Hybrid optimization of information granulation‐based fuzzy radial basis function neural networks

The purpose of this paper is to propose an improved optimization methodology of information granulation‐based fuzzy radial basis function neural networks (IG‐FRBFNN). In the IG‐FRBFNN, the membership functions of the premise part of fuzzy rules are determined by means of fuzzy c‐means (FCM) clustering. Also, high‐order polynomial is considered as the consequent part of fuzzy rules which represent input‐output relation characteristic of sub‐space and weighted least squares learning is used to estimate the coefficients of polynomial. Since the performance of IG‐RBFNN is affected by some parameters such as a specific subset of input variables, the fuzzification coefficient of FCM, the number of rules and the order of polynomial of consequent part of fuzzy rules, we need the structural as well as parametric optimization of the network. The proposed model is demonstrated with the use of two kinds of examples such as nonlinear function approximation problem and Mackey‐Glass time‐series data.

The type of polynomial of each fuzzy rule is determined by selection algorithm by considering the local error as performance index. In addition, the combined local error is introduced as a performance index considered by two kinds of parameters such as the polynomial type of each rule and the number of polynomial coefficients of each rule. Besides this, other structural and parametric factors of the IG‐FRBFNN are optimized to minimize the global error of model by means of the hierarchical fair competition‐based parallel genetic algorithm.

The performance of the proposed model is illustrated with the aid of two examples. The proposed optimization method leads to an accurate and highly interpretable fuzzy model.

The proposed hybrid optimization methodology is interesting for designing an accurate and highly interpretable fuzzy model. Hybrid optimization algorithm comes in the form of the combination of the combined local error and the global error.