A full fuzzy-interval credibility-constrained nonlinear programming approach for irrigation water allocation under uncertainty

Abstract

To address the water shortage caused by various natural conditions and ineffective irrigation water management in the Zhanghe Irrigation District (ZID) of the Yangtze River basin in China, a full fuzzy-interval credibility-constrained nonlinear programming (FFICNP) model is developed under uncertainty. Derived through incorporating fuzzy credibility constrained programming into the Jensen model optimization framework, FFICNP can not only address intervals (single uncertainty) and fuzzy-interval sets (dual uncertainties) in the model objectives and double-sided constraints, but also reflect nonlinear responsive relationships between the crop yields and irrigation levels by introducing the crop water production functions (CWPFs) under different growth stages. Moreover, an expected-value-based (EVB) approach is introduced to solve the FFICNP model. The FFICNP model is then applied to the case study of irrigation water allocation in the ZID for demonstrating its applicability. Optimal solutions can be generated from the FFICNP model for solving the irrigation water allocation problem under uncertainty. The results indicate that a lower credibility level corresponds to a higher level of system benefits and system efficiency. The system benefits of ZID in a wet year are [17.72, 24.23] × 109 CNY when λ = 1.0 and [17.79, 25.03] × 109 CNY when λ = 0.6. These findings from the FFICNP model can support in-depth analysis of interrelationships among irrigation water allocation schemes, system benefits, and credibility levels, and thus contribute to the effectiveness of irrigation water management under various inflow levels and complex uncertainties.