Research On Fuzzy Characterization Of Rough Set And Characters Of Knowledge Granule

In this paper, fuzzy characterization of rough set and the characters of knowledge granule are studied. The main contents of this paper are as follows:Rough sets theory proposed by Z.Pawlak in 1982 is a new mathematical tool for dealing with the incomplete and imprecise information. In recent years, rough set theory has been applied in computer science field and many other fields successfully In Chapter 1 of this paper, a survey of the advances of rough set theory is given. It includes the introduction of rough set theory and its development, main problems studied in rough set theory and the basic concepts of rough set.In rough sets theory, an imprecise concept sometimes possesses a fuzzy boundary that can not be definitely divided, on the other hand, the existence of the boundary usually causes fuzziness in rough sets. In the applications of the rough sets theory, sometimes it is necessary to find out the fuzziness degree of a rough set, and compare fuzziness in two rough sets to find out which is greater or the similarity degree between them. Therefore, seeking an appropriate measure to characterize the fuzziness of knowledge is an important direction in the rough sets theory research.Pawlak and Skowron presented to characterize fuzziness of knowledge using rough membership function. In fact, through the rough membership degree of elements , the fuzziness in a rough set can be expressed by a fuzzy set. Chakrabarty presented a method to measure fuzziness degree of a rough set by the distance between the fuzzy set and the nearest ordinary set to it, and he also gave a common definition of fuzziness degree of a rough set and the concrete form of the linear fuzziness degree and the quadratic fuzziness degree, and studied the basic...