Design of fuzzy radial basis function neural networks with the aid of multi-objective optimization based on simultaneous tuning

In this paper, we concerns a design of fuzzy radial basis function neural network (FRBFNN) by means of multi-objective optimization. A multi-objective algorithm is proposed to optimize the FRBFNN. In the FRBFNN, we exploit the fuzzy c-means (FCM) clustering to form the premise part of the rules. As the consequent part of fuzzy rules of the FRBFNN model, four types of polynomials are considered, namely constant, linear, quadratic, and modified quadratic. The least square method (LSM) is exploited to estimate the values of the coefficients of the polynomial. In fuzzy modeling, complexity, interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. Since the performance of the RBFNN model is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules and the orders of the polynomials in the consequent parts of the rules, we carry out both structural as well as parametric optimization of the network. The proposed multi-objective algorithm is used to optimize the parameters of the model while the optimization is of multi-objective character as it is aimed at the simultaneous minimization of complexity and maximization of accuracy.