Dynamic rough fuzzy set model based on fuzzy β-covering

Rough fuzzy sets (RFSs) offer significant advantages in handling uncertain information, but traditional models often rely on fixed equivalence relations, which limits their adaptability in dynamic environments. This paper introduces a novel dynamic rough fuzzy set (,B-DRFS) model, which incorporates fuzzy ,B-covering approximation spaces from an application oriented perspective. In this framework, we define a fuzzy ,B-equivalence relation over a family of fuzzy sets, allowing the induced dynamic partition of the universe U varies with ,B This dynamic adjustment enables the model to flexibly adapt to different levels of granularity in data analysis. Based on the dynamic equivalence relation, we construct a new rough fuzzy set model and systematically explore its mathematical properties. Furthermore, to enhance computational efficiency and logical precision, we develop a matrix method for calculating lower and upper approximations within the proposed model. Finally, we introduce a decision algorithm based on this model and demonstrate its effectiveness in controlling the Asian corn borer pest, showcasing its practical applicability in real-world uncertain data analysis.