Abstract
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 mathematicaltool to modify the approximations. Relationships between these types are established via proof andcounter examples. Also, some basic concepts of near approximations set are investigated and studied therelations between these different types of sets in MSAS. This set is a specific importance to help withthe modifications of an approximation space via adding new concepts and facts. Finally, we use thisconcept to introduce the definitions of near lower approximation, near upper approximation, nearboundary region, near rough and near exact sets and study some of the properties of this notion.
Highlights
Introduction and PreliminariesIn 1963, Levine [1] introduced the notion of a semi-open set which is weaker than the notion of an open set in topological spaces
Since several interesting generalized open sets have come into existence, which one of them is preopen set
The concept of a preopen set was introduced by Mashhour et al [2]
Summary
Introduction and PreliminariesIn 1963, Levine [1] introduced the notion of a semi-open (briefly s-open) set which is weaker than the notion of an open set in topological spaces. We used minimal structure concepts to introduce definitions of near approximation and near boundary regions. We used minimal structure concepts to introduce definitions of near rough and near exact sets. We introduce new types of lower and upper based on minimal structure approximation space.
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