Affiliations: Department of Mathematics, Faculty of Arts and Sciences, Adiyaman University, Adiyaman, Turkey. [email protected]
Note: [] Address for correspondence: Department of Mathematics, Faculty of Arts and Sciences, Adiyaman University, Adiyaman, Turkey
Abstract: In 1999, Molodtsov introduced the theory of soft sets, which can be seen as a new mathematical approach to vagueness. In 2002, near set theory was initiated by J. F. Peters as a generalization of Pawlak's rough set theory. In the near set approach, every perceptual granule is a set of objects that have their origin in the physical world. Objects that have, in some degree, affinities are considered perceptually near each other, i.e., objects with similar descriptions. Also, the concept of near groups has been investigated by İnan and Öztürk [30]. The present paper aims to combine the soft sets approach with near set theory, which gives rise to the new concepts of soft nearness approximation spaces (SNAS), soft lower and upper approximations. Moreover, we give some examples and properties of these soft nearness approximations.
Keywords: Near set, soft set, rough set, soft rough set, soft near set, approximation space, nearness approximation space, soft nearness approximation space
