Fuzzy rough sets are an effective tool for dealing with uncertainty information. The theory of three-way decisions provides a method of decision-making, when a two-way decision may be difficult to make. In this paper, we investigate the combination of fuzzy rough sets and three-way decisions, and construct robust fuzzy rough set models from a three-way decision perspective. In fuzzy rough sets, by introducing a pair of thresholds, we propose three-way approximations of the fuzzy similarity degree, and we construct three-way lower and upper approximations based on the idea of a three-way decision. Furthermore, we discuss the special cases of three-way approximations about of both the fuzzy similarity degree and dual approximations. Sixteen fuzzy rough set models are constructed for under different special cases. Among them, three improved models and the original model are selected to be compared as examples. Finally, for the four fuzzy rough set models, including one model based on three-way decisions, two models based on two-way decisions, and one original model, we design the experiments by introducing two types of data noise to test the robustness of the models. The results verify the better performance of the improved model based on three-way approximations in comparison with the two-way and original models.

模糊粗糙集是处理不确定性信息的有效工具。当可能难以做出双向决策时，三级决策理论提供了一种决策方法。在本文中，我们研究了模糊粗糙集和三向决策的组合，并从三向决策的角度构造了鲁棒的模糊粗糙集模型。在模糊粗糙集中，通过引入一对阈值，我们提出了模糊相似度的三项近似，并基于三项决策的思想构造了三项上下近似。此外，我们讨论了关于模糊相似度和对偶近似的三向近似的特殊情况。针对不同的特殊情况，构造了十六个模糊粗糙集模型。他们之中，选择三个改进模型和原始模型作为示例进行比较。最后，对于四个模糊粗糙集模型，包括一个基于三路决策的模型，两个基于两路决策的模型以及一个原始模型，我们通过引入两种类型的数据噪声来测试实验的鲁棒性来设计实验。模型。结果证明，与双向模型和原始模型相比，基于三向近似的改进模型具有更好的性能。