We introduce an incremental learning method for the optimal construction of rule-based granular models from numerical data streams. We take into account a multiobjective function, the specificity of information, model compactness, and variability and coverage of the data. We use α-level sets over Gaussian membership functions to set model granularity and operate with hyper-rectangular forms of granules in nonstationary environment. Rule-based models are formed in a systematic fashion and can be used for time series prediction and nonlinear function approximation. Precise estimates and enclosures are given by linear piecewise and inclusion functions related to optimal granular mappings. An application example on early detection and monitoring of the severity of the Parkinson's disease shows the usefulness of the method.