I will analyze Pawlak’s rough sets and extend the usual setting of characterization via an equivalence relation to any arbitrary relation, or a full relation. I extract the specification of rough sets by two operators: probable operator and sure operator. This would provide a general framework to analyze full rough sets and to compare them with Pawlak’s rough sets. It also facilitates all the computation and further expansion. This paper extends Pawlak’s approximation approach to any arbitrary relations and explicitly defines several computational operators to study the closeness regarding the characterization of operations on sets.