Recurrent Fuzzy Neural Networks and Their Performance Analysis

There are many papers that consider different structure and training algorithms of FNN. Within their structural range, the networks may differ by type of signals (singleton, interval, general fuzzy, triangle shaped or other), topology (layered, fully-connected, with or without feed-back connections, feed-back connections in all or some of the layers etc), type of neurons (transfer function, same type in all layers or different depending on layer). Note also that FNN is further complicated when we deal with applications of temporal character such as dynamic control, forecasting, identification, recognition of temporal sequences (e.g. voice recognition). It is obvious that in this case classical FNN with feedforward structure, operable mainly for memory-less problems, would be ineffective. In this respect there is a strong demand for recurrent fuzzy neural networks (RFNN) with dynamic mapping capability, temporal information storage, dynamic fuzzy inference, and as a result, capable of solving temporal problems [7,24,27]. Paper [48] discusses delay feedback neuro-fuzzy networks and their usability to effectively tackle dynamic systems. This is a simplified version of recurrent network with feedback connections at only one layer of the network. To train unknown parameters of RFNN the author of [1] uses a supervised learning algorithm that requires differentiability of the membership functions that is not always possible. In [25] a recurrent self-organizing neuro-fuzzy inference network is proposed. The main characteristic of this system is the ability to deal with temporal problems including dynamic fuzzy inference. The system with on-line learning feature is capable also of building the structure and (crisp) parameters of the network. The learning algorithm is based on the use of the ordered derivative (partial derivative) produced with the use of an ordered set of equations. The efficiency of the proposed neuro-fuzzy system is verified on the basis of various simulations on benchmark temporal problems, including time-sequence prediction, adaptive noise cancellation, dynamic plant identification, and non-linear plant control. In [27] a recurrent multi-layered connectionist network for realizing fuzzy inference using dynamic fuzzy rules is presented. The paper distinguishes as containing good methodological support encompassing important aspects of neuro-fuzzy systems class. The back-propagation algorithm is used as the learning algorithm minimizing the cost function to achieve necessary connection weights and biases. As in [25], several examples and O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m