Compatibility Relations Based On Gray Gray Rough Sets And Its Application In Data Mining Research,

Data Mining is the important theory of intelligent systems research. It is used to find valuable and implicit knowledge from the large amounts of data through complicated methods such as artificial intelligence, computational intelligence artificial neural networks, genetic algorithms, pattern recognition and mathematical statistics, and so on.Rough set theory, initialized by Professor Z. Pawlak in early 1980's, has been proved to be an excellent mathematical tool dealing with uncertain and vague description of objects, whose basic idea is to derive classification rules of conception by knowledge reduction with the ability of classification unchanged. In recent years, Rough set theory has become one of the most active areas of research in artificial intelligence and information science. It is also successfully applied in some other areas like data mining, pattern recognition, machine learning, knowledge discovery and decision-making.Classical rough set is mainly applied to deal with classified data or multivalued, discrete data, but information system is very complicated in the real world and many measurements are usually in the form of interval data to describe. There are no definitions on rough approximate, attribute reduction and decision rules extraction of interval data in classical rough set. And the recent method of rough set can't deal with the process of interval data. According to these problems, some grey rough set models are purposed by several researches. But there also have some problems in these models, so these problems are discussed and some solutions are presented in this paper.Firstly, grey system theory and rough set theory are introduced in this paper. With the deep analysis on some recent grey rough set models, a grey rough set model which is based on grey tolerance relation is presented. Furthermore, the lower approximation set and upper approximation set are also defined. At the same time the related properties of this model are analyzed. After the model is established, attribute reduction need to be considered. To find all reductions and a minimal reduction has been proved to be NP-Hard. But many heuristic algorithms especially some methods based on discernable matrix have been provided recently. Secondly, this paper puts forward the method of finding discernable matrix of grey decision information system and analyses the related properties of discernable matrix. On this basis, a new attribute reduction algorithm based on grey rough set which combines Jelonek and HORAFA reduction algorithms is presented and is suitable for the consistent and in consistent grey decision information system and generally finds out all attribute reduction sets of information system. Thirdly, after finding attribute reduction, the main work is getting decision rules. The related knowledge of decision rule extraction is presented. By the research of construction method of decision tree the method of decision tree rules based on grey rough set which is based on grey tolerance relation is presented. Finally, all models and algorithms are brought about by seven MATLAB programs, and the effectiveness of each model or algorithm is proved by one same example.