Abstract: Using function S-rough sets, it gives the concepts of f-heredity of f-heredity laws,generation of f-heredity laws, F-heredity of function one direction singular rough sets and F-law heredity generation. The envelope theorem of F-heredity law and separation theorem of F-transfer law are presenten. It puts forwards the function one diretion S-rough sets. discovery and applications of investment risk F-laws by using these results.

Key words: envelope theorem , law heredity, F-law discovery, investment risk law, function S-rough sets