In this paper, we explore finite-time \(\text {H}_\infty \) synchronization control for a class of discrete-time interval type-2 fuzzy Markov jump systems (FMJSs) which include partially unknown transition probabilities, randomly occurring coupling delays, and the controller with stochastic failures. A quantized dynamic event-triggered mechanism is suggested by incorporating the hysteresis-uniform quantizer with a dynamic event-triggered scheme to further reduce data communication overhead. Utilizing the mode-dependent Lyapunov function, the finite-time \(\text {H}_\infty \) synchronization problem of FMJSs is studied in depth from the mean-square sense. Based on the reciprocal convex method and Wirtinger’s integral inequality, sufficient conditions of the FMJSs synchronization are derived. Finally, the single-link robotic arm systems and H \(\acute{e}\) non systems are utilized to illustrate the practicality and validity of the proposed scheme.
