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Actions of soft groups

Yıl 2019, Cilt: 68 Sayı: 1, 1163 - 1174, 01.02.2019
https://doi.org/10.31801/cfsuasmas.509926

Öz

The soft set theory proposed by Molodtsov is a recent mathematical approach for modeling uncertainty and vagueness. The main aim of this study is to introduce the concept of soft action by combining soft set theory with the action which is an important concept in dynamical systems theory. Moreover, different types of soft action are presented and some important characterizations are given. Finally, we define the concept of soft symmetric group and present the relation between the soft action and soft symmetric group, as a similar result to the classical Cayley's Theorem.

Kaynakça

  • Atagun, A. O. and Sezgin, A., Soft substructures of rings, fields and modules, Computers and Math.with Appl., 61 (2011), 592-601.
  • Molodtsov, D. A., Soft set theory-First results, Comput. Math. Appl., 37(4-5) (1999), 19-31.
  • Aktas, H. and Cagman, N., Soft sets and soft groups, Inform. Sci., 77(13) (2007), 2726-2735.
  • Rotman, J. J., An Introduction to the Theory of Groups. 4th ed. Springer, New York, 1995.
  • Veress, L. A., Group actions on sets and automata theory, Applied Mathematics and Computation, 113(2-3) ( 2000), 289-304.
  • Shabir, M. and Naz, M., On soft topological spaces, Comput. Math. Appl., 61(7) (2011), 1786-1799.
  • Hirsch, M.W., Smale, S. and Devaney, R.L., Differential Equations, Dynamical Systems and an Introduction to Chaos, Elsevier, San Diego, CA, 2004.
  • Maji, P. K., Biswas, R. and Roy, A. R., Soft set theory, Comput. Math. Appl., 45(4-5) (2003), 555-562.
  • Smale, S., Differentiable Dynamical Systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
  • Sardar, S. K. and Gupta, S., Soft category theory-an introduction, Journal of Hyperstructures, 2 (2013),118-135.
  • Wagner, S., Free Group Actions from the Viewpoint of Dynamical Systems, Muenster J. of Math., 5(2012), 73-98.
  • Shah, T. and Shaheen, S., Soft topological groups and rings, Ann. Fuzzy Math. Inform., 7(5)(2014), 725-743.
  • Santos, W. F. and Rittatore, A., Actions and Invariants of Algebraic Groups, CRC press, 2005.
Yıl 2019, Cilt: 68 Sayı: 1, 1163 - 1174, 01.02.2019
https://doi.org/10.31801/cfsuasmas.509926

Öz

Kaynakça

  • Atagun, A. O. and Sezgin, A., Soft substructures of rings, fields and modules, Computers and Math.with Appl., 61 (2011), 592-601.
  • Molodtsov, D. A., Soft set theory-First results, Comput. Math. Appl., 37(4-5) (1999), 19-31.
  • Aktas, H. and Cagman, N., Soft sets and soft groups, Inform. Sci., 77(13) (2007), 2726-2735.
  • Rotman, J. J., An Introduction to the Theory of Groups. 4th ed. Springer, New York, 1995.
  • Veress, L. A., Group actions on sets and automata theory, Applied Mathematics and Computation, 113(2-3) ( 2000), 289-304.
  • Shabir, M. and Naz, M., On soft topological spaces, Comput. Math. Appl., 61(7) (2011), 1786-1799.
  • Hirsch, M.W., Smale, S. and Devaney, R.L., Differential Equations, Dynamical Systems and an Introduction to Chaos, Elsevier, San Diego, CA, 2004.
  • Maji, P. K., Biswas, R. and Roy, A. R., Soft set theory, Comput. Math. Appl., 45(4-5) (2003), 555-562.
  • Smale, S., Differentiable Dynamical Systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
  • Sardar, S. K. and Gupta, S., Soft category theory-an introduction, Journal of Hyperstructures, 2 (2013),118-135.
  • Wagner, S., Free Group Actions from the Viewpoint of Dynamical Systems, Muenster J. of Math., 5(2012), 73-98.
  • Shah, T. and Shaheen, S., Soft topological groups and rings, Ann. Fuzzy Math. Inform., 7(5)(2014), 725-743.
  • Santos, W. F. and Rittatore, A., Actions and Invariants of Algebraic Groups, CRC press, 2005.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Gülay Oguz Bu kişi benim 0000-0003-4302-8401

İlhan Icen

M. Habil Gursoy

Yayımlanma Tarihi 1 Şubat 2019
Gönderilme Tarihi 11 Ekim 2017
Kabul Tarihi 29 Haziran 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA Oguz, G., Icen, İ., & Gursoy, M. H. (2019). Actions of soft groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 1163-1174. https://doi.org/10.31801/cfsuasmas.509926
AMA Oguz G, Icen İ, Gursoy MH. Actions of soft groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):1163-1174. doi:10.31801/cfsuasmas.509926
Chicago Oguz, Gülay, İlhan Icen, ve M. Habil Gursoy. “Actions of Soft Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 1163-74. https://doi.org/10.31801/cfsuasmas.509926.
EndNote Oguz G, Icen İ, Gursoy MH (01 Şubat 2019) Actions of soft groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 1163–1174.
IEEE G. Oguz, İ. Icen, ve M. H. Gursoy, “Actions of soft groups”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 1163–1174, 2019, doi: 10.31801/cfsuasmas.509926.
ISNAD Oguz, Gülay vd. “Actions of Soft Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 1163-1174. https://doi.org/10.31801/cfsuasmas.509926.
JAMA Oguz G, Icen İ, Gursoy MH. Actions of soft groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1163–1174.
MLA Oguz, Gülay vd. “Actions of Soft Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 1163-74, doi:10.31801/cfsuasmas.509926.
Vancouver Oguz G, Icen İ, Gursoy MH. Actions of soft groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):1163-74.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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