Fuzzy Relationship Of Rough Approximation Operators And Related Attribute Reduction Theory

The rough sets theory was put forword at the beginning of 1980s by Polish mathematician Z.Pawlak[9] ,as a math theory to study uncertain knowledge. Its main thought is to depicts approximately learning of inaccurate and uncertain by using the known. The rough sets theory can analysis and process effectively all kinds of immaturity information as inexactness, uncertain, uncompleted, find implicative knowledge and open out potential rules.The rough sets theory was established above the classified mechanism. In the Pawlak rough sets the partition was understanded as equivalence classes in specific univerce, and the family of equivalence classes defines a partition of the universe, so the partition of equivalence classes in universe was considered equally with knowledge, and every partition was called conception. The relation in the Pawlak rough sets is equivalent , but in many actual problems, the dual relations of universe is not often equallent, this caused the application of the Pawlak rough sets to be restricted. In reference[ 1 ] the dual equivallent relations was expanded to general dual relations, which made the rough sets theory be used more. But even if it is under the general dual relations, the attribute value in the policy-making table which corresponding to rough sets model still limited in little integers. When the attribute values is of real numbers it iwill be helpless.In view of the data limitation in real life, which causes the equivallent relation to attenuate and the Pawlak rough sets results in the application to be limitted, this paper first produced several concepts of neighborhood related to the paramete A of the object in the universe under fuzzy relationship through quoting the neighborhood system concept in the topological space, and explained these neighborhoods' nature with the dual fuzzy relationship. Then, in this foundation,the Pawlakrough approximation operators is expanded and produces the definition of rough approximation operators related to the paramete λ, also discussed its natures. In succession. embarking from the dual angle, we reproduces two pair of roughapproximation operators related to the paramete X based on successor neighborhood related to the paramete A, and the nature is considered. We also discussed the relation of dual fuzzy relation, neighborhood operators related to the paramete X and three kind of rough approximation operators. Finally, the attributes discovery theory in the fuzzy information system is produced based on the concepts in reference[ 7 ], which applied the fuzzy relationship to processing knowledge in policy-making table.