| The information system based on rough set theory is proposed by Pawlak. Some applications of the theory, such as rule extraction, uncertain decision making, classification and feature extraction are all related to the information system. The reduction of information system is an important problem in information system research. Besides, the research of the relations in the information systems is another necessary issue. From a mathematical point of view, connection between information systems can be understood as the mapping between them, on the basis of the mapping, the original complicated information system can be studied by the simple image information system, the original information system is regarded as a coding system, and the image information system can be regarded as a decoding system. The homomorphism is a special mapping, In this thesis, the invariant characterization of information systems based on the homomorphism is studied, the following two aspects are included:Firstly, invariant characterizations of knowledge bases under homomorphisms are researched. Knowledge bases are special relation information systems. By using the relevant conclusions of the relation information system, some invariant features and inverse invariant features of knowledge bases under homomorphisms are obtained, such as: knowledge dependence, knowledge reduction, coordination and the necessary relations.Secondly, invariant characterizations of fuzzy information systems under homomorphisms are also discussed. A fuzzy information system is a kind of information system under fuzzy environment. Some invariant features and inverse invariant features of fuzzy information system under homomorphisms are concluded, such as: coordination, reduction and the core. And the fuzzy sets in the fuzzy information system are divided into three kinds according to the importance, which are necessary fuzzy set, relative necessary fuzzy set and unnecessary fuzzy set. |
PDF Full Text Request