Near Approximations in Vector Spaces

Abstract

Near set theory is a concept that emerged from the comparison of similarities between digital images. Another set theory, soft set, was obtained by Molodstov[3]. The space where we obtain the near sets is the nearness approximation space. Tasbozan [25] introduce the soft sets based on a near approximation space. The group and ring structure of algebraic structures on near sets are defined. In this article, the structure of vector spaces will be discussed with close approximations. First I defined a pair of near approximation operators with respect to congruence based on a subspace, investigated near subsets in the vector space and its basic properties. Then considered a near soft set over a vector space has a properties of vector space defined lower and upper near soft approximation operators in vector spaces.