasks such as inference and interpolation even more difficult. An initial idea of hierarchical fuzzy interpolation is presented in this paper. The proposed approach combines hierarchical fuzzy systems and fuzzy rule interpolation, to overcome the “curse of dimensionality” problem and the sparse rule base problem simultaneously. Hierarchical fuzzy interpolation is applicable to situations where a multiple multi-antecedent rules system needs to be reconstructed to a multi-layer fuzzy system and the sub-layer rules base is sparse. This approach is based on fuzzy rule interpolative reasoning that utilities scale and move transformation. Illustrative example and experimental scenario are provided to demonstrate the potential of this approach.