Complex neuro-fuzzy intelligent approach to function approximation

A complex neuro-fuzzy self-learning approach using complex fuzzy sets to the problem of function approximation is proposed in this paper. The concept of complex fuzzy sets (CFSs) is an extension of traditional fuzzy set whose membership degrees are within a unit disk in the complex plane. The Particle Swarm Optimization (PSO) algorithm and the recursive least square estimator (RLSE) algorithm are used in hybrid way to train the proposed complex neuro-fuzzy system (CNFS). The PSO is used to adjust the premise parameters of the CNFS, and the RLSE is used to update the consequent parameters. With the experimental results, the CNFS shows better performance than the traditional neuro-fuzzy system (NFS) that is designed with regular fuzzy sets. Moreover, the PSO-RLSE hybrid learning method for the CNFS improves the rate of learning convergence and shows better performance in accuracy. In order to test the feasibility and approximation performance of the proposed approach, two benchmark functions are used for the proposed approach. The results by the proposed approach compared to other approaches. Excellent performance by the proposed approach has been observed.