Recognition Of Function S-rough Sets And System Rules

Rough sets theory is put forward by Poland mathematician Z.Pawlak in 1982, in which an undefined set X can be defined by the lower approximation and the upper approximation. In rough sets, the object set X is a static set. Professor SHI Kaiquan extended Z.Pawlak rough sets into singular rough sets, called S-rough sets for short, which has two forms: one direction S-rough sets, two direction S-rough sets. The boundary of X in S-rough sets is dynamic. Z.Pawlak rough sets is the special case of S-rough sets and S-rough sets is the general form of Z.Pawlak rough sets. On the basis of S-rough sets, Professor SHI developed the element equivalence class into function equivalence class, and advanced function S-rough sets. In this paper, we combine S-rough sets theory with biological heredity theory and message transfer theory, and combine function S-rough sets with gray system theory and give discussion and research. The paper emphasizes both theorem and applications. The concrete results of this paper: We introduce the concepts of S-rough sets and its two forms: one direction S-rough sets and two direction S-rough sets, and gives their mathematical structures, put forward the heredity characteristics and heredity theorem of S-rough set, which is applied into the message transfer theorem and establish one direction S-massage transfer model and two direction S-massage transfer model; introduce the concepts of function S-rough sets and its three forms: function one direction S-rough sets, function two direction S-rough sets and dual function one direction S-rough sets, gives their mathematical structures, put forward the heredity...