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论文类型：期刊论文

发表时间：2019-10-01

发表刊物：NEURAL PROCESSING LETTERS

收录刊物：SCIE

卷号：50

期号：2

页面范围：1589-1609

ISSN号：1370-4621

关键字：Neuro-fuzzy; TS system; Split-complex valued; Neural networks; Convergence

摘要：In order to broaden the study of the most popular and general Takagi-Sugeno (TS) system, we propose a complex-valued neuro-fuzzy inference system which realises the zero-order TS system in the complex-valued network architecture and develop it. In the complex domain, boundedness and analyticity cannot be achieved together. The splitting strategy is given by computing the gradients of the real-valued error function with respect to the real and the imaginary parts of the weight parameters independently. Specifically, this system has four layers: in the Gaussian layer, the L-dimensional complex-valued input features are mapped to a Q-dimensional real-valued space, and in the output layer, complex-valued weights are employed to project it back to the complex domain. Hence, split-complex valued gradients of the real-valued error function are obtained, forming the split-complex valued neuro-fuzzy (split-CVNF) learning algorithm based on gradient descent. Another contribution of this paper is that the deterministic convergence of the split-CVNF algorithm is analysed. It is proved that the error function is monotone during the training iteration process, and the sum of gradient norms tends to zero. By adding a moderate condition, the weight sequence itself is also proved to be convergent.