Synergistic optimization of water-energy-environment nexus under uncertainty: An interval type-2 fuzzy...

Intensifying socio-economic development and climate variability in coastal mountainous basins have increased water withdrawals, energy demand, and pollutant discharges, amplifying pressures on the water-energy-environment (WEE) nexus. There is an urgent need for integrated approaches capable of addressing coupled interactions and multi-source uncertainties. This study develops a chance-constrained bi-objective interval fractional programming model to maximize net economic benefits and pollutant-load efficiency. The framework characterizes multi-source uncertainties and coupled interactions within the WEE nexus using interval type-2 trapezoidal fuzzy sets and is applied to the Minjiang River Basin. Compared with conventional nexus models, this structure enhances decision robustness across confidence levels and scenarios. Furthermore, a hybrid multi-criteria decision-making approach combining Fuzzy Analytic Hierarchy Process and Technique for Order Preference by Similarity to Ideal Solution is employed for solution prioritization. Results show that industrial and domestic sectors jointly account for over 75% of total demand, whereas agricultural and ecological sectors act as principal adjustment levers during dry seasons. Spatially, allocation is strategically divergent, directing 62% of water to downstream economic zones and 35% to ecologically preserved upstream areas. Expanding seawater desalination alleviates scarcity but involves energy and discharge trade-offs, requiring coordination with reclaimed-water reuse and demand management. Chemical oxygen demand and total phosphorus emerge as binding pollutants, and the preferred scheme achieves a 15.8% reduction in discharge at a 6.8% economic cost. This study presents a scientific framework for systematic optimization and risk-informed management of the WEE nexus and provides theoretical support for future nexus-oriented policymaking in coastal mountainous basins.