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Union soft substructures of near-rings and N-groups

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Abstract

In this paper, we introduce union soft subnear-rings and union soft ideals of a near-ring and union soft N-subgroups and union soft N-ideals of an N-group by using Molodtsov’s definition of soft sets and investigate their related properties with respect to soft set operations, soft anti-image and lower α-inclusion of soft sets. Since these notions show how a soft set affects on substructures of near-rings and N-groups in the mean of union and inclusion of sets, they can be regarded as a bridge among classical sets, soft sets and near-rings. We then obtain significant relation between soft substructures of near-rings and union soft substructures of near-rings, soft substructures of N-groups and union soft substructures of N-groups.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Science,, Amasya University, 05100, Amasya, Turkey

    Aslıhan Sezgin

  2. Department of Mathematics, Faculty of Arts and Science, Bozok University, 66100, Yozgat, Turkey

    Akın Osman Atagün

  3. Department of Mathematics, Faculty of Arts and Sciences, Gaziosmanpaşa University, 60250, Tokat, Turkey

    Naim Çağman

Authors
  1. Aslıhan Sezgin
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  2. Akın Osman Atagün
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  3. Naim Çağman
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Correspondence to Naim Çağman.

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Sezgin, A., Atagün, A.O. & Çağman, N. Union soft substructures of near-rings and N-groups. Neural Comput & Applic 21 (Suppl 1), 133–143 (2012). https://doi.org/10.1007/s00521-011-0732-1

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  • DOI: https://doi.org/10.1007/s00521-011-0732-1

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