Studies On Attribute Reduction Of Information Systems Based On Dominance Relations And Some Properties Of Fuzzy Relation Mappings

Both rough sets and fuzzy sets are mathematical tool to deal with incomlete and inaccurateknowledge in information systems. They have been successfully applied in many fields ofartificial intelligence, such as machine learning, malfunction diagnosis, decision analysis,process control and knowledge discovery in databases. Therefore, the research on rough sets andfuzzy sets have important values of applications. In this thesis, attribute reductions based ondominance-relation rough sets are firstly studied. Then some properties of fuzzy relationmappings are discussed. At last, fuzzy set approximations under relation mappings areinvestigated. The main results are summarized as follows:1. The concept of positive region are introduced in information systems based ondominance relations, and a new approach to knowledge reductions based on positive region isprovided from the general point of view (including consistent systems and inconsistent systems).An example shows that the proposed method is effective to complex data.2. Based on the extension principle of fuzzy relation mappings, another description aboutthe extension principle and its properties are studied by using cut sets. Then, the composition offuzzy relation mappings and its properties are examined.3. Based on equivalence relations, we define consistent functions and study theirproperties and discuss the problem of fuzzy set approximations under relation mappings. At last,invariant properties and attribute reductions are investigated in information systems with fuzzytargets.