This paper introduces a granular, interval-based evolving modeling (IBeM) approach to develop system models from a stream of data. IBeM is an evolving rule-based modeling scheme that gradually adapts its structure (information granules and rule base) and rules antecedent and consequent parameters from data (inductive learning). Its main purpose is continuous learning, self-organization, and adaptation to unknown environments. The IBeM approach develops global model of a system using a fast, one-pass learning algorithm, and modest memory requirements. To illustrate the effectiveness of the approach, the paper considers actual time series forecasting applications concerning electricity load and stream flow forecasting.