This article presents a framework to derive Takagi-Sugeno (TS) models from experimental data through the identification and linearization of reduced nonlinear dynamic models at different operating points, using the Sparse Identification of Nonlinear Dynamics (SINDy) technique. The proposed approach combines the modeling of multiple simplified nonlinear representations with their local linearization. Besides, it permits accurately capturing the dynamics of complex systems inside an operating region of interest. Finally, a detailed implementation of the proposed framework is applied to model a simple biomass production bioreactor.