A Recurrent Fuzzy Neural Network: Learning and Application

A novel recurrent neurofuzzy network is proposed in this paper. More specifically, in this work we generalize the recurrent neurofuzzy network structure proposed in [1], which is in turn is an improvement of the feedforward structure introduced in [2]. The network structure is composed by two structures: a fuzzy inference system and a neural network. The fuzzy inference system contains fuzzy neurons modeled with the aid of logic operations processed via t-norms and s-norms. The neural network is composed by nonlinear elements placed in series with the previous logical element. The network model implicitly encodes a set of if-then rules and its recurrent multi layer structure performs fuzzy inference. The topology induces a clear relationship between the network structure and an associated fuzzy rule-based system. This means that linguistic knowledge can efficiently be inserted or extracted from the network. The recurrent fuzzy neural network is particularly suitable to model nonlinear dynamic systems and to learn sequences. The temporal recurrent relations are embedded in the second layer of the network. They provide the memory elements of the network and expand its basic ability to include temporal representations. Since the recurrent neuron has an internal feedback loop, it captures dynamic responses and contributes to simplify the neural fuzzy network model (Figure 1). Figure 1: Recurrent NeuroFuzzy Network Structure. Network learning involves three main phases. The first phase uses a convenient modification of the vector quantization approach to granulate the input universes. The next phase simply set network connections and their initial, randomly chosen weights. The third phase uses two main paradigms to update the network weights: gradient descent and associative reinforcement learning [3]. More precisely, the output layer weights are adjusted via an error gradient descent method whereas a reward and punishment scheme updates the hidden layer weights. The result is an accurate and fast learning procedure. The performance of the recurrent neurofuzzy network is verified with an example of single-step-ahead and multi-step-ahead prediction of a chaotic series. The example illustrates the potential application in sequence learning. Computational experiments show that the fuzzy neural model learned is simpler and that learning is faster than its counterpart.