Hierarchical Bidirectional Fuzzy Rule Interpolation

The “curse of dimensionality” and “sparse rule base” are two common and important problems in conventional fuzzy systems. Using hierarchical fuzzy systems is an effective way to deal with the “curse of dimensionality” problem, whilst fuzzy rule interpolation offers a useful means for enhancing the robustness of fuzzy models, making inference possible in systems containing only a sparse rule base. In particular, backward fuzzy interpolation can be employed to allow interpolation to be carried out when certain antecedents of observation variables are absent, whereas conventional methods do not work. In order to deal with both “curse of dimensionality” and “sparse rule base” simultaneously, an initial idea of hierarchical bidirectional fuzzy interpolation is presented in this paper, combining hierarchical fuzzy systems and forward/backward fuzzy rule interpolation. Hierarchical bidirectional fuzzy interpolation is applicable to situations where a multiple multi-antecedent rules system needs to be reconstructed to a multi-layer fuzzy system and any sub-layer rule base is sparse. The implementation of this approach is based on fuzzy rule interpolative reasoning that utilities scale and move transformation. An illustrative example and application scenario are provided to demonstrate the efficacy of this proposed approach.