A Bidirectional Reasoning Based on Fuzzy Interpolation

Abstract

In order to deal with both the “curse of dimensionality” and the “sparse rule base” simultaneously, an initial idea of hierarchical bidirectional fuzzy interpolation is presented in this article, combining hierarchical fuzzy systems and forward/backward fuzzy rule interpolation. 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. 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.