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Machine learning (ML) models have been applied to monthly streamflow forecasting in recent decades. In this study, forecasting skills of eight ML models are evaluated based on the Model Parameter Estimation Experiment (MOPEX) dataset. We consider two skill scores, i.e., the Nash–Sutcliffe efficiency (NSE) and the adjusted NSE (ANSE), and the latter is the skill score based on the interannual mean monthly value (MMV) as the reference (benchmark) model. Furthermore, NSE of the MMV model (NSEmmv) is used as a measure of the seasonality of monthly streamflow, as it is the ratio of variance explained by the MMV process. An important result is that forecasting skills of ML models for monthly streamflow are largely controlled by NSEmmv. Moreover, based on comparisons of different ML models, we have found that the selection of models is not a dominating factor impacting the final skill. Three key factors influencing NSE, i.e., NSEmmv, the base flow index (BFI) and the aridity index (AI), are explored in this paper. Specifically, NSEmmv impacts NSE directly and is the predominant factor; BFI influences the memory of the monthly streamflow and therefore influences NSE. The relationship between AI and NSE is much complex and indirect. Firstly, basins with higher AI tend to have lower NSEmmv, and this will lead to lower NSE; secondly, basins with higher AI tend to have lower BFI, which will also lead to lower NSE; thirdly, for a given BFI level, basins with higher AI tend to have higher memory and higher NSE. For ANSE, basins with AI between 1 and 2 show higher ANSE, which corresponds to higher autocorrelation coefficients.

Set pair potential, indicates an identical-discrepancy-contrary trend of two sets discussed in the case of specific problems. This trend can show weak tendency of regional water environmental system vulnerability, consequently set pair potential has been used to analyze its driving factors. In traditional set pair, contrary degree is restricted since that contrary degree does not vanish is the necessary condition by definition, as a result that traditional set pair potential does not have general validity. Therefore taking advantage of exponential function to improve the traditional set pair potential, and a new definition of set pair exponential potential was proposed. Then an analysis model of driving factors of regional water environmental system vulnerability was established based on this new potential and the model was used to analyze the factors in Anhui province, China. Some results have been obtained that the driving factors of water environmental system vulnerability in Anhui province mainly include: degree of regional development level, per capita water resources, marsh area ratio, soil erosion area ratio, industrial wastewater standard discharge rate and the ratio of investment in water environmental governance (protection) to GDP.

The flood disaster is one of the most serious natural disasters. It is the important basis of making plan for flood control to assess flood losses accurately. The results of the common assessment methods are discrete values and low resolution which are applied widely at present. The research to more precise, more intuitive method of loss evaluation for flood disaster is the focus. The set pair analysis assessment model was established by the α-cut set of triangle fuzzy number A in this paper. The case study shows this method not only presents the concrete rank of flood lose, but also finds that the evaluating rank is a confidence interval; in addition, we can obtain priorities of different areas by the expectation and square difference method for priorities of interval numbers.

Benefit and loss matrix of uncertain decision-making analysis reflects both the objective information structure of uncertain decision-making problem and the risk information of benefit chance and loss chance faced by decision-maker. The transform vector consisted of the natural state weights is quantitative expression of uncertain decision-making rule adopted by decision-maker. The essential for resolving uncertain decision-making problem is how to transform benefit and loss matrix into compressed real vector with one dimension, where the biggest weight of the vector corresponds to the best action scheme. Now the information of benefit and loss matrix has been not mined sufficiently using the common methods for uncertain decision-making problems. Therefore in this paper, the whole difference weights of the natural states can be determined using projection pursuit method, the local difference weights of the natural states can be determined directly using information entropy and accelerating genetic algorithm based fuzzy analytic hierarchy process, and the two kinds of weights can be combined into comprehensive weights according to the minimum relative information entropy principle, which can form a new uncertain decision-making analysis method based on information entropy principles, named UDM-IEP for short. The application result show that the information of benefit and loss matrix can be mined more sufficiently using UDM-IEP than the common methods, that the decision-making information can be more provided by UDM-IEP than the common methods, that decision-maker can actively or safely choose the best scheme based on the comparison between of benefit chance risk and loss chance risk contained in the benefit and loss matrix, that UDM-IEP is both simple and general, that its computation result is objective and stability, and that UDM-IEP can be widely applied in theory and practice of systems engineering.