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To achieve carbon neutrality, the power structure is bound to usher in fundamental transformations. In this study, an energy–carbon–water nexus (F-ECWN) system model is developed to assess trade-offs among different decision-making objectives within a power system under varying policy orientations. The model incorporates forecast data derived from various global climate models, leverages neural network prediction, draws upon multi-criteria decision-making theory, and incorporates fuzzy theory. Moreover, to effectively handle a multitude of fuzzy parameters within the model, a novel dual-interval algorithm for solving fuzzy linear programming is proposed. The F-ECWN model has the capability to derive the fuzzy membership function for each variable within the model ensuring that errors remain below 1 %, reflecting the uncertainty stemming from diverse policy orientations and technology choices. Various scenarios were formulated to gauge the impact of policy orientation on the allocation decisions of regional energy systems. Additionally, sensitivity analysis has been conducted to assess the effects of uncertain parameters on modeling outputs. The results of the applied research in Fujian Province have revealed that the presence of uncertainties in the energy system's parameters can significantly influence model outputs and decision-making processes. Furthermore, the modeling results demonstrate the region's substantial potential for reducing carbon emissions. Under optimal policy guidance and climate conditions, the total carbon emissions can be reduced by 65 %, with a 36.14 % increase in the total system cost. These findings are anticipated to provide valuable support for formulating optimal decisions regarding regional energy-carbon-water nexus system and related environmental policies. [Display omitted] • A new algorithm for solving fuzzy multi-objective programming problems is proposed. • A robust fuzzy number reduction algorithm based on probabilistic integration is proposed. • E -C-W nexus in Fujian Province under different policy orientations is quantified. • Incorporation of CMIP6 forecast data into renewable energy parameters construction. • Carbon and water synergy effects in regional power system optimization are observed. [ABSTRACT FROM AUTHOR]