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China is facing an increasingly serious aging problem, which puts forward higher requirements for the smoothness of the endowment insurance system. Accurate evaluation of the efficiency of the system can help the government to find problems and improve the system. Some scholars have used data envelopment analysis (DEA) method to measure the efficiency of endowment insurance system. However, according to the literature, the impact of government policy adjustment and economic shocks on output of the data was ignored. In this study, a robust optimization method is applied to deal with uncertainty. Robust DEA models proposed in this paper are based on three kinds of uncertainty sets. A data-driven robust optimization method is also applied to resolve the over-conservative problem. Compared with the robust DEA method, based on analysis it is found that the data-driven robust DEA method is more flexible and reliable for efficiency estimating strategies. The results of data-driven robust DEA models illustrate that the government should increase its support for the endowment insurance system, especially for the underdeveloped regions.

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To combat global warming, China proposed the “dual carbon” policy in 2020. In this context, it becomes crucial to improve carbon emissions efficiency. Currently, some scholars have utilized data envelopment analysis (DEA) to study carbon emissions efficiency. However, uncertainty about climate and government economic policy is ignored. This paper establishes a robust DEA model to reduce uncertainty and improve robustness. First, robust optimization theory is combined with DEA to establish the robust DEA model. Second, considering three uncertainty sets (box set, ellipsoid set, and polyhedron set), a robust DEA model for different situations is considered. Finally, to address the problem of over-conservatism in robust optimization, this paper applies the data-driven robust DEA model to further analyze the carbon emissions efficiency of China. The results of the data-driven robust DEA model suggest that the government should focus on coordinated regional development, promote the transformation and upgrading of the energy structure, innovate in green technology, and advocate for people to live a green and low-carbon lifestyle.

Individual opinion is one of the vital factors influencing the consensus in group decision-making, and is often uncertain. The previous studies mostly used probability distribution, interval distribution or uncertainty distribution function to describe the uncertainty of individual opinions. However, this requires an accurate understanding of the individual opinions distribution, which is often difficult to satisfy in real life. In order to overcome this shortcoming, this paper uses a robust optimization method to construct three uncertain sets to better characterize the uncertainty of individual initial opinions. In addition, we used three different aggregation operators to obtain collective opinions instead of using fixed values. Furthermore, we applied the numerical simulations on flood disaster assessment in south China so as to evaluate the robustness of the solutions obtained by the robust consensus models that we proposed. The results showed that the proposed models are more robust than the previous models. Finally, the sensitivity analysis of uncertain parameters was discussed and compared, and the characteristics of the proposed models were revealed.