## 1 Introduction
The presence of these uncertainties can cause gain perturbation in the estimator and can result in a decrease in the overall estimation performance, so such an estimator is also called a \"fragile\" estimator. To ensure the robustness of the estimator, the non-fragility need to be fully considered during the design process. In the past few years, there has been much attention from scholars on the non-fragile set-membership estimation of MNNs. In [19], a non-fragile estimation approach based on SMF for MNNs with logarithmic quantization has been proposed under the framework of Maximum Error First protocol. A non-fragile estimation approach has been proposed for discrete measurement-saturated MNNs based on set-membership filtering under the framework of weighted try-once-discard (WTOD) protocol [20]. In [21], a non-fragile distributed secure SMF framework has been designed to estimate nonlinear systems influenced by channel fading and cyber-attacks. However, it is worth noting that, under the framework of non-fragile estimation based on SMF, the main structure of the linear matrix inequality (LMI) for estimating the error changes significantly when the system is suffering from stochastic cyber-attacks. Therefore, the matrix blocks of the non-fragile parts that deal with the parameter uncertainty and the estimator gain perturbation also need to be changed along with the change of main structure. Based on our knowledge, we have not seen research reports concerning the non-fragile estimation based on SMF for MNNs under stochastic cyber-attacks. Moreover, alongside the aforementioned gain perturbation, the use of the communication network and inferior sensors also brings some detrimental influences on the state estimation problem of MNNs despite its numerous conveniences. The inferior sensors mentioned above are cheap, but, due to their physical limitations and the influence of intermittent faults, encountering sensor-related problems is inevitable during the measuring process of the system, such as measurement saturations and missing measurements (MMs). The occurrence of these sensor-related problems can influence the estimation performance seriously. Therefore, scholars have conducted research on the problem of set-membership estimation when measurement saturations and MMs exist from different perspectives. For time-varying systems influenced by sensor saturation, refs. [22; 23] have proposed corresponding event-based distributed set-membership filters and controllers, respectively. Reference [24] has reviewed various processing approaches for systems influenced by measurement saturation and MMs. For a class of discrete nonlinear systems influenced by measurement saturation and MMs simultaneously, ref. [25] has proposed a distributed filter based on a random access (RA) protocol. A sector-bounded approach has been employed to partition the saturation function into linear and nonlinear components to deal with the saturation phenomena for the sensor-saturated systems; then, an SMF was designed for state estimation in [26]. In [27], a recursive joint state and fault estimation (JSFE) filter based on the Round-Robin (RR) protocol has been designed for a class of nonlinear systems with MMs and random component faults. Reference [28] has studied an \(H_{\infty}\) filter problem for a class of uncertain stochastic nonlinear systems with probabilistic MMs, time-delays and external random disturbances. However, currently, most of the literature only considers these sensor-related problems; there exists little research on reducing the influence of these problems on the estimation of performance. How to solve this problem to a certain extent is a research motivation of this paper. The network communication mentioned above has the advantages of easy maintenance and low modularity, which reduce communication costs during data transmission effectively.