In this paper, we introduce the upper and lower
approximations on the invers set-valued mapping and the
approximations an established on a powerful set valued
homomorphism from a ring R1 to power sets of a ring R2.
Moreover, the properties of lower and upper
approximations of a powerful set valued are studies. In
addition, we will give a proof of the theorem of
isomorphism over approximations F-rough ring as new
result. However, we will prove the kernel of the powerful
set-valued homomorphism is a subring of R1. Our result is
introduce the first isomorphism theorem of ring as
generalized the concept of the set valued mappings
Keywords : Upperapproximations; Poerful Set Vauled Mapp;T-Rough Set.