In this paper, we use the notions of a minimal structure approximation space (short MSAS)
and the notion of near open sets to introduce a new approximation of uncertain sets as a mathematical
tool to modify the approximations. Relationships between these types are established via proof and
counter examples. Also, some basic concepts of near approximations set are investigated and studied the
relations between these different types of sets in MSAS. This set is a specific importance to help with
the modifications of an approximation space via adding new concepts and facts. Finally, we use this
concept to introduce the definitions of near lower approximation, near upper approximation, near
boundary region, near rough and near exact sets and study some of the properties of this notion.