Abstract In order to use three-way decision (TWD) to solve multiple attribute decision making (MADM) problems, in this article, a new TWD model with intuitionistic fuzzy numbers (IFNs) is proposed. First of all, we define the relative loss functions to demonstrate some features of loss functions in TWDs, which is the basis for future research. Then, based on the correlation between the loss functions and the IFNs, we get the relative loss functions based on IFNs. At the same time, the classification rules of the TWDs are discussed from different viewpoints, including the thresholds and their properties. Aiming at MADM problems with unreasonable values, a new integrated method of relative loss functions is established to obtain a fairer loss integration result of alternatives. In addition, considering that there are no decision attributes and only condition attributes in MADM, we use grey relational degree to calculate the condition probability. In the end, a novel TWD model is proposed to solve MADM problems with IFNs, and a practical example on selecting suppliers is used to demonstrate its effectiveness and practicability.

中文翻译：

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直觉模糊数的多属性决策三向模型

摘要 为了利用三路决策（TWD）解决多属性决策（MADM）问题，本文提出了一种新的具有直觉模糊数（IFNs）的TWD模型。首先，我们定义了相对损失函数来展示 TWD 中损失函数的一些特征，这是未来研究的基础。然后，基于损失函数和干扰素之间的相关性，我们得到基于干扰素的相对损失函数。同时，从不同的角度讨论了 TWD 的分类规则，包括阈值及其属性。针对数值不合理的MADM问题，建立了一种新的相对损失函数积分方法，以获得更公平的备选损失积分结果。此外，考虑到MADM中没有决策属性，只有条件属性，我们采用灰色关联度来计算条件概率。最后，提出了一种新的TWD模型来解决干扰素的MADM问题，并通过一个供应商选择的实例来证明其有效性和实用性。