A fuzzy covering-based rough set model and its generalization over fuzzy lattice

In this paper, we study a new type of fuzzy covering-based rough set model by introducing the notion of fuzzy β-minimal description. We mainly address the following issues in this paper. First, we present the definition of fuzzy β-minimal description and study its properties. Then, we define a novel type of fuzzy covering-based rough set model and investigate the properties of this model. Furthermore, the axiomizations and matrix representations of the fuzzy covering lower and fuzzy covering upper approximations are the vital problems we investigate in this paper. Moreover, we explore the conditions under which two fuzzy β-coverings generate the same fuzzy covering lower or fuzzy covering upper approximations. Finally, we generalize the model to L-fuzzy covering-based rough set which is defined over fuzzy lattices. Similar to the fuzzy covering-based rough set model, we also address the issues mentioned above to the L-fuzzy covering-based rough set.