System law inference and law recognition

By introducing the analysis tool of function to S-rough sets, and improving S-rough sets, function S-rough sets (function singular rough sets) are put forward in this paper. Dual of function one direction S-rough set is one of the basic forms of function S-rough sets, and it is defined by R-function equivalence classes [u]; u_i ¿[u] a function, and a function is a law. Dual of function one direction S-rough sets have one direction dynamic characteristic and law characteristic. Using the law characteristic of dual of function one direction S-rough sets, the concepts of law inference and the law recognition of law inference are proposed, the law recognition theorem of law inference and the law recognition principle of law inference are presented and the applications are given. The law recognition of law inference is a new research direction to discover the unknown laws in system.