<p>This paper investigates the parameter identification problem of Takagi-Sugeno (T-S) fuzzy systems under quantized output measurements. In contrast to conventional identification theories that rely on continuous-valued observations, quantization mechanism introduces nonlinear and non-smooth error structures, which fundamentally alter the statistical properties of the identification problem and render classical analytical methods inapplicable. To address this issue, the authors first consider the case where the membership weights are known. By constructing a periodic structure involving the input and the membership functions, a parameter identification algorithm based on periodic excitation is developed, and the strong consistency of the parameter estimates is rigorously established. Subsequently, for the case with unknown membership weights, a set of nonlinear equations incorporating the parameters of the membership functions is formulated. The identifiability and local solvability conditions of this system are analyzed, and a data-driven approach is proposed to achieve joint identification of the local model parameters and the membership function parameters. Finally, numerical simulations are conducted to validate the effectiveness and convergence performance of the proposed methods. This work systematically reveals the underlying principles of T-S fuzzy system identification under quantized observations, and provides a generalizable theoretical foundation for the identification and analysis of nonlinear systems with finite-precision measurements.</p>