The Research On The Several Problems Of Rough Sets

Rough set theory is a new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. Rough set theory by Z.Pawlak has three parts: (1) the representation of uncertain knowledge by using upper approximation and lower approximation (2) data reduction (3) reasoning with vague and /or imprecise knowledge. In the theory,an object,impossible to be determined on the basis of known knowledge,belongs to the boundary region which is the minus of upper approximation and lower approximation.The number of vague elements in the boundary region can be calculated on the basis of the mathematical description of upper and lower approximations by the equivalence relation,this realizes the idea of the boundary region by GFrege.Rough set theory has many important applications in artificial intelligence and cognitive science,especially in the representation of and reasoning with vague or imprecise knowledge,machine learning,knowledge acquisition,decision analysis, knowledge discovery from databases,pattern recognition and expert systems.The main work of this paper is as follows: Recognition of approximation quality in Rough sets Rough approximation space provides the accuracy factor a of an object set approximation and the degree factor y of dependency for sets of attributes. The precision factor n of approximation can be introduced to compare with a. By approximation error rates based on the distance measure of sets,the factors a,r and can be reinterpreted. By developing one dimension data space to k dimension space.k dimension approximation space and its approximate factors can be obtained. A method for discovering functional dependencies based on the stripped partition database This efficient method is based on the concept of agree sets. From agreee sets,maximal sets and its complements are derived,and all minimal non-trival functional dependencies can be generated. The computation of agree sets can be decreased by using the stripped partition database. A levelwise algorithm is used for computing the left hand sides of minimal non-trivalfunctional dependencies. This method is better than other methods for discovering functional dependencies on time complex. Data reduction based on rough sets Rough sets allow people to determine for a given information system the most important attributes from a classificatory point of view. The discernibility matrix and the discernibility function can help people to construct efficient algorithms related to the generation of reducts. The reduction on decision tables includes attribute reduction,attribute value reduction and minimal decision algorithms. Rough sets and other data reasoning In this paper,the relationships between rough sets and probability logic,Bayes' rule,Dempster-Shafer evidence theory,modal logic are discussed respectively. Formal concept analysis based on routh sets Formal concept analysis is useful for representation and analysis of data. This paper presents a approach for formal concepts to respectively approximate a given object set,a given feature set and a pair of a given object set and a given feature set. This approach is based on rough set. A perspective on measures for rough set data analysis based on rough inclusion degree In this paper,the relationships between inclusion degree and each of various measures in rough set theory are discussed. The fact that various measures in rough set can be redefined by using the concept of inclusion degree will be helpful for people to understand the essence of rough set.