Construction of fuzzy systems using least-squares method and genetic algorithm

Abstract

The fuzzy basis function network which was proposed in Wang and Mendel (IEEE Trans. Neural Networks 3(5) (1992b) 807) provides a way of representing fuzzy inference systems in a simple structure similar to those of radial basis function networks. In this paper, two new algorithms based on the least-squares method and genetic algorithm are proposed for autonomous learning and construction of fuzzy basis function networks when training data are available. The proposed algorithms add a significant fuzzy basis function node at each iteration during training, based on error reduction measures. The first, a least-squares algorithm, provides a way of sequentially constructing meaningful fuzzy systems which are not possible to achieve with the orthogonal least-squares algorithm, while the second, an adaptive least-squares algorithm based on the combined least-squares and genetic algorithm, realizes hybrid structure-parameter learning without human intervention. Simulation studies are performed with numerical examples for comparison of its performance against the orthogonal least-squares algorithm, backpropagation algorithm, and conventional genetic algorithm. The adaptive least-squares algorithm is also applied to a real world problem to construct a fuzzy basis function network model for surface roughness in a grinding process using experimental data.