Two fuzzy covering rough set models and their generalizations over fuzzy lattices

By introducing the new concepts of fuzzy β-covering and fuzzy β-neighborhood, we define two new types of fuzzy covering rough set models which can be regarded as bridges linking covering rough set theory and fuzzy rough set theory. We show the properties of the two models, and reveal the relationships between the two models and some others. Moreover, we present the matrix representations of the newly defined lower and upper approximation operators so that the calculation of lower and upper approximations of subsets can be converted into operations on matrices. Finally, we generalize the models and their matrix representations to L-fuzzy covering rough sets which are defined over fuzzy lattices.