  This paper further studies the fuzzy rough sets based on fuzzy coverings. We
first present the notions of the lower and upper approximation operators based
on fuzzy coverings and derive their basic properties. To facilitate the
computation of fuzzy coverings for fuzzy covering rough sets, the concepts of
fuzzy subcoverings, the reducible and intersectional elements, the union and
intersection operations are provided and their properties are discussed in
detail. Afterwards, we introduce the concepts of consistent functions and fuzzy
covering mappings and provide a basic theoretical foundation for the
communication between fuzzy covering information systems. In addition, the
notion of homomorphisms is proposed to reveal the relationship between fuzzy
covering information systems. We show how large-scale fuzzy covering
information systems and dynamic fuzzy covering information systems can be
converted into small-scale ones by means of homomorphisms. Finally, an
illustrative example is employed to show that the attribute reduction can be
simplified significantly by our proposed approach.
