Abstract
An interval nonlinear double-sided fuzzy chance-constrained programming (INDFCCP) approach is formulated to effectively allocate irrigation water among competing water users. The INDFCCP approach is formulated by combining inexact quadratic programming (IQP) and double-sided fuzzy chance-constrained programming (DFCCP) within a general optimization framework. This approach has the following features. (1) It’s able to handle interval and fuzzy uncertainties, and nonlinearity existing in the objective functions. (2) It’s capable of addressing these fuzzy constraints and fuzzy variables where different confidence levels and satisfaction degree levels should be satisfied. (3) Each fuzzy chance-constraint can be further analyzed with the maximum and minimum reliability scenarios, which makes it possible to reflect variations of system conditions. (4) Interval quadratic crop water production functions (IQCWPFs) are employed in place of deterministic ones to quantitatively describe the mathematical relationships between crop yields and actual crop evapotranspiration (or irrigation water applied). Then, to demonstrate its applicability and feasibility, the INDFCCP approach is applied in the Yingke Irrigation District (YID), northwest China for allocating irrigation water to three crops in three subareas under uncertainty. Finally, more flexible decision solutions regarding optimal irrigation water allocation have been generated and analyzed under different predetermined confidence levels, showing several advantages of the INDFCCP approach with respect to the deterministic one. Under the same confidence level, system benefits under the minimum reliability scenario (e.g. [499.6, 909.7] × 106 Yuan, α = 0.5) are higher than that under the maximum reliability scenario (e.g. [498.7, 908.9] × 106 Yuan, α = 0.5). From above outcomes, the INDFCCP approach provides more appropriate results and reliable scientific bases needed for better managing irrigation water in irrigated agricultural areas.
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