This paper is concerned with the set-membership filtering problem for a class of time-varying systems with mixed time-delays and communication protocols. Two kinds of well-known protocols (Round-Robin protocol and Weighted Try-Once-Discard protocol) are considered, with which the data transmission between the sensor nodes and the filter is implemented via a shared communication network that allows only one sensor node to send its measurement data at each transmission instant in order to prevent the data from collisions. The transmission order of sensor nodes is orchestrated by the underlying protocol of the network. The aim of the problem addressed is to design a set-membership filter capable of confining the state estimate of the system to certain ellipsoidal region subject to the bounded non-Gaussian noises. Sufficient condition is first derived for the existence of the desired filter at each time step in terms of a recursive algorithm. Then, two optimization problems are solved by optimizing the constraint ellipsoid of the estimation error subject to the underlying protocol. Simulation results demonstrate the effectiveness of the proposed filter design scheme. (C) 2016 Elsevier Ltd. All rights reserved.