Soft Nearness Approximation Spaces

  • Authors:

  • Mehmet Ali Öztürk;Ebubekir İnan

  • Affiliations:

  • Department of Mathematics, Faculty of Arts and Sciences, Adiyaman University, Adiyaman, Turkey. maozturk@adiyaman.edu.tr;Department of Mathematics, Faculty of Arts and Sciences, Adiyaman University, Adiyaman, Turkey. maozturk@adiyaman.edu.tr

  • Venue:
  • Fundamenta Informaticae - Cognitive Informatics and Computational Intelligence: Theory and Applications
  • Year:
  • 2013

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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.