<p>This article designs a new timer-related sampled-data fuzzy observer, and proposes a novel aperiodic-sampling-dependent free-matrix approach, to estimate the state of nonlinear chaotic systems. The nonlinear systems are approximated by the Takagi-Sugeno (T-S) fuzzy model. Different from the traditional one, the designed observer incorporates the sampling timer starting from each sampling moment so as to become more flexible. Under the interferences from the external disturbance and the mismatched grades of membership, the objective for the observer is to achieve the given criterion of state estimation. For determining the observer, the aperiodic-sampling-dependent free-matrix formulas are applied, whose free-weighting matrices take various values to cope with aperiodic sampling, thereby improving the previous approach. Additionally, a discontinuous Lyapunov functional is constructed to further relax the observer results. Furthermore, the sampled-data grades of membership for the observer are provided and analyzed, in order to satisfy the criterion while limiting interference. Based on the new measures mentioned above, the results derived are less conservative compared to the literature, thus determining more efficient observers. At the end, the improved results of sampled-data observers are validated through two examples.</p>