<p>Multi-attribute group decision-making problems are increasingly prevalent in numerous engineering problems, especially those involving uncertainty and hesitation. Many decision makers favor interval-valued hesitant fuzzy information systems to characterize such kind of decision-making problems. In this context, this paper aims to address interval-valued hesitant fuzzy multi-attribute group decision-making problems by proposing a novel three-way decision model. Specifically, we design an attribute-oriented interval-valued hesitant fuzzy state set, which can intuitively represent the standard states of objects under various attributes. On this basis, we utilize possibility degree to further estimate the conditional probabilities of objects with respect to the standard state. Meanwhile, an overlap function is employed to aggregate the relative loss functions on objects under all attributes, so that the losses of the objects can be considered comprehensively. Furthermore, the expected losses on objects are calculated by combining conditional probabilities with overall losses, and the reasonable categorization and ranking results of objects can be obtained. To validate the practicality of the established model, this paper applies it to a mine wells priority ranking problem. Importantly, the experimental result of our model demonstrates a high correlation (greater than 0.7) with classical decision methods, thereby underscoring its accuracy and reliability. In addition, comparative and experimental analyses are conducted to verify the stability and effectiveness of the model. In conclusion, the proposed three-way decision model offers a robust framework for handling multi-attribute group decision-making under uncertainty, and can be applied in the energy region successfully.</p>