In this paper we introduced four new types of open and closed sets in tri-topological spaces, where we have introduced the definition of open sets of the pattern Nα and closed sets of the pattern Nα in tritopological spaces, as the we know from the open sets of the pattern Sα and closed sets of the pattern Sα in these spaces, and we studied the basic properties of these new types of sets, as the we have created the relationship between them and open and closed sets in these tri-topological spaces. Then use this new concept of open and closed sets in the definition of closure and interior set, where we know the closure and interior set of the pattern Nα by relying on these new varieties of open and closed sets, we also found the basic properties of closure and the interior of the pattern Nα.