Title: Neuro-Fuzzy Adaptive Systems for Intelligent Forecasting in Nonlinear Dynamic Environments

Abstract: One of the biggest problems in forecasting for Nonlinear and Times Variant systems is the changeable system nature, noise presence, and undulate behavior. A great many classical statistical techniques and several modern machine learning techniques do not apply because of their inflexibility and black-box character. In this article, we propose a new Neuro￾Fuzzy Adaptive System (NFAS) which is expected to give forecasts with a high degree of accuracy and interpretability in nonlinear dynamic systems. The novel structure uses the learning of patterns from neural networks and the reasoning and adaptability of fuzzy systems. It modifies the fuzzy rule bases and the membership functions in response to the environment while the neural network technique of backpropagation modifies the outputs of the forecast. The system underwent testing with multiple datasets, both real and simulated, that differed in complexity, nonlinearity, and noise. The results crowning the research conducted indicate that the suggested NFAS surpasses the traditional and present-day NFASs in the accuracy of the forecasts produced, the sensitivity, and the broad applicability of the predictions. Moreover, fuzzifying the interpretability analysis demonstrates the use of adaptive fuzzy rules for making decisions understandable, thus allowing easier deployment of the control system in vital forecasting tasks such as energy consumption, financial Market fluctuations, and industrial process control. This shows increases the credibility of applying systems with neuro-fuzzy structure for intelligent forecasting of dynamic systems.

Keywords: Neuro-Fuzzy Systems, Adaptive Forecasting, Nonlinear Dynamic Environments, Intelligent Time Series Prediction.