Research On Data Reduction Based On Rough Sets And Extension Of Rough Set Models

Rough set theory is a valid tool which deals with imprecise, incomplete and inconsistent data. Since 1980's when professor Pawlak created rough set theory, it has been widely applied in many fields, including data mining, machine learning, pattern recognition and artificial intelligence etc., in which data reduction is one of its most important applications. The theory and application of data reduction based on rough set theory have been developed for more than 20 years, but there exist some problems to deal with, such as how to deal with tremendous data. The application fields of rough set theory are limited in comparison with other theories(for example, evolutionary algorithm). Researchers presented a lot of extension versions of rough set theory in order to extend its application fields. In this dissertation, we mainly investigate attribute reduction and extension of rough set models.Firstly, we present a new concept called absolute reduct corresponding to objects in an inconsistent decision system. We compare various reducts corresponding to objects, and get their relations of super-set or subset. Moreover, we prove that the relative reduct in the view of information theory is equal to μ-decision reduct and μ-reduct. This result unites reducts in the view of information theory and reducts in the view of algebra. We also get the super-set or subset relations among various reducts with respect to the whole decision system.Secondly, we investigate the method of discernibility matrix and function. We prove that the results of X.Hu's improved discernibility matrix and function are general decision reducts, and also prove that the results of Ye's improved discernibility matrix and function are relative reducts(also called Pawlak's reducts). We present a novel discernibility matrix and function between two decision systems. This novel method could parallel compute, distributed compute and increasingly compute. Thirdly, we investigate some properties of incomplete decision systems with increase information. We present the criteria of attribute reducts in this case: (1) Preserve positive region. (2) The reduced attributes should have no missing values in the negative positive region. In terms of these criteria the attribute reduction at some moment could not put a disadvantage to attribute reduction in the future, and important information could not be lost.At last, we present two novel models of rough sets. The first model is rough sets based on accessible relation, and the second is rough sets based on concepts systhesis.In rough sets based on accessible relation, we merge rough set theory and accessible relation into one model. Compared with classical rough set models(including Pawlak rough set model and various precise rough set model), the new model is more general. We think that rough sets based on accessible relation are a new methodology.The classical models of rough sets usually deal with how a concept is represented with some granules. The rough sets based on concepts systhesis extend rough set theory, and deal with how a series of concepts are represented with a granule.However, the two new models of rough sets are initial, there are many problems to investigate.In the dissertation we mainly investigate attribute reduction and extension of rough set models theoretically. We will focus on application of rough set theory in our future research.