Research On Rough Set Theory And Models With Semantics

Data is usually presented by an information table or a decision table in rough set theory, while the rows show all objects and the columns present the values of each object on given attributes. If the set of attributes is divided into a condition attribute set and a decision attribute set, then this kind of information table is also called decision table. In many applications, as the classical information table cannot express all information, such as some difficult semantics in corresponding applications, it is difficult to get the proper result from the classical information table by using some current learning methods. Less work is concentrating on the systemically learning with semantics in current researches. Many applications need domain or professional knowledge. In this dissertation, we focus our concentration on learning from the information table incorporating some semantics, which include users' requirements and decision semantics in real applications, reduct semantics in rough set model and ordered relation semantics in information tables.Firstly, many attribute reductions have been studied in rough set theory, all these reductions are only concentrating on the data set, and it is difficult to choose the proper attribute reduction for different users in their different real applications. We propose a generalized sematic attribute reduction, which considers not only the data set but also the users'preference or interesting. Most of the present attribute reduction definitions can be interpreted as examples of the generalized attribute reduction. In view of the generalized definition, we also define an attribute reduction based on minimum decision cost, which can avoid the difficulties with the interpretations of region preservation based attribute reduction in probabilistic rough set models. The new defined reduction can help users make proper decisions with minimum decision cost.Secondly, in classical rough set theory, the knowledge is usually expressed by rules, while inducing rules is the next procedure after getting attribute reduct from an information table. In this dissertation, we propose a viewpoint that inducing rules is a kind of attribute-value reduction, which is independent of attribute reduction actually. By using attribute-value reduction, users may get a more proper result rather than applying attribute reduction first.Thirdly, for the information table incorporating order relations, we study the incremental learning problem by means of dominance-based rough set approach, and an incremental computing core algorithm and an incremental inducing rules algorithm are proposed in this dissertation. These incremental algorithms can improve the learning efficiency apparently. We also study the relationship between algorithms and data. Through analyzing some data distribution characters, we can find what kind of data is suited for the algorithm.Fourthly, we apply a three-way decisions rough set solution to spam filtering problem in natural language processing area. The three-way decisions solution can reduce the error rate of classifying a legitimate email to spam, and provide a more meaningful decision procedure for users. Based on the spam filtering problem, we present an optimization viewpoint on decision-theoretic rough set model. The decision cost can be expressed as an optimization problem with cost functions and required thresholds. The cost functions are the basis of the decision-theoretic rough set model, which can be used to derive other probabilistic rough set models. In previous work, these cost functions are assumed given by experts. By solving the optimization problem, we can learn cost functions and thresholds from data automatically, which is a first try in this area. An adapted learning algorithm is also proposed.