Neuro-Fuzzy System Modeling with Density-Based Clustering

Neuro-fuzzy system is widely used for nonlinear system modeling. How to partition the input space optimally is the core issue in fuzzy system modeling. Previous ways suffer from two main drawbacks, the difficulty to determine of the number of partitions and rule redundancy, which hinders the application of fuzzy system. The authors present a new approach to neuro-fuzzy system modeling based on DENCLUE using a dynamic threshold and similar rules merging (DDTSRM). They first introduce DDT, which uses a dynamic threshold rather than a global threshold in merging density-attractors in DENCLUE. DDTSRM is good at determining the number of rules because DDT does not depend on input parameters. Additionally, the modeling performance is improved for DDT can find arbitrary shape and arbitrary density clusters. Rule redundancy is caused by similar fuzzy sets in the input and output data space. After structure identification, similar rules are merged by considering similarity measures between fuzzy sets. This is also effective for the model to avoid overfitting to the sample data. Finally, BP method is used to precisely adjust the parameters of the fuzzy model. DDTSRM is applied to a nonlinear function and Box and Jenkins system. Experimental results show that DDTSRM has overcome the drawbacks with a good performance.