Multi-attribute three-way decision (MA3WD) has been a novel tool to solve multi-attribute decision-making (MADM) problems by considering the transforming relationship between loss functions and decision matrix. However many practical decision-making problems face the information with uncertainty and complexity, which makes it impossible to obtain relative loss functions in MA3WD. By introducing the thinking of ideal solutions (IS), this study extends MA3WD to interval-valued intuitionistic fuzzy environment, giving a more flexible and general model to handle with uncertain MADM problems. In this paper, we firstly propose an interval-valued intuitionistic fuzzy three-way decision (IVIF3WD) model by obtaining relative loss functions derived from evaluation values, and introduce ideal solutions to construct an ideal-solution based three-way decision model with single interval-valued intuitionistic fuzzy attribute. Then in consideration of all the attributes, two multi-attribute IVIF3WD models are proposed in the perspectives of individual ideal solutions and global ideal solutions respectively. Finally, two cases of investment with different fuzzy information are utilized to illustrate the application and superiority of proposed models.

多属性三路决策（MA3WD）通过考虑损失函数和决策矩阵之间的转换关系，已成为解决多属性决策（MADM）问题的新工具。然而，许多实际决策问题面临着不确定性和复杂性的信息，这使得在 MA3WD 中无法获得相对损失函数。通过引入理想解（IS）的思想，本研究将 MA3WD 扩展到区间值直觉模糊环境，给出了一个更灵活和通用的模型来处理不确定的 MADM 问题。在本文中，我们首先通过获得从评估值导出的相对损失函数，提出了区间值直觉模糊三向决策（IVIF3WD）模型，并引入理想解，构造具有单区间值直觉模糊属性的基于理想解的三向决策模型。然后综合考虑所有属性，分别从个体理想解和全局理想解的角度提出了两个多属性IVIF3WD模型。最后，利用具有不同模糊信息的两个投资案例来说明所提出模型的应用和优越性。