A novel Online Self-organizing Fuzzy Neural Network for function approximation

In this paper, we propose a novel Online Self-constructing Fuzzy Neural Network (OSFNN) which extends the ellipsoidal basis function (EBF)-based fuzzy neural networks (FNNs) by permitting input variables to be modeled by dissymmetrical Gaussian functions (DGFs). Due to the flexibility and dissymmetry of left and right widths of the DGF, the partitioning made by DGFs in the input space is more flexible and more economical, and therefore results in a parsimonious FNN with high performance under the online learning algorithm. The geometric growing criteria and the error reduction ratio (ERR) method are used as growing and pruning strategies respectively to realize the structure learning algorithm which implements an optimal and compact network structure. The proposed OSFNN starts with no hidden neurons and does not need to partition the input space a priori. In addition, all the free parameters in premises and consequents are adjusted online based on the ε-completeness of fuzzy rules and the linear least square (LLS) approach, respectively. The performance of the proposed OSFNN paradigm is compared with other well-known algorithms like ANFIS, OLS, GDFNN, SOFNN and FAOS-PFNN, etc., on a benchmark problem in the field of function approximation. Simulation results demonstrate that the proposed OSFNN approach can facilitate a more powerful and more economical FNN with better performance of approximation and generalization.