Research On Decision Systems Reduction With Rough Sets

Feature selection or feature extraction is one of the most important research topics in datamining, machine learning and artificial intelligence, mining out a potential effective informationfrom mass data. Information table (or called information system) and decision table (or calleddecision system), the concrete embodiments of massive data, are the two main objects to beresearched in feature selection. It is a fact that decision system is the particular and extension ofinformation system and decision system reduction can be degenerated into information systemreduction. As a result, the dissertation focuses on the research of decision system reduction,which aims to take out irrelevant and redundant data with maintaining invariable classificationability and gets a compact data.Rough set theory is a mathematical tool of uncertainty information analysis and processingbased on set theory. It can effectively analyze and process inconsistent, inaccurate, incompleteuncertainty information and knowledge. Without needing any prior knowledge, decision systemreduction based on rough set theory can effectively eliminate the redundancy, obtain the reducedrule set and improve application efficiency of decision system. Therefore, there is an importanttheoretical and practical value to research on rough sets theory and its application to featureselection in machine learning and artificial intelligence.The dissertation mainly researches and explores attribute reduction in decision systemsand rule extraction from the following aspects:(1) In order to solve the problem that empty sets could be got by attribute reduction basedon dependency, this dissertation puts forward a novel approach—conditional knowledge gran-ularity based attribute reduction. Examples show that the proposed method can well reflect theimportant degree of attributes.(2) Dealing with attribute reduction in inconsistent decision systems, rough communica-tion with mapping establishes a link between consistent decision systems and inconsistent de-cision systems. As a result, attribute reduction in inconsistent decision systems is convertedinto attribute reduction in consistent decision systems with important significance. ThroughUCI standard data sets, experiment results show the validity and effectiveness of the proposedmethod.(3) Classical attribute reduction approaches only consider information from the positive re-gion, thereby the information from the boundary region and negative region is overlooked. In-tuitionistic fuzzy sets(IFSs) are introduced into decision systems. According to the relationshipamong positive region, negative region and boundary region, membership and non-membership degree of IFSs are defined. With similarity measures in IFSs, the dissertation studies a novelattribute reduction approach called a relative similarity reduct in decision systems. A rela-tive similarity reduct is a generalization. Simultaneously, positive reduct, negative reduct andpositive-negative reduct are its special cases. Experimental results show that selecting appro-priate similarity measures, classification performance could be improved largely.(4) This dissertation systematically analyzes the relationship between feature selection andattribute reduction, especially researching the relationship between reducts and local optimalsolutions, globally optimal solutions of heuristic optimization algorithms. We point out theproblem that solutions of heuristic optimization algorithms (called an approximate reduct) maybe not reducts (called a fake reduct). Therefore, a novel attribute reduction algorithm withan order is proposed to solve the problem. Furthermore, to solve the problems brought fromfake reducts and inconsistent decision systems, a novel attribute value reduction algorithm isproposed. A few examples show the feasibility and effectiveness of the proposed algorithm.