Study On The Learning Method Of Complex-valued TSK Fuzzy Neural Networks

Nowadays,complex-valued neural networks(CVNN)have already been paid widelyattentions by domestic and foreign scholars,which can process complex-valued data sets and show stronger computing power than real-valued correspondences on classification problems.Such as,complex-valued BP neural network,complex-valued radial basis neural network,complex-valued extreme learning machine,complex-valued recurrent neural network and so on.However,these mature theories are all based on the traditional neural network frameworks for research.There are relatively few theories for the promotion of complex domains for fuzzy neural networks(FNN),which possess both the reasoning ability of fuzzy logic and the adaptive learning ability of networks.Especially lack mathematical theoretical analysis in terms of convergence.Therefore,this paper will aim at Takagi-Sugeno-Kang(TSK)fuzzy neural network,a typical fuzzy neural network,and use a simple but practical split-complex-valued strategy to extend it to the complex fields.So,a split-complex-valued-adapted-zero-order TSK fuzzy neural network(SCA0TSKFNN)and a split-complex-valued-adapted-higher-order TSK fuzzy neural network(SCA1TSKFNN)are proposed in this paper.And their learning methods based on the gradient descent method as well as adaptive momentum technology are studied.Specifically,we use the following strategies: Specify some parameters,input,and output values as complex numbers;Use split-complex activation functions;Derive learning rules through calculating partial derivatives for real and imaginary parts.Strict mathematical theories prove that the SCA0 TSKFNN with adaptive momentum and SCA1 TSKFNN learning methods presented in this paper have good convergence under loose conditions.All experimental results on the XOR classification,six regression problems and Sonar dataset also verify the corresponding convergence theorems,and show that SCA0 TSKFNN with adaptive momentum has faster convergence speed than the cases with no momentum and fixed momentum.SCA1 TSKFNN can solve regression and classification problems better than other existing methods.Especially on the Sonar data set,the classification accuracy is improved by nearly 4% compared with the best method.