Year 2019, Volume 68, Issue 1, Pages 1163 - 1174 2018-04-11

Actions of soft groups

Gülay OGUZ [1] , Ilhan ICEN [2] , M. Habil GURSOY [3]

6 95

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.
Soft set, soft group, soft action, soft symmetric group
  • 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.
Primary Language en
Subjects Mathematics
Journal Section Articles
Authors

Orcid: 0000-0003-4302-8401
Author: Gülay OGUZ

Author: Ilhan ICEN

Author: M. Habil GURSOY

Bibtex @research article { cfsuasmas509926, journal = {Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, issn = {1303-5991}, eissn = {2618-6470}, address = {Ankara University}, year = {2018}, volume = {68}, pages = {1163 - 1174}, doi = {10.31801/cfsuasmas.509926}, title = {Actions of soft groups}, key = {cite}, author = {OGUZ, Gülay and ICEN, Ilhan and GURSOY, M. Habil} }
APA OGUZ, G , ICEN, I , GURSOY, M . (2018). Actions of soft groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68 (1), 1163-1174. DOI: 10.31801/cfsuasmas.509926
MLA OGUZ, G , ICEN, I , GURSOY, M . "Actions of soft groups". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2018): 1163-1174 <http://dergipark.org.tr/cfsuasmas/issue/36517/509926>
Chicago OGUZ, G , ICEN, I , GURSOY, M . "Actions of soft groups". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2018): 1163-1174
RIS TY - JOUR T1 - Actions of soft groups AU - Gülay OGUZ , Ilhan ICEN , M. Habil GURSOY Y1 - 2018 PY - 2018 N1 - doi: 10.31801/cfsuasmas.509926 DO - 10.31801/cfsuasmas.509926 T2 - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JF - Journal JO - JOR SP - 1163 EP - 1174 VL - 68 IS - 1 SN - 1303-5991-2618-6470 M3 - doi: 10.31801/cfsuasmas.509926 UR - https://doi.org/10.31801/cfsuasmas.509926 Y2 - 2018 ER -
EndNote %0 Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Actions of soft groups %A Gülay OGUZ , Ilhan ICEN , M. Habil GURSOY %T Actions of soft groups %D 2018 %J Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics %P 1303-5991-2618-6470 %V 68 %N 1 %R doi: 10.31801/cfsuasmas.509926 %U 10.31801/cfsuasmas.509926
ISNAD OGUZ, Gülay , ICEN, Ilhan , GURSOY, M. Habil . "Actions of soft groups". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 / 1 (April 2018): 1163-1174. https://doi.org/10.31801/cfsuasmas.509926