The Reliability Characteristic Of Element Transfer And F-random Structure

In2002, Professor SHI Kaiquan extended the Pawlak rough sets theory, andproposed the singular rough sets, called S-rough sets for short, which have two forms:one direction S-rough sets and two direction S-rough sets. The classical rough set isjust a rough set which is from static set X Uand helpless for dealing withdynamic problems, for above reason, it can not be widely used. We all know that inpractical problems, if there were the interference of external factors, the system cannot stay stable, as a result, the information set X has some changes in structure.S-rough sets provide a theoretical approach for the research of dynamic characteristicin system.This paper is divided into two sections.The one section was concerned about Z.Pawlak rough set and S-rough sets andtheir applications. At the beginning, we introduced basic concepts about the classicalrough sets and S-rough sets, and then gave more in-depth discussions about elementtranfer f, element transfer f, one direction S-rough sets, two direction S-rough setsand so on. The relation between S-sough sets and new material discovery was shownin Chapter3.In the other section,the concrete results of this paper, Firstly, based on S-roughsets, the reliability characteristic of element transfer and their realization inprobability were given. Then the impacts of element transfer in probability on roughset structure were discussed, and the relevant theorems were given. For explanation tothe dynamic process of S-rough sets with the element transfer, the F-random structurewas put forward. Lastly, the distribution of profit from subsidiary company of oneorganization affected by unidirectional S-rough sets be shown as an example inChapter4.