Construction of rough approximations in fuzzy setting

In this paper, two L-rough approximation operators are defined by an arbitrary mapping from the set of all singletons to the set of all L-sets, which is a graded extension of Järvinen's method. It also provides a convenient method to compute rough sets in fuzzy setting. Then the algebraic structure of rough sets and the relation to L-topology are investigated. In the end, three special cases are discussed: ϕ is extensive, symmetric, and intensive.