Properties and axiomatization of fuzzy rough sets based on fuzzy covering

Some expanded fuzzy rough sets models have been investigated to handle fuzzy databases with uncertain, imprecise and incomplete real-valued information. In this paper, we make further research on fuzzy rough sets models in fuzzy environment, and we generalize rough fuzzy sets model based on a covering to fuzzy rough sets model based on a fuzzy covering. The lower and upper approximations of fuzzy subsets are defined based on a fuzzy covering, and basic properties are investigated. Then, the axiom definition of the lower approximation operator is given. It is shown that the rough fuzzy sets model based on a covering is a special instance of the fuzzy rough sets model based on a fuzzy covering.