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This paper proposes relaxed stabilization conditions of discrete-time nonlinear systems in the Takagi-Sugeno (T-S) fuzzy form. By using the algebraic property of fuzzy membership functions, a novel nonparallel distributed compensation (non-PDC) control scheme is proposed based on a new class of fuzzy Lyapunov functions. Thus, relaxed stabilization conditions for the underlying closed-loop fuzzy system are developed by applying a new slack variable technique. In particular, some existing fuzzy Lyapunov functions and non-PDC control schemes are special cases of the new Lyapunov function and fuzzy control scheme, respectively. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.