A new approach to soft set through applications of cubic set

The notions of (internal, external) cubic soft sets, P-(R-)order,P-(R-)union, P-(R-)intersection and P-OR, R-OR, P-AND and R-AND are introduced, and related properties are investigated. We show that the P-union and the P-intersection of internal cubic soft sets are also internal cubic soft sets. We provide conditions for the P-union (resp. P-intersection) of two external cubic soft sets to be an internal cubic soft set. We give conditions for the P-union (resp. R-union and R-intersection) of two external cubic soft sets to be an external cubic soft set. We consider conditions for the R-intersection (resp.P-intersection) of two cubic sof sets to be both an external cubic soft set and an internal cubic soft set.