A probabilistic, recurrent, fuzzy neural network for processing noisy time-series data

The rapidly increasing volumes of data and the need for big data analytics have emphasized the need for algorithms that can accommodate incomplete or noisy data. The concept of recurrency is an important aspect of signal processing, providing greater robustness and accuracy in many situations, such as biological signal processing. Probabilistic fuzzy neural networks (PFNN) have shown potential in dealing with uncertainties associated with both stochastic and nonstochastic noise simultaneously. Previous research work on this topic has addressed either the fuzzy-neural aspects or alternatively the probabilistic aspects, but currently a probabilistic fuzzy neural algorithm with recurrent feedback does not exist. In this article, a PFNN with a recurrent probabilistic generation module (designated PFNN-R) is proposed to enhance and extend the ability of the PFNN to accommodate noisy data. A back-propagation-based mechanism, which is used to shape the distribution of the probabilistic density function of the fuzzy membership, is also developed. The objective of the work was to develop an approach that provides an enhanced capability to accommodate various types of noisy data. We apply the algorithm to a number of benchmark problems and demonstrate through simulation results that the proposed technique incorporating recurrency advances the ability of PFNNs to model time-series data with high intensity, random noise.