Hierarchical Three-Way Decisions With Intuitionistic Fuzzy Numbers in Multi-Granularity Spaces

Intuitionistic fuzzy sets, as extensions of fuzzy sets, are described by intuitionistic fuzzy numbers (IFNs) that describe the uncertain concepts with the membership and non-membership degrees together. Three-way decisions are effective classification methods, which are always utilized for solving uncertain problems with fixed cost parameter values and fixed attribute values in reality. However, under dynamic intuitionistic fuzzy environments, three-way decisions face a great challenge for processing uncertain problems with IFN cost parameters and IFN attribute values. In this paper, by considering the impact of IFNs, a hierarchical three-way decision model with IFN cost parameters (H3WDIF-I) is established in multi-granularity spaces for handling dynamic and uncertain problems first. The change rules of H3WDIF-I are discussed to analyze the relationships of decisions based on the granularity structures. In addition, when the IFN cost parameters and IFN attribute values arise together, a hierarchical three-way decision model with IFNs (H3WDIF-II) is proposed to explore three-way decisions in depth under dynamic intuitionistic fuzzy environments. Similarly, the change rules of H3WDIF-II are also discussed from the viewpoint of classification losses in multi-granularity spaces. Finally, the presented change rules are verified by many examples and experiments.