Reduced Interval Type-2 Neural Fuzzy System Using Weighted Bound-Set Boundary Operation for Computation Speedup and Chip Implementation

This paper proposes a reduced interval type-2 neural fuzzy system using weighted bound-set boundaries (RIT2NFS-WB) for the simplification of type-reduction operations. The objective of this simplification is to reduce the system training time in software implementation and chip size in hardware implementation, especially when the number of rules is large. The antecedent part in the RIT2NFS-WB uses interval type-2 fuzzy sets (IT2FSs), and the consequent part can be of the Takagi–Sugeno–Kang (TSK) or Mamdani type. The RIT2NFS-WB is built through an online structure and parameter learning to improve model accuracy. In addition, the interpretability of the RIT2NFS-WB is improved by considering distributions of the IT2FSs in input variables. A distinguishability-oriented cost function is used in parameter learning to generate distinguishable IT2FSs and improve semantics-based interpretability. For highly overlapped IT2FSs, they are merged to reduce the number of IT2FSs and improve complexity-based interpretability. The software-implemented TSK-type RIT2NFS-WB is hardware-implemented on a field-programmable gate array chip. To accelerate the chip execution speed, the chip utilizes not only the parallel execution properties of fuzzy rules and bound-set boundaries but the pipeline technique as well. In particular, the flexibility of the chip is considered so that no redesign of the circuits is required when the RIT2NFS-WB is applied to different problems. The characteristics of the software- and hardware-implemented RIT2NFS-WB are verified through various examples and comparisons with various type-1 and interval type-2 fuzzy models.