Soft Rough Approximation Operators on a Complete Atomic Boolean Lattice

The concept of soft sets based on complete atomic Boolean lattice, which can be seen as a generalization of soft sets, is introduced. Some operations on these soft sets are discussed, and new types of soft sets such as full, keeping infimum, and keeping supremum are defined and supported by some illustrative examples. Two pairs of new soft rough approximation operators are proposed and the relationship among soft set is investigated, and their related properties are given. We show that Jarvinen's approximations can be viewed as a special case of our approximation. If B = p(U), then our soft approximations coincide with crisp soft rough approximations (Feng et al. 2011).