Adaptive Neuro-Fuzzy Inference Systems: Architecture, Learning, Input Selection, and Applications - A Survey

Adaptive Neuro-Fuzzy Inference System (ANFIS) is a hybrid intelligent modeling framework that fuses the linguistic interpretability of fuzzy if-then rules with the parameter-learning capability of artificial neural networks. Since its introduction by Jang in 1993, ANFIS has become one of the most widely adopted neuro-fuzzy architectures for nonlinear function approximation, system identification, and time-series prediction. This paper surveys the ANFIS framework from three complementary angles. First, it reviews the network architecture and the hybrid learning rule that combines gradient descent with least-squares estimation, drawing on Jang's foundational formulation. Second, it examines a practical challenge in applying ANFIS to real-world, high-dimensional problems determining which candidate variables should serve as network inputs and reviews a computationally efficient input-selection heuristic based on single-epoch training error. Third, it presents a case study of ANFIS applied to high-frequency financial trading, in which an event-based volatility model, the Intraday Seasonality Observation Model (ISOM), is used to pre-filter training data and materially improves trading performance metrics such as return on investment and the Sharpe ratio. The paper closes with a comparative discussion of strengths, limitations, and open research directions for neuro-fuzzy modeling.