Data envelopment analysis (DEA) is a linear programming and production theory-based nonparametric approach that is generally used for efficiency analysis. Older DEA models, such CCR and BCC, can only identify decision-making units (DMUs) efficient or inefficient. The super-efficiency DEA model enables efficient DMUs to be ranked. A change in efficient DMUs can be measured using Malmquist index model, and the Malmquist productivity change index can be decomposed multiplicatively into an efficiency-change component (Effch) and a technical change component (Techch). This paper analyzes the water use efficiency in Shandong Province between 2006 and 2015 using Malmquist productivity index (TFP). The results show that: (1) the mean of super-efficiency scores of 17 cities in Shandong Province for the period 2006–2015 is between 0.965 and 2.760; (2) the water use efficiency was positive in 2006–2007, 2007–2008, and 2013–2014; however, it was negative in the other periods between 2006 and 2015; and (3) technical change is the key influencing factor on water use efficiency of 17 cities in Shandong Province. So, we suggest that Shandong Province encourage technological innovation to promote water use efficiency.

As a new development form for evaluating the regional water resources carrying capacity, forewarning regional water resources of their carrying capacities is an important adjustment and control measure for regional water security management. Up to now, most research on this issue have been qualitative analyses, with a lack of quantitative research. For this reason, an index system for forewarning regional water resources of their carrying capacities and grade standards, has been established in Anhui Province, China, in this paper. Subjective weights of forewarning indices can be calculated using a fuzzy analytic hierarchy process, based on an accelerating genetic algorithm, while objective weights of forewarning indices can be calculated by using a projection pursuit method, based on an accelerating genetic algorithm. These two kinds of weights can be combined into combination weights of forewarning indices, by using the minimum relative information entropy principle. Furthermore, a forewarning model of regional water resources carrying capacity, based on entropy combination weight, is put forward. The model can fully integrate subjective and objective information in the process of forewarning. The results show that the calculation results of the model are reasonable and the method has high adaptability. Therefore, this model is worth studying and popularizing.

This paper establishes a water resources vulnerability framework based on sensitivity, natural resilience and artificial adaptation, through the analyses of the four states of the water system and its accompanying transformation processes. Furthermore, it proposes an analysis method for water resources vulnerability based on connection entropy, which extends the concept of contact entropy. An example is given of the water resources vulnerability in Anhui Province of China, which analysis illustrates that, overall, vulnerability levels fluctuated and showed apparent improvement trends from 2001 to 2015. Some suggestions are also provided for the improvement of the level of water resources vulnerability in Anhui Province, considering the viewpoint of the vulnerability index.

As an important indicator for assessing regional water resources, the study of the spatiotemporal evolution and driving factors of water resources carrying capacity (WRCC) is essential for achieving sustainable water resource utilization. This study focuses on Yulin City, a typical arid region located on the Loess Plateau in northwestern China. By constructing an evaluation index system for regional WRCC and combining an improved fuzzy comprehensive evaluation model with the TOPSIS evaluation model, a comprehensive WRCC evaluation model is established. Additionally, Geodetector is used to explore the main driving factors behind the evolution of regional WRCC. This multidimensional analytical framework aims to deeply analyze the dynamic evolution trends of WRCC and the driving mechanisms of different factors in its spatiotemporal changes. The results indicate that (1) from 2011 to 2020, the overall WRCC of Yulin City showed a trend of positive improvement, with Shenmu, Yuyang, and Fugu areas performing the best, and by 2020, more than half of the counties had achieved Grade 3 or above; (2) the spatial variability of WRCC in Yulin City was more significant than its temporal changes; and (3) in terms of driving mechanisms, the northern six counties gradually shifted from traditional economic-driven factors to ecological and environmental drivers, whereas the southern six counties remained constrained by economic factors. Overall, water resource factors remain the primary driving force for the socio-economic development and environmental sustainability of the entire Yulin City. The study provides valuable information for water resource allocation and differentiated management in arid regions.

There are many uncertain factors, such as stochastic, fuzzy and gray information in the risk analysis on natural hazard. The set pair analysis (SPA) deals effectively with the various uncertain factors contributing to evaluation of the risk level of natural disasters. The evaluation indicators and standards of natural disasters risk are analyzed by identity-discrepancy-contrary (IDC). The result, the connection numbers, still has uncertainty information. Thus, yielding the risk evaluation model of natural disasters based on connection function, which construct a set pair relation between the indicators of connection numbers and comprehensive evaluation standards, and describe uncertainty of the connection numbers by using connection function. The study showed that the proposed model takes into account only the uncertainty of risk evaluation indicator identification on natural disasters, also the uncertainty of result connection numbers. This approach gives full consideration to the uncertainty of systematic evaluation process along with the actual meaning of comprehensive evaluation functions. Therefore, this means it is able to reduce the uncertainty of final evaluation results and improve the accuracy and reasonability of evaluation results. This model is capable of reflecting actual situation of the risk evaluation on natural disaster affected by various uncertain factors and has a promotional value in the natural disaster risk assessment.