Research Article
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Actions of soft groups

Year 2019, Volume: 68 Issue: 1, 1163 - 1174, 01.02.2019

Gülay Oguz İlhan Icen M. Habil Gursoy

https://doi.org/10.31801/cfsuasmas.509926
Cited By: 5

Abstract

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.

Keywords

Soft set soft group soft action soft symmetric group

References

  • 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.

Year 2019, Volume: 68 Issue: 1, 1163 - 1174, 01.02.2019

Gülay Oguz İlhan Icen M. Habil Gursoy

https://doi.org/10.31801/cfsuasmas.509926
Cited By: 5

Abstract

References

  • 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.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Gülay Oguz This is me 0000-0003-4302-8401

İlhan Icen

M. Habil Gursoy

Publication Date February 1, 2019
Submission Date October 11, 2017
Acceptance Date June 29, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

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. February 2019;68(1):1163-1174. doi:10.31801/cfsuasmas.509926
Chicago Oguz, Gülay, İlhan Icen, and M. Habil Gursoy. “Actions of Soft Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 1163-74. https://doi.org/10.31801/cfsuasmas.509926.
EndNote Oguz G, Icen İ, Gursoy MH (February 1, 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, and M. H. Gursoy, “Actions of soft groups”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 1163–1174, 2019, doi: 10.31801/cfsuasmas.509926.
ISNAD Oguz, Gülay et al. “Actions of Soft Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 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 et al. “Actions of Soft Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 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.

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

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