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Improvements of recent stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems are proposed. The key idea is to bring together the so-called local transformations of membership functions and new piecewise fuzzy Lyapunov functions. By relying on these special local transformations, the associated linear matrix inequalities that are used to prove the system's stability can be relaxed without increasing the number of conditions. In addition, to enhance the usefulness of the proposed methodology, one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives. A standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases.