The Disscussion Topological Of Rough Sets

Rough sets theory is a new mathematical tool for dealing with uncertain knowledge. It can be used effectively to analyze incomplete and inconsistent information and to discover the knowledge hidden in information systems. There are many important results in the theory and application of rough set theory after thirty years of development. Topology is an important branch of pure mathematics. It has been applied in many fields of mathematics. The thesis is devoted to the discussion of the topological structure, algebraic structures and the related problems of rough sets. The main achievements are as follows.1. The topological space induced by lower approximations in an approximation space is investigated. The topological properties of approximation operators with respect to rough sets model based on general binary relation and reflexive and symmetric relation are discussed. The related rough topological spaces induced by lower approximations are constructed. For general universe, it is proved that there exists a one-to-one correspondence between the set of all topologies induced by lower approximations based on reflexive and transitive relation on U and the set of all topologies on U. The notion of continuous mapping of generalized approximation space is proposed and some basic properties of continuous mapping are obtained.2. The rough topological space M induced by two-tuples rough sets is studied. The analytic expression of interior and closure operators of M with respect to Pawlak approximation operators and the topological basis of M are presented. Based on rough approximation operators induced by reflexive and transitive relation, when the universe is an infinite set the structure and properties of rough topological space M are analyzed. The interior and closure operators are constructed. The rough fuzzy topological space consisting of rough fuzzy sets is constructed based on rough fuzzy approximation operators.3. The non-classic logical algebraic structure of rough set algebra is studied. In residuated lattice, the necessary and sufficient condition for the existing of adjoint pair with respect to a multiplication operation is given. The adjoint implication is constructed. The union, the intersection, the complement, the implication and the multiplication operations on the set of all rough sets are defined. It is proved that the rough sets algebra is a lattice with respect to these operations. The BL algebra and MV algebra of rough sets are constructed respectively. The filter of rough algebra is discussed and the structure of the filter is portrayed.4. Based on symmetry restriction tolerance relation, the judgment theorem of attribute reduction of set-valued information system is given. The reduction method is proposed with the assistance of discernibility matrix and discernibility function. The reduction theory and methods of set-valued decision table based on symmetry restriction tolerance relation are discussed. The judgment theorems of distribution reduction and positive region reduction of set-valued decision table are presented. The reduction methods are proposed with the assistance of discernibility matrix and discernibility function. In the end, as an application of the reduction theory of set-valued decision table, we propose an approach to analyze the cause road traffic accidents.