Singular Rough Sets And Research On Its Several Characteristics

Professor Z.Pawlak presented rough sets theory in 1982, by using of rough sets, an undefinable set can be defined by the lower approximation and the upper approximation. Professor Shi Kaiquan extended Z.Pawlak rough sets in 2002, and presented singular rough sets, briefly call S-rough sets, it has two kinds of forms: one direction S-rough sets, two direction S-rough sets. Z.Pawlak rough sets has static boundary, but S-rough sets has dynamic boundary. So by using of S-rough sets, this paper engrafts S-rough sets with system recognition, information communication, and gives their research and discussion. This paper is divided into six chapters, main content and creative results are: I. Research Content1. By using of concepts of Z.Pawlak rough sets, this paper gives concept of singular rough sets, briefly called S-rough sets. S-rough sets has two kinds of forms: one direction S-rough sets(one direction singular rough sets), two direction S-rough sets(two direction singular rough sets). With respect to dynamic characteristics of elements in assistant set of S-rough sets, they will be discussed in this paper, and related content is: one direction S-rough sets, dual of one direction S-rough sets, two direction S-rough sets, α-generation of assistant sets of S-rough sets and α-generation theorem, generation granulation degree of assistant set of S-rough sets and its characteristic theorem, η-embedding of assistant set of S-rough setsand η-embedding theorem, embedding granulation degree of assistant setsof S-rough sets and its characteristic theorem.2. In system recognition, knowledge in recognition object is not stable, but variable, by using of dynamic boundary characteristic of S-rough sets, this paper engrafts S-rough sets with system recognition theory, presents one...