Research Of Features In The Variable Precision Rough Sets Model

Rough sets theory is a hotspot for dealing with intelligent information which has been used in many domains successfully. But it has some limitations, for instance, it is sensitive for data sets which have noise data, therefore some potential useful knowledge can not be mined. In order to overcome these limitations, variable precision rough sets theory extends standard inclusion relation to majority inclusion relation. Based on this extended notion, some degree of misclassification in the largely correct classification is allowed. Features of reduct, reduction mergence, hiberarchy of interval reduct and attribute core are also discussed in order to find weak dependence relationship, more general association and decision rules.In classical rough sets model, quality of classification, relative positive region and lower approximation are decreasing along with attributes reducing. In variable precision rough sets, monotonic decreasing principles of them are broken because of bounce phenomena, and there is no equivalence among them. Attribute reduction is discussed from quality of classification, relative positive region and lower approximation respectively, and their relations are also analyzed.Reduction mergence becomes more complicated in variable precision rough sets model because of inclusion degree. All types of class mergence are discussed in this thesis. The dynamic changes of inclusion degree should be analyzed when positive region is considered, so foundation of interval reduct is established.Reduct anomalies are discussed in detail. The definition of reduct extends from a specific value to a range of inclusion degree, combining with the characteristics of variable precision rough sets model. Reducts are defined and studied from different levels, viz. the quality of classification, relative positive region and the lower approximation of decision classes. There are different anomalies on different levels. Reduct anomalies are eliminated gradually when definition restrictions are enhanced. A kind of measure for interval reduct is also given for evaluating and selecting interval reduct.The conception of interval core is also put forward in this thesis, combining with interval characteristic, so variable precision rough sets theory is developed further. Sort discernibility matrix is constructed and three types of interval sets are defined and analyzed, thus interval core can be obtained. Heuristic algorithm for interval reduct can also be achieved.Finally, the thesis uses UCI dataset for experiment, the results of experiment illustrate correlative theory further.