This study addresses the problem of distributed event-triggered set-membership filtering for a class of discrete time-varying systems in the presence of unknown-but-bounded noises. First, an event-triggered mechanism is introduced to choose those necessary data packets to be transmitted. Second, a partial information transmission scheme is proposed, by which, once an event is triggered, not all the information of the data packet, but parts of them are released to the communication network. As a result, communication network resources can be saved significantly. Third, some sufficient conditions on distributed networked set-membership filtering are derived using a time-varying convex optimisation approach. Moreover, based on an intersection method, a novel global estimation is proposed to integrate the local estimations by locating the intersection of all the local estimations within a volume-minimal external ellipsoid. Finally, simulation results demonstrate the feasibility and effectiveness of the proposed methods.