### Multiobjective Space Search Optimization and Information Granulation in the Design of Fuzzy Radial Basis Function Neural Networks

Abstract

This study introduces an information granular-based fuzzy radial basis function neural networks (FRBFNN) based on multiobjective
optimization and weighted least square (WLS). An improved multiobjective space search algorithm (IMSSA) is proposed to optimize the
FRBFNN. In the design of FRBFNN, the premise part of the rules is constructed with the aid of Fuzzy C-Means (FCM) clustering while
the consequent part of the fuzzy rules is developed by using four types of polynomials, namely constant, linear, quadratic, and modified
quadratic. Information granulation realized with C-Means clustering helps determine the initial values of the apex parameters of the
membership function of the fuzzy neural network. To enhance the flexibility of neural network, we use the WLS learning to estimate the
coefficients of the polynomials. In comparison with ordinary least square commonly used in the design of fuzzy radial basis function
neural networks, WLS could come with a different type of the local model in each rule when dealing with the FRBFNN. Since the performance
of the FRBFNN 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 present in the consequent parts of the rules, we carry out both structural as well as parametric
optimization of the network. The proposed IMSSA that aims at the simultaneous minimization of complexity and the maximization of accuracy
is exploited here to optimize the parameters of the model. Experimental results illustrate that the proposed neural network leads to better
performance in comparison with some existing neurofuzzy models encountered in the literature.