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• A multi-attribute group decision method based on the interval-valued intuitionistic fuzzy set is proposed. • A sustainability evaluation of an agricultural water-land-energy-carbon nexus is provided. • Multidimensional indicators are combined through stability, coordinativity and connectivity. • The water, land, energy and carbon subsystems of the agricultural system are quantified based on dual uncertainty. • The model is shown to solve real-world relationship management problems. The interactions between agricultural subsystems, resource scarcity and ecological degradation increase the need for agricultural sustainability assessments in relation to water, land, energy and carbon emissions. In addition, uncertainties caused by natural factors and human activities complicate sustainability assessments. Therefore, this study proposes a regional agricultural sustainability assessment method based on the water-land-energy-carbon (WLEC) nexus system under high uncertainty. This method couples the interval-valued intuitionistic fuzzy set (IVIFS) and multi-attribute group decision making (MAGDM) methods to quantitatively characterise and assess element management and corresponding relationships within the agricultural WLEC nexus system in a multidimensional manner. The paper is able to (1) clarify the role of the coupled agricultural "water-land-energy-carbon" nexus and (2) address the double ambiguity and uncertainty in the indicators and more objectively reflect the interval fluctuations of natural resources and social activities in both positive and negative scenarios. (3) Sustainability management of agricultural resources is carried out according to different regional conditions. The method was applied to Heilongjiang Province in northeast China, and the coupling of agricultural WLEC nexus system in 13 administrative regions of the study area was quantitatively analysed. The degree of agroecological sustainability from a multidimensional perspective is higher in Daxinganling and lower in the provincial capital, Harbin. The recommended range of groundwater use in the study area is [16%,28%] to ensure ecological sustainability when total agricultural output fluctuates between 285,395.18 and 404,495.33 billion yuan. This methodology helps policy makers understand the overall dynamics of agricultural sustainability in an environment of multiple uncertainties and gives suggestions for better assessing management. [ABSTRACT FROM AUTHOR]