Triangular Fuzzy Number Intuitionistic Fuzzy Covering Rough Sets and Applications to Decision Making

The triangular fuzzy number intuitionistic fuzzy set, as an extension and generalization of intuitionistic fuzzy set, has more advantages than the single value representation of membership degree and non-membership degree and interval number representation of intuitionistic fuzzy set. In this paper, the triangular fuzzy number intuitionistic fuzzy set and rough set are fused, and the triangular fuzzy number intuitionistic fuzzy rough set model is constructed based on the intuitionistic fuzzy approximation relation of triangle fuzzy number. Firstly, the approximate operators, correlation properties and three-way regions are discussed and verified by numerical examples. Furthermore, combined with the covering rough set, the triangular fuzzy number intuitionistic covering rough set is constructed, which can be used for multi-attribute decision making. Then, combined with the covering rough set, the triangular fuzzy number intuitionistic fuzzy covering rough set is constructed, which can be used for multi-attribute decision making. Finally, the multi-attribute decision making is carried out with an example considering the expert weight. The results show that the triangular fuzzy number intuitionistic fuzzy covering rough set become novel and effective for multi-attribute decision making. This study provides an in-depth insight into decision making from model and method.