Rough Sets Based On Covering With Its Extension And Application

Rough set theory is a new mathematical tool of dealing with uncertain information, scientist Pawlak put forward this theory at 1982.At present it has developed to be a important researching direction of artificial intelligent, it has very extensive latent applying background at the field of Data Mining.The initial rough set theory of Pawlak was established at the base of equivalent relation. In the later research of Rough set theory, the researchers put forward all kinds of rough set models in order to expand its applying space. In these research results, Z. Bonikowski established covering generalized rough sets model using a covering of a universe, in Z. Bonikowski's model, the covering upper approximation operation and covering lower approximation operation are not dual to each other. William Zhu proved them determining each other, but he cannot give the quantity relation of them. In this paper, we reasonably modified the definition of the covering upper approximation and covering lower approximation in Z. Bonikowski's model, make them dual to each other, and at the same time, discussed the proposition of covering upper approximation operation and covering lower approximation operation and the reduction of coverings under the new definition. Furthermore, the lower and upper approximation operations have been axiomized.Some practical problems allow certain degree error of classification, in order to solve the problems, this paper extended our model and put forward the degree rough set model based covering. In addition, this paper established fuzzy rough set model based covering. Finally, we applied the model to incomplete system, and abstracted rules from incomplete system.