Research Article
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Characterization of Soft Sets by  ̃-soft Operations

Year 2018, Volume: 21 Issue: 3, 707 - 713, 01.09.2018
https://doi.org/10.2339/politeknik.389631

Abstract

The purpose of this paper is to introduce new structures of



















-soft sets in soft ditopological (SDT) spaces and study


-soft
operations such as


-soft interior,


-soft closure,


-soft boundary
and


-soft exterior.
This study is therefore organized the analogies between the concepts of


-soft
operations, on the other, are strongly emphasized. Moreover, a result which play
a pivotal role in the characterization of


-soft open sets
is found out.

References

  • [1] Molodtsov, D.A., “Soft set theory-first results”, Computers and Mathematics with Applications, 37: 19-31, (1999).
  • [2] Molodtsov, D., Leonov, V.Y., Kovkov, D.V.: “Soft sets technique and its application”. Nechetkie Sistemy i Myagkie Vychisleniya, 1(1): 839, (2006).
  • [3] Maji, P.K., Biswas, R., Roy, A.R., “An Application of Soft Sets in A Decision Making Problem”, Computers and Mathematics with Applications, 44: 1077- 1083, (2002).
  • [4] Maji, P.K., Biswas, R., Roy, A.R., “Soft set theory”, Computers and Mathematics with Applications, 45: 555-562, (2003).
  • [5] Pie, D., Miao, D., “From soft sets to information systems”, Granular Comput, 2005 IEEE Inter. Conf., 2: 617-621, (2005).
  • [6] Chen, D, “The parametrization reduction of soft sets and its applications”, Comput. Math. Appl., 49: 757-763, (2005).
  • [7] Aygünoğlu, A. Aygün, H., “Some notes on soft topological spaces”, Neural Computation and Application, 21: 113-119, (2012).
  • [8] Çağman, N., Karatas, S, Enginoğlu, S., “Soft topology”, Computers & Mathematics with Applications, 62(1): 351-358, (2011).
  • [9] Hussain, S, Ahmad, B., “Some properties of soft topological spaces”, Comput. Math. Appl., 62: 4058-4067, (2011).
  • [10] Shabir, M., Naz, M., “On soft topological spaces”, Computers and Mathematics with Applications, 61: 1786-1799, (2011).
  • [11] Dizman, T. et. al., “Soft Ditopological Spaces”, Filomat, 30(1): 209-222, (2016).
  • [12] Şenel, G., The Theory of Soft Ditopological Spaces, International Journal of Computer Applications, 150(4):1-5, (2016).
  • [13] Aktaş, H., Çağman, N., “Soft sets and soft groups”, Information Sciences, 177(1): 2726-2735, (2007).
  • [14] Ça˘gman, N., Engino˘glu, S., “Soft set theory and uni-int decision making”, European Journal of Operational Research, 207: 848-855, (2010).
  • [15] Şenel, G., “A Comparative Research on the Definition of Soft Point”, International Journal of Computer Applications, 163(2):1-5, (2017).

Characterization of Soft Sets by  ̃-soft Operations

Year 2018, Volume: 21 Issue: 3, 707 - 713, 01.09.2018
https://doi.org/10.2339/politeknik.389631

Abstract

The purpose of this paper is to introduce new structures of



















-soft sets in soft ditopological (SDT) spaces and study


-soft
operations such as


-soft interior,


-soft closure,


-soft boundary
and


-soft exterior.
This study is therefore organized the analogies between the concepts of


-soft
operations, on the other, are strongly emphasized. Moreover, a result which play
a pivotal role in the characterization of


-soft open sets
is found out.

References

  • [1] Molodtsov, D.A., “Soft set theory-first results”, Computers and Mathematics with Applications, 37: 19-31, (1999).
  • [2] Molodtsov, D., Leonov, V.Y., Kovkov, D.V.: “Soft sets technique and its application”. Nechetkie Sistemy i Myagkie Vychisleniya, 1(1): 839, (2006).
  • [3] Maji, P.K., Biswas, R., Roy, A.R., “An Application of Soft Sets in A Decision Making Problem”, Computers and Mathematics with Applications, 44: 1077- 1083, (2002).
  • [4] Maji, P.K., Biswas, R., Roy, A.R., “Soft set theory”, Computers and Mathematics with Applications, 45: 555-562, (2003).
  • [5] Pie, D., Miao, D., “From soft sets to information systems”, Granular Comput, 2005 IEEE Inter. Conf., 2: 617-621, (2005).
  • [6] Chen, D, “The parametrization reduction of soft sets and its applications”, Comput. Math. Appl., 49: 757-763, (2005).
  • [7] Aygünoğlu, A. Aygün, H., “Some notes on soft topological spaces”, Neural Computation and Application, 21: 113-119, (2012).
  • [8] Çağman, N., Karatas, S, Enginoğlu, S., “Soft topology”, Computers & Mathematics with Applications, 62(1): 351-358, (2011).
  • [9] Hussain, S, Ahmad, B., “Some properties of soft topological spaces”, Comput. Math. Appl., 62: 4058-4067, (2011).
  • [10] Shabir, M., Naz, M., “On soft topological spaces”, Computers and Mathematics with Applications, 61: 1786-1799, (2011).
  • [11] Dizman, T. et. al., “Soft Ditopological Spaces”, Filomat, 30(1): 209-222, (2016).
  • [12] Şenel, G., The Theory of Soft Ditopological Spaces, International Journal of Computer Applications, 150(4):1-5, (2016).
  • [13] Aktaş, H., Çağman, N., “Soft sets and soft groups”, Information Sciences, 177(1): 2726-2735, (2007).
  • [14] Ça˘gman, N., Engino˘glu, S., “Soft set theory and uni-int decision making”, European Journal of Operational Research, 207: 848-855, (2010).
  • [15] Şenel, G., “A Comparative Research on the Definition of Soft Point”, International Journal of Computer Applications, 163(2):1-5, (2017).
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Güzide Şenel

Publication Date September 1, 2018
Submission Date October 23, 2017
Published in Issue Year 2018 Volume: 21 Issue: 3

Cite

APA Şenel, G. (2018). Characterization of Soft Sets by  ̃-soft Operations. Politeknik Dergisi, 21(3), 707-713. https://doi.org/10.2339/politeknik.389631
AMA Şenel G. Characterization of Soft Sets by  ̃-soft Operations. Politeknik Dergisi. September 2018;21(3):707-713. doi:10.2339/politeknik.389631
Chicago Şenel, Güzide. “Characterization of Soft Sets by  ̃-Soft Operations”. Politeknik Dergisi 21, no. 3 (September 2018): 707-13. https://doi.org/10.2339/politeknik.389631.
EndNote Şenel G (September 1, 2018) Characterization of Soft Sets by  ̃-soft Operations. Politeknik Dergisi 21 3 707–713.
IEEE G. Şenel, “Characterization of Soft Sets by  ̃-soft Operations”, Politeknik Dergisi, vol. 21, no. 3, pp. 707–713, 2018, doi: 10.2339/politeknik.389631.
ISNAD Şenel, Güzide. “Characterization of Soft Sets by  ̃-Soft Operations”. Politeknik Dergisi 21/3 (September 2018), 707-713. https://doi.org/10.2339/politeknik.389631.
JAMA Şenel G. Characterization of Soft Sets by  ̃-soft Operations. Politeknik Dergisi. 2018;21:707–713.
MLA Şenel, Güzide. “Characterization of Soft Sets by  ̃-Soft Operations”. Politeknik Dergisi, vol. 21, no. 3, 2018, pp. 707-13, doi:10.2339/politeknik.389631.
Vancouver Şenel G. Characterization of Soft Sets by  ̃-soft Operations. Politeknik Dergisi. 2018;21(3):707-13.