Research On The Knowledge Reduction Based On Rough Set Theory For Decision Table

During the process of knowledge discovery, it is necessary to develop the theories and methods which can deal with imprecise and uncertain information caused by noise or incompleteness. Rough set theory is a novel mathematical tool to handle uncertain information. Knowledge discovery based on rough set theory is a process of finding new, applicable and non-trivial patterns by rough set theory and method. As one of the fundamental contents in rough set theory, knowledge reduction is intensively studied in terms of discernible matrix, heuristic information algorithms and database systems. Knowledge reduction in vague objective system is discussed by introducing rough set theory.Since the existing discernible matrices can only adapt to consistent or partially consistent decision table, they can not obtain correct reduction results for completely inconsistent one. A improved knowledge reduction algorithm based on discernible matrix is proposed.A simplified discernible matrix can be constructed by equivalence class instead of single element. The core attribute calculation of algebraic and conditional information entropy reductions is discussed from the view of discernible matrix. It is pointed out that the algebraic core of a decision table is the subset of its information core. It is proved that distribution and assignment consistent sets must be algebraic consistent ones. However, not all algebra reductions can find corresponding distribution or assignment reductions to include them, which is illustrated by some numerical examples. Based on the thought that equivalent discernible matrix has the same attribute reduction and core, the existing discernible matrices for distribution, maximum distribution, assignment and algebraic reductions are rewritten as a uniform form. The inconsistence and intrinsic relation between different types of knowledge reductions are analyzed under inconsistent decision table. New methods of transforming distribution or assignment reductions into algebra reduction, distribution reduction into assignment reduction are presented. A new approximate quality is proposed, based on which a heuristic reduction algorithm is established. The attribute significance based on positive region is analyzed. It is found that the classes which can be completely predicted by decision-making attribute or is completely composed of inconsistent objects have no influence on attribute significance. Therefore, these classes can be eliminated to narrow the search space. A new approximate quality and a new formula measuring attribute significance are established. Theoretical analysis and experimental results show that the proposed heuristic algorithm is efficient.The approximate quality is based on basic equivalence class. The significance of an attribute can not be described precisely by approximate quality for its huge partition granularity. It is reasonable to describe the significance of an attribute with its discernibility, for rough set is on the basis of classification. For attribute discernibility is embodied in attribute discernible matrix, the calculation formulas of attribute discernibility for decision table is obtained by combining them. Thus, a heuristic reduction algorithm based on attribute discernibility is presented. Experimental results show that the proposed method can explore the optimal reduction more easily.The drawbacks of the existing rough set model based on database systems are analyzed. A simple judgement theorem for algebraic core attribute is presented, which simplifies the calculation by comparing the cardinality of two positive regions instead of the elements of them. A simple method of calculating the core based on database system is presented, which is able to deal with all kinds of decision tables, whether consistent or not. Most existing reduction algorithms, which adopt a bottom-up strategy, can not guarantee their completeness. Since all conditional attributes are algebraic consistent sets, one can obtain an algebraic reduction by traversing them only once with a strategy of up-bottom. To get an optimal or sub-optimal reduction, a heuristic algorithm based on database systems is proposed.A similarity measure between vague sets based on fuzzy entropy is proposed. Based on the rough set theory, knowledge reduction in vague objective system is discussed.Rough set, vague set and D-S evidence theories are the methods to process incomplete and uncertain problems in information systems. Though they deal with problems in different points of view and have their own advantages and disadvantages. It can resolve the incomplete and uncertain problems by combining them. The fusion research between rough set, vague set and D-S evidence theories will be one of the future research topics.