Bayesian Neuro-Fuzzy Inference System for Temporal Dependence Estimation

When it comes to time-series forecasting, it is crucial to learn the intricate temporal relationship between past and future, and historical information is of paramount importance for this purpose. Traditional neuro-fuzzy systems generally resort to an empirical (offline) method to determine the number of past instances (i.e., historical information) required for a particular model, hence often unsuitable in an online time-series scenario. In this article, we propose a Bayesian neuro-fuzzy inference system (BaNFIS), where the temporal dependence on past instances is estimated with an online Bayesian probabilistic mechanism, and the uncertainty associated with real-world data is handled by the fuzzy inference system. The BaNFIS retains historical information only as per necessity and employs it in two ways: globally or locally. Moreover, an online learning method is employed here to update the BaNFIS parameters. Hence, the BaNFIS is able to capture both the system dynamics and uncertainty efficiently in an online manner. Three real-world time-series problems are employed here to evaluate the online performance of the BaNFIS compared to seven state-of-the-art neuro-fuzzy methods both under standard train–test and prequential test–train protocols. Numerical results clearly indicate that the BaNFIS provides a statistically improved prediction performance than its peers in terms of accuracy.