Two operators in rough set theory

In order to understand the essence of certain increment operator and the uncertain decrement operator, we redefine these two operators. Furthermore, the certain increment operator and the uncertain decrement operator are developed by introducing multiple sets, and some properties based on the two multiple sets operators are analyzed. Meanwhile, two equalities well known in the rough set theory can also be extended. Moreover we measured the approximation classification accuracy, classification quality, and discussed the relation between the classification accuracy of X on U and X on Si in dual vertically partitioned data base. Finally, examples are provided to understand the significance of two multiple sets operators.