Interval two-stage stochastic fuzzy credibility constrained model for double water resources considering ecological environment in irrigation areas

Water has been one of the essential resources for human survival and development in the world. However, there are unprecedented water pressure and challenge with the rapid development of the social economy and the expansion of the population. The rational and optimal allocation is one of the effective ways to alleviate the shortage of water resources, and then curb the continuous deterioration of the ecological environment. Taking the Jiansanjiang region in Heilongjiang Province as an example, this study aims to develop an interval two-stage stochastic fuzzy credibility-constrained programming, particularly on the reasonable distribution of surface and groundwater resources for the typical crops under the conditions of uncertainty and complexity. The ecological environment was also considered to fully meet the ecological water requirement and compensation for the water quality pollution. The objective function was combined as the cost of water quality pollution treatment (ecological compensation cost) with the economic benefit of the system. The discrete intervals, probability distributions, and fuzzy variables were introduced into the programming framework to solve the multiple uncertainties. The interval two-stage stochastic programming was coupled with the fuzzy credibility-constrained programming, in order to solve the fuzzy risk with the probability of violation risk. Therefore, the failure risk of the system was set as the different credibility levels. The improved model was divided into two stages to determine the optimal target of water distribution and the optimal allocation of water among surface and groundwater. According to the system benefit, the target value of water distribution was firstly predefined for each crop, and then the penalty coefficient was used to appropriately adjust the water supply targets for the less economic loss of the system. The treatment (compensation) cost of the ecological environment was reflected in the cost of agricultural water. For instance, nitrogen and phosphorus were diluted to prevent pollution from the water environment. According to the outstanding probability characteristics of natural inflows, the predicted annual inflow was assumed to be high, middle, and low levels, and the probability was assumed to be 0.2, 0.6, and 0.2, respectively. The available water presented both stochastic and fuzzy attributes, which were represented in the fuzzy sets using credibility theory. Other uncertain parameters were expressed in the interval form. The uncertainty model was solved to obtain the optimal water distribution scheme of crops using the interactive algorithm, in terms of the ecological environmental compensation costs under different inflow levels and water sources. The maximum economic benefits were achieved in the system under different credibility levels. The results showed that the improved model truly reflected the uncertainty of effectively balancing the system benefits and violation risks. The coordinated development of economic benefits was also promoted to fully meet the ecological water demand and agricultural pollution constraints in the system. More importantly, the ecological compensation cost decreased with the increase in the inflow level. When the inflow levels were low, medium, and high, the ecological compensation cost of surface water in the study area were 1 442.18×106-2 443.62×106, 1 075.39×106-1 921.47×106, and 568.78×106-1 509.16×106 Yuan, respectively, while the ecological compensation costs of groundwater were 239.11×106-462.46×106, 160.18×106-283.06×106, and 43.67×106-113.34×106 Yuan, respectively. When the credibility level was 1.0, the maximum economic benefit of the system was between 29.88×108, and 52.18×108 Yuan. By contrast, the maximum benefit was between 31.17×108, and 53.44×108 Yuan at the credibility level of 0.5. The maximum benefit of the system increased with the decrease in credibility level. Consequently, the efficient and sustainable utilization of water resources can be achieved in reasonable decision-making schemes under the actual situation and risk preference. The uncertainty optimization model of crop water allocation can provide a strong reference for the optimal allocation of multiple water sources in similar irrigation areas.