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Neuro-fuzzy systems is a popular hybridization in soft computing that abstracts a fuzzy model from given numerical examples using neural learning techniques to formulate accurate predictions on unseen samples. The fuzzy model incorporates the human-like style of fuzzy reasoning through a linguistic model that comprises if-then fuzzy rules and linguistic terms described by membership functions. However, modeling data using neuro-fuzzy systems involves the contradictory requirements of interpretability versus accuracy. This monograph focuses on increasing interpretability without compromising accuracy using a novel hybrid intelligent Rough set-based Neuro-Fuzzy System (RNFS), which synergizes rough set-based knowledge reduction with neuro-fuzzy systems. RNFS employs novel bio-inspired algorithms to generate human- interpretable membership functions from numerical data, and rough set-based algorithm to identify fewer if-then fuzzy rules that facilitate human interpretation. Example applications of using the RNFS are provided on real life data that involve predicting traffic flow, stock price and cancerous microarray gene expressions.