Three-Way Fuzzy Sets and Their Applications (II)

Recently, the notion of a three-way fuzzy set is presented, inspired by the basic ideas of three-way decision and various generalized fuzzy sets, including lattice-valued fuzzy sets, partial fuzzy sets, intuitionistic fuzzy sets, etc. As the new theory of uncertainty, it has been used in attribute reduction and as a new control method for the water level. However, as an extension of a three-way decision, this new theory has not been used in multi-criteria decision making (MCDM for short). Based on the previous work, in this paper, we present rough set models based on three-way fuzzy sets, which extend the existing fuzzy rough set models in both complete and incomplete information systems. Furthermore, the new models are used to solve the issue of MCDM. Firstly, three-way fuzzy relation rough set and three-way fuzzy covering rough set models are presented for complete and incomplete information systems. Because almost all existing fuzzy rough set models are proposed under complete information, the new proposed models can be seen as a supplement to these existing models. Then, a relationship between the three-way fuzzy relation rough set and the three-way fuzzy covering rough set is presented. Finally, a novel method for the issue of MCDM is presented under the novel three-way fuzzy rough set models, which is used in paper defect diagnosis.