Linking agricultural water-food-environment nexus with crop area planning: A fuzzy credibility-based multi-objective linear fractional programming approach

To readily addressed three key issues including fuzzy parametric information, multiple objectives and fractional ratios in planning problems, this study presents a fuzzy credibility-based multi-objective linear fractional pro-gramming approach for building the linkage between agricultural water-food-environment nexus and crop area planning. This approach is developed by incorporating fuzzy credibility-constrained programming into multi -objective linear fractional programming within the optimization model. To demonstrate its applicability, the approach is then applied to the Hetao Irrigation District in the northwest China to unite the multiple objective problems in agricultural irrigation with crop area planning. Three ratio optimization problems associated with agricultural, economic and environmental objectives are concurrently considered including maximum economic benefit per unit of irrigation water, maximum crop yield per unit of irrigated area and minimal grey water footprint per unit of crop production. Therefore, this study has the following advantages. (1) Fuzzy parameters existing in the objective and violated constraints can be effectively tackled. (2) The multiple ratio optimization problems can be efficiently solved through a linearization procedure in a straightforward manner, thereby reflecting desired system efficiency and reducing computational difficulties. (3) The mathematical and practical interactions of agricultural water-food-environment nexus can be investigated based on intermediate variables, i. e., irrigated area, irrigation water, crop yield, economic benefits and greywater footprint. (4) Optimal solutions can be flexibly generated to facilitate crop area planning through given aspiration levels of objective goals and credibility levels of constraints. The results indicate that optimal objective values have slight changes with the form of each objective (e.g., maximization or minimization). The results are useful for facilitating insightful interpretation of inter-relationships among sustainable agricultural production, efficient irrigation water use, and favorable agro-ecological conditions.