The Applications Of Topology In Rough Set Theory

The rough set theory was put forward by Professor Z.Pawlaw, as a math theory to study uncertain knowledge .It can analysis and process effectively all kinds of immaturity information as inexactness, uncertain, uncompleted ,find implicative knowledge and open out potential rules . At the last few years, it has been used extensively in the fields of machine-learning and knowledge acquisition, data mining, decision support and analysis. At present, the theory of rough sets has always become the most lively domain in the information science.The second part of this paper puts forward the concepts of minimum description element and topological covering approximation space and elaborates the relation between minimum description elements and topological approximation space. Original rough membership function is defined by using equivalence classes, we will extend it in Generalized covering spaces based on the concept of minimumdescription element, we can use this kind of rough membership function to define afuzzy set, so we can integrate the concept of rough and fuzzy sets. Then some examples will be illustrated to describe the conclusions. Finally, A generalization in Pawlak rough set model was obtained base on the membership degree of Generalized covering spaces, and the relevant properties are also given.The third part of this paper puts forward the lower and upper approximations of the fuzzy rough set model. Some conclusions about the lower and upper approximations have been obtained.