By using function one direction S-rough sets （function one direction singular rough sets）, the concept of one direction rough law is proposed, where one direction rough law is the law pair { w（x）-, w（x） - } composed by w（x）- and w（x）-, ffthe attribute set {a_ , a-} of function one direction S-rough sets changes, then one direction rough law { w（x）_, w（x）- } will change, too. By employing ellipse curves, the concept of one direction rough law security is presented, the security theorem of one direction rough law is proposed and the applications are given. One direction rough law security, which is generated by the intersection and penetration between function one direction S-rough sets and ellipse curves, is a new applied research direction of function S-rough sets.
By using function one direction S-rough sets,the concept of F-interior hiding image is presented; the theorem of F-interior hiding and the recognition criteria of interior hiding are proposed; and the applications of F-interior hiding image are given. F-interior hiding image is a new application area of function S-rough sets,and function S-rough sets is a new theory and new tools for iconology research.
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.
