Labeled fuzzy approximations based on bisimulations

This paper focuses on the labeled fuzzy approximation space, which is considered as a relational structure consisting of a nonempty universal set and some fuzzy relations. To deduce knowledge hidden in the labeled fuzzy approximation space, based on the notion of bisimulations, lower and upper fuzzy rough approximation operators are constructed. Then basic properties of the fuzzy rough approximation operators are investigated. When the largest bisimulation is a trivial identity relation in some cases, the concept of simulations is proposed. Moreover, the lower and upper fuzzy rough relation approximation operators are first proposed and properties of the new operators are examined. Finally, the relationships between two kinds of approximations are discussed.