The Extension Of Rough Set Models And Study On Related Knowledge Reduction

Rough set theory, introduced by Z.Pawlak in the early 1980s of the 20th century, is a new mathematical tool of dealing with uncertain information. With more than twenty years development, rough set theory has been successfully applied to many areas including machine learning, pattern recognition, decision analysis, process control, knowledge discovery from databases, and expert systems. But the applications of the theory show that there still exist some limitations. Thus, it is important to optimize Pawlak Rough set theory .The primary contributions are as follows:Firstly, we proposed the concept of incomplete and fuzzy information systems based on incomplete approximation spaces and fuzzy sets, and give the VPRS model of incomplete fuzzy information systems. The properties and the concepts of precision reduction are also presented here.Then, based on two-direction s-rough sets and generalized relations of s-rough sets model, this paper presents a research report on the concept of generalized two-direction variable s-rough sets of the variable precision. A majority inclusion relation on generalized two-direction s-rough sets is defined and a generalized two-direction s-rough sets model is given by means of the error parameterα,α∈[0,0.5)proposed in this paper. With the use of the specific example, this paper analyzes and validates the variable relationship and the trend among upper approximation, lower approximation, approximation boundary and classification approximation precision.At last, we discuss the set-valued decision information system. A new relationship based on a variable precision parameter in the set-valued decision information system is defined .By changing the value of the parameter; we can classify the objects more reasonably. The knowledge reduction in set-valued decision information system is discussed here, the discernibility matrices and an algorithm are also proposed.