Research on multi-granularity sequential three-way decisions based on the fuzzy T-equivalence relation

The fuzzy decision-theoretic rough set (FDTRS) is a data processing method based on the fuzzy theory designed to handle decision problems with uncertainty and fuzziness. It simplifies the complexity of decision-making and provides decision strategies by integrating multiple sources of information. This approach makes the decision process more scientific and rational. The mainstream FDTRS model breaks the over restrictive limits of classical decision-theoretic rough sets, computes the fuzzy similarity relation between two objects utilizing the Gaussian kernel function, which is another major breakthrough and innovation in the field of decision-theoretic rough sets. However, this model suffers from the problems of insufficient decision information, single perspective and high decision-making cost when dealing with dynamic, complex and uncertain problems. Emerging in recent years, sequential three-way decisions not only provides a flexible mechanism to implement the idea of progressive computation, but also deals with dynamic, complex and uncertain problems. To this end, this paper proposes a sequential three-way decision model based on the fuzzy T-equivalence relation (FTE-based sequential three-way decision model) from the perspective of sequential three-way decisions, and gives relevant definitions and examples to effectively solve the problem of insufficient information. Then in order to solve the single-view problem, we extend the sequential three-way decisions to the case of multi-granularity, and propose FTE-based multi-granularity sequential three-way decisions in four aggregation strategies with the corresponding properties and algorithms. In addition, the rationality of models are tentatively analyzed through specific examples. Finally, six sets of UCI standard datasets are used to validate the proposed models, which demonstrate their good performance. These models contribute to the field of fuzzy decision-theoretic rough sets and sequential three-way decisions.