Research On Rough Set Theory In Incomplete Information Systems

Rough set theory is a new data analysis tool, which was first proposed by Poland researcher Pawlak. Such a theory plays a fundamental role in the imitating of human brain's thinking and cognition. Since the traditional rough set model is constructed on the basis of a strict indiscernibility relation(equivalence relation), reseach on how to expand the rough set model is very important for the development of rough set theory. In this thesis for the doctorate, several expanded rough set models are deeply investigated in the incomplete information systems.In the incomplete information system in which all unknown values are considered as "lost", a new rough set model is proposed based on the concept of difference relation, from which we can generate all negative rules from the incomplete decision system. In general incomplete information system, the variable precision classification based rough set model is proposed. It is proved that the rough set models based on tolerance relation, similarity relation are special forms of the variable precision classification rough set.In the incomplete information system in which unknown attributes values are considered as not only "lost" but also "do not care condition", three new characteristic relations are proposed to make up for the limitations of the original characteristic relation. The relationships between these characteristic relations based rough set models are also investigated.In the incomplete information system in which all unknown values are "do not care condition", the concept of↑and↓, descriptors are proposed by considering the preference-ordered domains of the attributes. The discernibility matrix approach to obtain the↑and↓, descriptors'reductions are then studied. With respect to the proposed descriptors, the practical approach to generate all optimal certain rules from the incomplete decision system is investigated. By comparing with the expanding dominance relation based rough set model, we can obtain the decision rules, which including more useful information from the viewpoint of↑and↓, descriptors.In the incomplete information system in which all unknown values are "lost", the concept of similarity dominance relation is proposed by considering the preference-ordered domains of the attributes. By the similarity dominance-based rough set models, not only four types of approximate distribution reducts are proposed but also the relationships between these reducts are discussed. Moreover, the similarity dominance-based rough set model is introduced into the incomplete fuzzy decision system for knowledge reduction and knowledge acquisition.In the interval-valued information system, six types of relative reducts are proposed, from which one can obtain the optimal decision rules supported by a special object. Moreover, by considering the dominance degree between objects, the fuzzy rough approach is employed for knowledge acquisition in the interval-valued decision system.