Research Of Rough Sets Theory And Its Applications Based On Two New Operators

Rough sets theory is a new mathematical approach to imperfect knowledge after fuzzy sets theory. Rough sets theory has found many interesting applications. The rough set approach seems to be of fundamental importance to AI (artificial intelligence) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery, expert systems, inductive reasoning and pattern recognition. After more than 20 years of pursuing rough set theory and its application, the theory has reached a certain degree of maturity. But, it is still young comparing with other mature theories and needs further study to perfect it.In this paper, the topology of rough set and two important inequalities in rough sets theory are mainly discussed. Some interesting results are given and the hierachical reduction algorithm of huge information system is proposed.Firstly, the concepts of the basic factor of inducing rough and the correlation basic factor of inducing rough are introduced. In the following, the borderline region of rough set is divided into two parts: the inducing rough region and inducing rough correlation region. This division will help us to analyze and discuss properties of the following contents.Secondly, two inequalities well known in the rough sets theory can now be modified to become equalities based on the certain increment operator and the uncertain decrement operator. Many properties in rough sets theory can be improved and in particular, the operations of approximation can be calculated step by step. In the same time, the operations and its properties of rough set and the roughness of fuzzy rough set are discussed on the equalities condition.At last, for figuring out the reductions of huge information system, a hierachical reduction algorithm is put forward. After the further study of the certain increment operator, we get a series of theorems, which settled theoretic basis for hierachical reduction algorithm. Then the hierachical reduction algorithms on the information...