Study And Applications Of Attribute Reduction Algorithms On Rough Sets

Rough Sets(RS) theory, introduced by Z.Pawlak, is a new mathematical tool to deal with knowledge, particularly when knowledge is imprecise or inconsistent. In this dissertation, the research trends and the attribute reduction theory of RS are presented firstly. Then the existing attribute reduction methods, which consists of X.H.Hu algorithm, Pawlak algorithm and algorithms based on discernibility matrix and information entropy, are summarized. Secondly, the discernibility matrix algorithm is improved by proposing a more objective approach to evaluate the significance of attributes. Thirdly, because the existing algorithms can only find the lesser attribute sets containing redacts at most cases, one new strategy with local retrospect is brought forward to conquer the difficulty. The relativities, not only between the selecting attributes and selected ones, but also among the unselected attributes, should be considered. This strategy is helpful to compute the minimal reduct. Fourthly, the decision rules are classified into three parts: one-one, one-multi and multi-one. Then the decision rules are recognised by digging the statistical information of data bases and their Bayes-error is proved to be minimal, which is a useful conclusion. Finally, all the above theoretical results are applied to the analysis of mellituria II and Monks problems. The conclusion is encouraging after the comparison with home precious machine learning algorithms including ID family and AQ family.