## 6 Conclusions  
This paper has investigated the non-fragile estimation problem based on set-membership filtering for a class of measurement-saturated MNNs with MMs and mixed time delays subject to stochastic cyber-attacks under the WTOD protocol. The occurrence of stochastic cyber-attacks follows a Bernoulli distribution. First, by utilizing the LMI technology, the estimation error has been ensured to still be limited within the specified ellipsoid despite the above sensor-related problems and network-induced phenomena. Simultaneously, through the set-membership filtering approach and mathematical induction, we have established the sufficient condition for the existence of the estimator, so that one can solve the LMI sequence to obtain the estimator gain. Moreover, by designing a non-fragile set-membership algorithm, the robustness of the estimation algorithm has been ensured under gain perturbation. Second, by solving the trace of the minimization matrix, the local optimal estimator gain has been obtained to achieve the optimal estimation performance at each sampling instant. Finally, numerical simulation examples have been presented to demonstrate the effectiveness of the proposed algorithm.  
Although the estimation performance of the proposed estimation framework in this paper has been superior to other estimation frameworks proposed in the literature, when the MMs occur in a sensor node, if we do not know in advance which sensors have a higher probability of MMs, we cannot pre-set the weight values of the WTOD protocol, which greatly increases the probability of the estimator receiving missing data. Therefore, in future research, we should propose a dynamic communication strategy to detect the occurrence of MMs and adjust weights in real time to avoid the influence of MMs on estimation performance. In addition, for the occurrence of cyber-attacks, our estimation framework has still been passive to detect attacks and recover estimation performance. In some engineering scenarios, cyber-attacks influence the estimation performance, which may bring serious consequences to the whole system. Therefore, in the follow-up research, we hope to make improvements in the estimation framework to actively protect data from cyber-attacks.  
Conceptualization, Z.W. and P.W.; methodology, J.L.; software, J.W.; validation, P.L. writing--original draft, Z.W. and P.W.; writing--review and editing, Z.W. and P.W.; supervision, Z.W. and P.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the project of National Natural Science Foundation of China (Grant numbers [32073029]), Shandong Province Modern Agricultural Technology System (Grant  
\begin{table}
\begin{tabular}{c c c c} \hline
**Estimation Approach** & **Calculated Load (s)** & **Sum of the MSE** & **MSE during MMs** \\ \hline approach in [55] & 1.869 & 1.275 & 10.970 \\ our approach & 2.023 & 0.098 & 1.892 \\ \hline \end{tabular}
\end{table}
Table 3: Estimation performance of Case 3.  
numbers [SDAIT-22]), the key project of Shandong Provincial Natural Science Foundation (Grant numbers [ZR2020 KC027]), National Key Research and Development Program of China (Grant numbers [2023 YFD2400405], [2023 YFD2400400]),the Science & Technology Specific Projects in Agricultural High-Tech Industrial Demonstration Area of the YellowRiver Delta (Grant numbers [2022 SZX18]) and Shandong Provincial Key R & D Plan (Grant numbers [2022 CXGC010611]).  
Not applicable.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding authors.  
The authors declare no conflicts of interest.