FUZZY EXTREME LEARNING MACHINE FOR A CLASS OF FUZZY INFERENCE SYSTEMS

Recently an Online Sequential Fuzzy Extreme Learning (OS-Fuzzy-ELM) algorithm has been developed by Rong et al. for the RBF-like fuzzy neural systems where a fuzzy inference system is equivalent to a RBF network under some conditions. In the paper the learning ability of the batch version of OS-Fuzzy-ELM, called as Fuzzy-ELM is further evaluated to train a class of fuzzy inference systems which can not be represented by the RBF networks. The equivalence between the output of the fuzzy system and that of a generalized Single-Hidden Layer Feedforward Network as presented in Huang et al. is shown first, which is then used to prove the validity of the Fuzzy-ELM algorithm. In Fuzzy-ELM, the parameters of the fuzzy membership functions are randomly assigned and then the corresponding consequent parameters are determined analytically. Besides an input variable selection method based on the correlation measure is proposed to select the relevant inputs as the inputs of the fuzzy system. This can avoid the exponential increase of number of fuzzy rules with the increase of dimension of input variables while maintaining the testing performance and reducing the computation burden. Performance comparison of Fuzzy-ELM with other existing algorithms is presented using some real-world regression benchmark problems. The results show that the proposed Fuzzy-ELM produces similar or better accuracies with a significantly lower training time.