By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ■-decomposition law and ■-decomposition rough law are proposed, and the measurement of rough law variation in the process of rough law ■-decomposition is researched. The concepts of law energy and attribute ■-interference degree are presented, which make the variation of rough law become measurable. ■-decomposition law energy characteristic theorem, ■-decomposition law energy inequality theorem,■-decomposition rough law energy characteristic theorem, and ■-decomposition law energy mean value theorem are presented.
The concept of F-knowledge is presented by employing S-rough sets.By engrafting and penetrating between the F-knowledge generated by S-rough sets and the RSA algorithm,the security transmission and recognition of multi-agent F-knowledge are proposed,which includes the security transmission of multi-agent F-knowledge with positive direction secret key and the security transmission of multi-agent F-knowledge with reverse direction secret key.Finally,the recognition criterion and the applications of F-knowledge are presented.The security of F-knowledge is a new application research direction of S-rough sets in information systems.
By using function one direction S-rough sets (function one direction singular rough sets), this article presents the concepts of Flaw, Frough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of Flaw relation metric, two orders theorem of Frough law relation metric, the attribute theorem of Frough law band, the extremum theorem of Frough law relation metric, the discovery principle of Frough law and the application of Frough law.
By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets (singular rough sets). S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By introducing the function equivalence class (law equivalence class) that proposes dynamic characteristic into S-rough sets, the first author improved S-rough sets and put forward function S-rough sets (function singular rough sets). Function S-rough sets have dynamic characteristic and law characteristic, and a function is a law. By using function S-rough sets, this paper presents law identification, law identification theorem, and law identification criterion and applications. Function S-rough sets are a new research direction of rough sets theory, and it is also a new tool to the research of system law identifica- tion.
