Research On Knowledge Acquisition And Reduction In Rough Set Theory

Rough sets theory (RST) is a mathematical tool, which can effectively analysis and process inaccurate, inconsistency, incomplete information. Compared with some other theories such that probability theory, fuzzy set and evidence theory, RST does not need any prior knowledge except data sets. With over30years development, rough set has been widely applied to many areas, such as machine learning, approximate reasoning, expert system, data mining, decision analysis, image processing, medical diagnosis, financial data analysis and so on.Rough set research areas include rough set model development research, knowledge acquisition and reduction, measurement of knowledge uncertainty, etc, the method of knowledge acquisition and reduction are keies in the RST. Therefore, this dissertation aims to study of the RST based on the decision rules acquisition and reduction algorithm, the main work and contributions are summarized as following:(1) Through the analysis of differences relation based rough set and probabilistic rough set, the former is only suitable for acquisition and reduction of negative decision rules in missing type Incomplete Decision Information System(IDIS), however, it is not suitable for handling the lossing type IDIS; the later can obtian negative decision rules, but has no reduction. In this dissertation, rough set model based on descriptors’s negative support set is proposed to acquire negative decision rules in lossing type IDIS. The lower/upper approximate distribution reduct based on discernibility matrix is presented, which can preserve the lower/upper approximation distribution about the descriptors’s negative support set. Some numureical examples of student global evaluation are employed to substantiate the conceptual arguments.(2) Existing rough set model can not be used to acquire positive and negative decision rules in incomplete and noised decision information systems. In this dissertation, the variable precision rough set (VPRS) based on descriptors is proposed to investigate the positive and negative decision rules in incomplete and noised decision information systems. The descriptors reduction is presented, which can simplify the positive and negative decision rules at the same time. However, this method can not obtain the optimal positive and negative decision rules. Therefore, a heuristic reduction algorithm is presented, which can preserve the positive region distribution consistent about positive decision class (negative decision class). And the results of examples about student global evaluation show its effectiveness. (3) To overcome the limitations of the optimistic multigranulation rough set (OMRS) be too relaxed and the pessimistic multigranulation rough set (PMRS) be too strict, the variable multigranulation rough set (VMRS) is presented, in our VMRS, the threshold β, is used to control the number of granulations. It is proven that VMRS is ageneralization of OMRS and PMRS, OMRS and PMRS is the special case of VMRS. Furthermore, several important measurements are introduced into VMRS; it is shown that the measurements of VGRS are between the measurements of OMRS and PMRS. Some methods of acquisition of decision rules in VMRS are deeply discussed and its judgment theorem is also presented. The reductions of VMRS are investigated and the heuristic reduction algorithms based on attribute dependency are proposed, which can preserve lower/upper approximate distribution consistent. These results are meaningful both in the theory and applications for multigranulation rough set.