A type-2 fuzzy interval programming approach for conjunctive use of surface water and groundwater under uncertainty

In this study, a type-2 fuzzy interval programming (T2FIP) method is developed for conjunctive use of surface water and groundwater under uncertainty. T2FIP can effectively tackle uncertainties expressed as a hybrid of type-2 fuzzy sets and interval numbers. In T2FIP, tradeoff between system benefit and system reliability can be analyzed to obtain the practical modeling outputs. Solution method based on interactive algorithm and type reduction technique is proposed to transform fuzzy-interval constraint into its deterministic equivalents. The T2FIP method is then applied to conjunctive use of surface water and groundwater in the Zhangweinan River Basin, China. Scenarios associated with different groundwater utilization ratios are examined to help generate the optimal conjunctive water use pattern. Results show that increased groundwater utilization ratio could lead to increased crop area and system benefit; however, when the utilization ratio of groundwater for irrigation increases to 50%, the system benefit would not increase. Results reveal that, for arid and semi-arid regions, effective conjunctive use of surface water and groundwater is critical for guaranteeing the agricultural sustainability. These findings can help identify desired decision alternatives among crop planning, agricultural irrigation, and groundwater utilization with a maximized system benefit and a minimized system-failure risk.