Fault occurrence in practical systems, if not addressed, can cause diminished performance or even system breakdown. Therefore, fault detection has emerged as a crucial challenge in ensuring system safety and reliability. This paper presents a novel fuzzy observer aimed at reconstructing actuator and sensor faults in nonlinear systems, even when subjected to external disturbances. The approach we propose utilizes the Takagi-Sugeno fuzzy model and Lyapunov function. Initially, by filtering the system output, we construct a system where actuator faults correspond to the original actuator and sensor faults. Subsequently, the impact of disturbance on state estimations is minimized by employing the H-infinity performance criteria. We demonstrate that, for non-disturbed systems, these estimations gradually converge to their true values. In designing the observer gains, transformation matrices are derived by solving linear matrix inequalities. Our approach boasts some advantages over existing methods. By assuming that the premise variables are immeasurable, we enhance the usability of our approach. As a proof of concept, we evaluate two practical systems. The simulation results underline the benefits of our proposed method in terms of rapid and accurate fault detection performance.