This paper focuses on the state estimator design problem for a class of Takagi-Sugeno fuzzy stochastic hybrid systems with intermittent measurements in discrete-time domain. The hybrid systems are characterized with the stochastic switching among a set of subsystems, and the switching is supposed to be governed by a semi-Markov process with finite sojourn time. The random packet dropouts are modeled by a Bernoulli distributed sequence, and the packet dropout rate, which is considered to be variable, is described by the semi-Markov stochastic process that governs the switching dynamics of the fuzzy stochastic hybrid system. A more general class of Lyapunov functions that not only depends on the system modes, but also on the time that the current mode has been in since the last mode switching, is employed to analyze the stability and H∞ performance of the estimation error system. Then, numerically testable conditions on the existence of a desired fuzzy mode-dependent state estimator are presented such that the estimation error system approaches to be mean square stable to an adjustable level and achieves a prescribed H∞ disturbance attenuation index. Finally, an illustrative example of a single-link robotic arm system is provided to demonstrate the effectiveness and the superiority of the design method of state estimator.