This paper is investigated with the robust finite-time synchronization of discrete-time Markovian jump neural networks with partially unknown transition probabilities. Firstly, a unified framework based on event-triggering approaches and quantization, a synchronization error model is first provided for discrete-time Markovian neural networks. Secondly, with the aid of Lyapunov-Krasovskii functional, sufficient conditions for the finite-time boundedness are deduced which can ensure synchronization of the system model, and the quantized finite-time controller and event-triggered parameters are co-designed so that Markovian neural networks are finite-time bounded by variable decoupled techniques. Finally, a simulation example is established to illustrate the availability of the presented methods.MSC Classification: 15A39 , 24D06 , 93B51 , 93D30 , 93E15