We describe in this paper a new approach to the identification of the stable regions of nonlinear systems, using cell mapping equipped with measures of fractal dimension and those from rough set theory. The proposed fractal-rough set approach divides the state space into cells, finds out the chaotic region using cell to cell mapping technique and classifies the cells according to the fractal dimension of each cell. Assigning the fractal dimension to each cell in the state space, cells are then classified as the members of lower approximation, upper approximation or boundary region of the stable region with the help of rough set theory. Rough sets with fractal dimension as their attributes are used to model the uncertainty on the stable region which is treated as a set of cells in this paper. This uncertainty is then smoothed by a reinforcement learning algorithm. Our approach is applied to the stability of a dynamical system with finger shaped boundary region.