The fuzzy-model-based H∞ filtering for a class of discrete-time wireless nonlinear networked systems with energy constraints is investigated in this paper. Due to the limitation of transmission power, the measurement data is not transmitted at each sampling instant, and it is scheduled here. Two techniques are proposed to reduce the transmission power, i.e., event-based transmission protocol and measurement size reduction scheme. Firstly, a new event-based transmission protocol is presented such that the transmission occurs only when the designed event occurs. Then, the measurement size reduction technique is applied. The so-called measurement size reduction technique consists of two parts: the logarithmic quantization and the stochastic measurement element selection. The simultaneous utilization of above two techniques can significantly reduce the energy consumption in such a wireless networked system. By constructing the fuzzy-mode-dependent Lyapunov functional, sufficient conditions are derived such that the filtering error system is stochastically stable with a prescribed H∞ performance level. An optimization problem is presented to determine the optimal filter gains. The effectiveness of the proposed filter design scheme is illustrated by a simulation study on the nonlinear truck-trailer system.