Research Of Data Reduction Method Based On Fuzzy Equivalence Relations

Classical rough set theory that Z. Pawlak proposed analyze data which contains only nominal attributes on the basis of the indiscernibility relation induced by attributes. The actual information system contains not only nominal attributes, as well as numeric attributes. Reduction of nominal attributes and hybrid data is the main contents of this thesis, both are considered by the same kind of way in the text-transforming reduction problem into construction and simpled problem of a matrix.In this paper, the reduction method which on the basis of discernibility matrix is adopted for the information system contains nominal attributes. The deficiency of general reduction algorithm is discussed, thus the method of using conjunction to simplify the process of constructing the discernibility matrix is proposed. The final reduction result can be obtained by the measure of attribute importance and the influence of removing attribute combined-item on matrix, which omit traditional model of transforming conjunctive normal form to disjunctive normal form.The existing documents started from discretization of numeric attributes with different symbols to denote sub-division of intervals for hybrid data, so as to the data of unified form can be reducted; Or using Fuzzy-rough set and genetic algorithm to extend indiscernibility relation. Fuzzy-rough set is one of the important models for hybrid data analysis. Constructing the fuzzy equivalence relation is the key to hybrid data analysis based on fuzzy-rough set model. In this paper, a weighted similarity measurement between objects which on the basis of Fuzzy-rough set is proposed to construct the fuzzy equivalence relation, that overcomes the limitation of existing methods and also ensures reduction must be on the basis of equivalence relation. The reduction algorithm based on quantization knowledge is designed by domain knowledge, which adding experience of domain experts and the needs,the preferences of users, that reducing the loop computing effectively. The validity and feasibility of the proposed method are demonstrated by attribute reductions on five data sets from UCI machine learning database.