Research Of Values Reduction Based On Rough Set Theory

Rough set theory is a new mathematical tool to deal with vagueness and uncertainty. A rapid growth of interest can be lately seen in rough set theory and its applications. Data reduction is a very important subject. This thesis researches on values reduction based on rough set primarily.The measurement of decision rules is analyzed such as support, certainty and converage; the properties of the measurements are also studied. Meanwhile this thesis discusses the process of values reduction. In view of the deficiencies of values reduction, dicernibility matrix is introduced into values reduction. The development and traits of dicernibility matrix are discussed; the problems of values reduction based on dicernibility matrix are comprehensively analyzed too. An improved dicernibility matrix is put forward, which can solve inconsistence of values reduction in algebra view. Moreover the improved dicernibility matrix is used in an incremental algorithm to update the existing decision rules with incremental way when a new example is added in decision table. This algorithm can acquire both consistent and inconsistent rules at the same time.According to the basic view of information entropy, decision entropy and condition entropy are studied. On the theory of values reduction, the reasons of anomalies in values reduction are analyzed in details. Furthermore a format description is proposed so that rules can keep their decisions and inconsistency after reduction. An algorithm based on dicernibility matrix that can adapt to inconsistent state is designed. Information entropy is introduced into dicernibility matrx. Values reduction anomalies can be eliminated and the rules can keep accord with the original information system using this method.Finally UCI dataset is used for experiment. The results of experiment illustrate correlative theory further.