Research On Attribute Reduction Of Rough Set

Rough set theory is a mathematical tool dealing with vague and uncertain problems. It is also a kind of promotion form of classical set theory. Attribute reduction is the key step in the data mining based on rough set theory. In order to get useful information from decision information system, it is necessary to study the effective and reasonable attribute reduction algorithm of rough set.The main works of this paper are as follows:(1) The paper analyzes the research status of rough set and studies the basic knowledge of the rough set theory. It introduces the application of rough set in real life under the background of data mining application.(2) The paper introduces two classical attribute reduction algorithms based on the discernibility matrix and the attribute importance respectively. Through specific examples, it analyzes the advantages and disadvantages of each algorithm.(3) This paper combines the discernibility matrix and attribute importance and puts forward a kind of attribute reduction algorithm based on ordered pair. The algorithm applies the improved discernibility matrix, in which the objects of original matrix are replaced with the condition classes. Using ordered pair to express indiscernibility condition class pair, the number of the ordered pair measures the importance of the corresponding condition attribute combination. For these decision tables which contain duplicate or inconsistent objects, the algorithm can effectively reduce the size of the matrix and obtain the minimum condition attribute sets in a short time. By comparing the algorithm of attribute reduction based on ordered pair with other algorithms, the space complexity of the matrix is obviously reduced by the algorithm, and it eventually can be applied into actual data to realize the attribute reduction.(4) The classical rough set theory conducts attribute reduction based on a single granularity space. Multi-granularity rough set gets the approximation approach of concepts by using the knowledge of multiple granularity space. This leads to obtain more reasonable and more satisfactory solution of the problem. In view of grade pessimistic multi-granularity rough set, it defines the granularity matrix. By using the granularity matrix, the measuring formula is provided to calculate the importance of granularity. This paper puts forward a kind of effective granularity reductionalgorithm about the approximate distribution of granularity for grade pessimistic multi-granularity rough set based on the granularity matrix and the granularity importance.