On the relationship among F-transform, fuzzy rough set and fuzzy topology

The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct and -transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces.