Properties And Relative Individual Reduction Of Covering Approximation Space

The theory of Pawlak rough set is established at the base of equivalence relation.The researchers put forward many kinds of generalized rough set models in order to expand its applying domain.Covering rough set is a kind of important extension of Pawlak rough set.Firstly,we defined some uncertainty measurement in two forms of covering rough-fuzzy set (constant covering rough-fuzzy set and interval-valued covering rough-fuzzy set), proposed some important properties of these uncertainty measurement in this paper,and opened out the relationship between covering rough set and fuzzy set.Secondly,knowledge reduction is the core of the covering approximation space.We put forward the relative individual reduction in the covering rough approximation space,discussed some properties of this reduction and pointed out the relationship between relative individual reduction and absolute reduction,extending the reduction theory in the covering approximation space.Lastly,rough set keep a close with generic topological and discussing the separation in topological spaces is a question for discussion.So we put forward some properties of the separation in covering approximation space,such as transmissibility and mapping,not only enriching the theory of rough set,but also expanding the actual application of generic topological.