Abstract
In this study, a centroid-based type-2 fuzzy-probabilistic programming (CT2FP) approach is developed for supporting conjunctive use of surface water and groundwater under multiple uncertainties. CT2FP can not only tackle uncertainties expressed as type-2 fuzzy sets (in both objective function and constraints) but also address complexity with characteristic of randomness and two-layer fuzziness (i.e., type-2 fuzzy random variables). Solution method based on α-plane theory, enhanced Karnik–Mendel algorithm (EKM) and interactive algorithm are proposed to transform type-2 fuzzy-probabilistic constraints into their deterministic equivalents. A case study in Zhangweinan River Basin (China) is used to demonstrate the applicability of the proposed approach. Scenarios associated with different constraint-violation risk levels are examined to generate applicable cropping patterns and water-allocation schemes. The amount of groundwater used for irrigation can be determined (i.e., more than [462.84, 495.78] × 106 m3 in dry season and no more than [470.83, 537.19] × 106 m3 in wet season, respectively) to address the conflict between food security and ecological protection. The relationship among crop area, water allocation, and economic benefit can be reflected to enhance the agricultural sustainable development for the study basin.
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