| Rough set theory is a new theory of data analysis, it was first put forward by Poland scientist Z.Pawlak. At present it has been developed to be a new mathematical tool to deal with vagueness and uncertainty. It has been applied successfully to many areas including machine learning, pattern recognition, decision support, data mining and process control.The theory of Pawlak rough set was established at the base of equivalence ralation. The reseachers put forward many kinds of generalized rough set models in order to expand its applying areas. Among these reseach areas, Z.Bonikowski established covering rough set model using a covering of a universe. The researchers reasonably modified the difinition of the covering approximation operation in Z.Bonikowski's model and proposed some pairs of covering approximation operators. In this paper, we discuss the properties of these covering approximation operators. The relationships among these operators were investigated. Furthermore, the relationships between these operators and the operators in Z.Bonikowski model were investigated.There are two basical ralational fomulas of rough set inclusion: . This means that the information may be lost in the operations of union, intersection and complement in rough set theory. Zhang Huaguang[28,29] solves the problems of information lost by introducing two operators in Pawlak model. In this paper, we will discuss the properties of information lost in the covering rough set. We solve this problems by introducing two new types of operators in covering rough set. We also discuss the algebraic properties of the covering rough set based on the two operators.Futhermore, we establish the covering rough set based on the Boolean algebra.
|
PDF Full Text Request