Researches On Rough Set Extension Models In IISs

Classical Pawlak rough set is based on the equivalent relation, and assumed that all attribute values of every object are known without a doubt. In many real applications, obtained data are often null (absenting or missing) and then equivalent relation does not hold for various causations. Therefore, traditional rough set theory must be extended. Rough set models and their properties in incomplete information systems (IISs shortly) and in incomplete and fuzzy decision information systems (IFDISs in short) are systematically studied in this dissertation on the basis of research conclusions which are achieved by the pre-researchers studied on rough set extension models in IISs and in IFDISs, with IISs as the main discuss object, rough set theory and fuzzy set theory as tools. The primary innovations are as follows:The symmetrical similarity relation-based rough set extension model in IISs is studied. After analyzing rough set models based on tolerance relation, non-symmetric similarity relation and limited tolerance relation, symmetric similarity relation and its rough set extension model are introduced, and the model properties are discussed. The extension model is improvements on other extensions, and it is more severe than the extension models based on tolerance relation and limited tolerance relation, and is looser than that of non-symmetric similarity. The roughness of the symmetric similarity relation-based extension model is between that of tolerance and non-symmetric similarity relation-based extension model.The variable rough set model in IISs is proposed. With rough set models based on tolerance relation, non-symmetric similarity relation and limited tolerance relation as special examples, the general binary relation and its variable rough set model are introduced, which is the generalization of rough set models based on various of special binary relations and is also that of variable precision rough set model in IISs.The rough set extension model based onγ-tolerance in IFDISs is researched. It is a rough set extension model in IFDISs, which is not only decision information system, but also the decision is fuzzy. For this reason, the research on the model is important significance. Theoretically proved thatγ- tolerance is the generalization of tolerance relation, andγ- tolerance relation is equivalent relation asγ=1 and information system is complete.