Learning analysis for correlation of fuzzy rules in applying RLS for neural fuzzy systems

It is well-known that Self-constructing neural fuzzy inference network (SONFIN) is a nice fuzzy inference system that has been equipped with structure learning capability. For the learning mechanisms, SONFIN can either be employed with the adaptive learning algorithm from neural network, which is often called backpropagation (BP) learning algorithm or use the Recursive Least Squares (RLS) algorithm in finding the parameters in the consequence part. In this paper, we reported the analysis on the use of RLS algorithm for neural fuzzy systems under the structure of SONFIN. Such a RLS algorithm is originally proposed to learn parameters in the consequence part only for TSK fuzzy systems. RLS has been demonstrated to be capable of providing great learning performance to neural fuzzy systems. From our previous work, it can be observed that the advantages of using RLS over BP and various issues, such as forgetting factor or reset operation are also investigated. All the above studies are based on the use of the full covariance matrixin the RLS algorithm. However, such an approach may result in heavy computational burden especially when the rule number is large. An alternative approach is to neglect the correlation among rules. In this study, we will report our analyses on the effects of correlation among rules. In order to have a clear demonstration on those effects, some special designs for the system are considered. From our study, it is clearly evidence that such neglect may results in large errors.