Constructing Robust Fuzzy Rough Set Models Based on Three-way Decisions

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.

Automated summary

The paper explores the combination of fuzzy rough sets and three-way decisions, constructing robust fuzzy rough set models from a three-way decision perspective. Experimental results demonstrate the better performance in terms of robustness of the improved model based on three-way approximations.