Training of Fuzzy Neural Networks via Quantum-Behaved Particle Swarm Optimization and Rival Penalized Competitive Learning

There are some difficulties encountered in the application of fuzzy radial basis function neural network. One of them is how to determine the number of hidden (rule) neurons and another difficulty is about interpretability. In order to overcome these difficulties, we have proposed a fuzzy neural network based on radial basis function network and takagi-sugeno fuzzy system. We have used a new structure of fuzzy radial basis function neural network, which has been proved that it is better than other structures in term of interpretability. Our model also uses rival penalized competitive learning and a swarm based algorithm called quantum-behaved particle swarm optimization to determine design parameters of hidden layer and design parameters of output layer, respectively-rival penalized competitive learning is the best clustering algorithm that is introduced so far. The particle swarm optimization is a well-known population-based swarm intelligence algorithm. The quantum-behaved particle swarm optimization is also proposed by combining the classical particle swarm optimization philosophy and quantum mechanics to improve performance of particle swarm optimization. We have compared the performance of the proposed method with gradient based method. Simulation results of nonlinear function approximation demonstrate the superiority of the proposed method over gradient based method.