Research On The Knowledge Reduction Methods Based On Inconsistent Decision Table

During the process of knowledge discovery, in order to solve the problem of information noise or information incompleteness, it is necessary to develop the theories and methods which can deal with imprecise and uncertain information. Rough set theory is one of important novel mathematical tool to meet those demands. The valuable and non-trivial patterns are mined by application of rough set theory and method in knowledge discovery.Knowledge reduction is one of the fundamental contents in rough set theory. At present, many research results have been achieved, but most of them are just effective for information system without decision attributes or consistent decision table and invalid for inconsistent decision table.For consistent decision table, the approach to knowledge reduction based on D-S evidence theory is consistent with algebraic reduction. For inconsistent decision table,the difference between generalized decision reduction based on D-S evidence theory and algebraic reduction has been illustrated by an example firstly. It is proved that generalized decision reduction is just equivalent to assignment reduction. The essential causes that algebraic reduction and generalized decision reduction obtain a different result for inconsistent decision table are analyzed. A new approach to algebraic reduction based on evidence theory is proposed by transferring the inconsistent decision table into consistent one. By establishing the relationship between positive region bases and belief function, a new approach which can obtain algebraic reduction based on D-S evidence theory is proposed and its correctness is illustrated by a numerical example.It is proved that knowledge reduction based on decision power is equivalent to that based on conditional information entropy after knowledge reduction based on decision power discussion. From the view of conditional probability, because the mathematical models for algebraic and conditional information entropy reductions are unified formally, the reason of Consistency of their application in consistent decision table and inconsistency of their application in inconsistent decision table can be discussed. A new decision power which coincides with positive region is presented and a heuristic algorithm is proposed, which ensures to obtain an algebraic reduction, its correctness is illustrated by a numerical example.Attribute discernibility and discernible matrix are studied to establish the relationship between attribute discernibility and the number of times in discernible matrix. Based on the thought that equivalent discernible matrix has the same attribute reduction and core, the existing discernible matrices are rewritten, and then, the method based on knowledge measurement computation is generalized to decision table. The calculation formulas of attribute discernibility for Hu's discernible matrix reduction and algebraic reduction are obtained. Accordingly, the heuristic reduction algorithms based on attribute discernibility are presented. The biggest advantage of these two algorithms is to calculate knowledge reduction without discernible matrices construction. Thus, they can avoid the low efficiency of discernible matrices. These methods have not only clear explanation but also solid theoretical foundation. Numerical examples and results of simulation experiment show that the proposed method can explore the optimal reduction more easily. At the same time, the new way to construct the high efficient heuristic reduction algorithm is given, by application of two general frameworks used to design heuristic reduction algorithm.