Fuzzy modeling of multivariable discrete-time nonlinear dynamical systems is approached analytically in this paper. We start by developing a proper framework based on the key notions of fuzzy quantization and function approximation. With the suitable formulation, an on-line scheme is developed that adaptively forms the fuzzy model from samples of a dynamical system by generating and modifying a set of fuzzy rules and membership functions. The convergence analysis of the scheme is carried out rigorously, based on the Lyapunov theory, and the major convergence result is established. The scheme is also applied to a real-world modeling problem to demonstrate its feasibility and effectiveness.