Research On Knowledge Reduction In Rough Sets

The rough set community, which is an excellent data analysis tool to handle uncertain information, such as imprecise, inconsistent, incomplete and so on, is one of the hardest fields. It has received much attention of the researchers around the world. Rough set community has been applied to many areas successfully including pattern recognition, machine learning, decision support, knowledge discovery, fault diagnosis, forecast modeling and so on. Knowledge reduction is one of the basic contents in rough set community, key technology of rough set community applied and important research contents in knowledge discovery, becoming one of the hottest research fields. Efficient and effective algorithms for knowledge reduction are the foundation of rough set community applied, also the guarantee of rough set community applied on a large scale. Surrounding the three key problems of knowledge reduction, i.e. attribute reduction, decision rule mining and the knowledge discovery tool based on knowledge reduction, the following five works have been done: attribute reduction in information system, attribute reduction in consistent decision system, attribute reduction in inconsistent decision system, decision rule mining and knowledge discovery tool based on knowledge reduction.Skowron's discernible matrix method is one of import concepts in rough sets community, it require the set of data must be centralized. Many results have been obtained based on it, but there is no more research on it-self. Therefore, the concepts of extended discenibility matrix and extended discernibility function are introduced, from which Skowron's discernible matrix method is extended, called extended discenibility matrix method.In order to overcome the drawbacks of the existing algorithms in inefficient and inadaptable the case of increase object. The relationship between increase of objects and attribute reductions are analyzed, the judgment theorem for the set of all absolute attribute reductions in information system is obtained, from which an incremental algorithm for the set of all absolute attribute reductions is proposed.There are some drawbacks of the existing relative attribute reduction algorithms in consistent decision system, such as their efficient and completeness. In order to overcome those drawbacks, the judgment theorem with respect to the set of all relative attribute reductions is obtained. Based on calculating the set of all relative reductions by the set of relative reductions, which have been calculated, from which an algorithm for the set of all relative reductions is proposed and its efficient is proved by expierment; A concept of relative discernibility is introduced based on a viewpoint that knowledge is an ability of classing thing, and prove the concept reasonableness, from which an algorithm for the optimal attribute reduction is developed. In addition, the proof of completeness of this algorithm is given. Theoretical analysis and experimental results show that the algorithm is better than those existing algorithm.In order to improvement the efficiency of attribute reduction algorithm in inconsistent decision system, the theory foundation of maximum distribution reduction, distribution reduction and possible reduction is obtained, from which the approaches to the set of all maximum distribution reduction, distribution reduction and possible reduction are presented. In addition, its efficient is proved by experiment. In order to reinforce the optimal attribute reduction algorithm in inconsistent decision system, the equivalence definitions with respect to maximum distribution reduction, distribution reduction and possible reduction are introduced, and the significance of attribute is defined, from which the heuristic algorithms for the optimal maximum distribution reduction, distribution reduction and possible reduction are proposed. Finally, the experimental results show that the algorithm is effective.There are some drawbacks of the existing learning algorithm for decision rules, such as their inefficient. In order to overcome those drawbacks, one side calculates the conjunctive normal form of discernible function for equivalence class, the other side calculates the new rules from the conjunctive normal form and the rules, which has been calculated, from which an improved learning algorithm for decision rules is proposed, and its reasonableness is proved by experiment.Based on the algorithms for knowledge reduction above, a knowledge discovery tool is designed.