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SOFT STRUCTURES DERIVED FROM GROUPS

Year 2018, Volume: 1 Issue: 3 - To memory of Prof. RNDr. Beloslav Rieˇcan, DrSc., 283 - 292, 24.10.2018

Mustafa Burç Kandemir

Abstract

In this paper, we get soft structures what we call cyclicizer soft set, centralizer soft set, normalizer soft set, cosetial soft set, orbital soft set and stabilizer soft set using some group concepts such as cyclic, centralizer and normalizer of an element, coset and group action, in any given group. At the same time, we mentioned that they are a soft group. We discuss their soft set theoretic properties and give some theorems for groups. We proposed some necessary and sucient conditions for two groups to be isomorphic using the soft set theory. We give relation between similarity of soft sets and groups.

Keywords

Soft set soft group group centralizer normalizer cyclic group

References

  • H. Aktaş, N. Çağman, Soft sets and soft groups, Inform. Sci. 177 (2007) 2726 - 2735.
  • H. Aktaş, Ş. Özlü, Cyclic soft groups and their applications on groups, The Scienti c World Journal Vol. 2014 (2014), Article ID 437324, 5 pages.
  • M. I. Ali, F. Feng, X. Y. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009) 1547 - 1553.
  • J. B. Fraleigh, A rst course in abstract algebra-4th Ed., Addison-Wesley Publishing Company (1989), pp. 518.
  • K. Gong, Z. Xiao, X. Zhang, The bijective soft set with applications, Comput. Math. Appl. 60 (2010) 2270 - 2278.
  • M. B. Kandemir, Monotonic soft sets and its applications, Ann. Fuzzy Math. Inform. 12 (2) (2016) 295 - 307.
  • Y. K. Kim, W. K. Min, Full soft sets and full soft decision systems, Journal of Intelligent &Fuzzy Systems 26 (2014) 925 - 933.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math.Appl. 45 (2003) 555 - 562.
  • W. K. Min, Similarity in soft set theory, Appl. Math. Let. 25 (2012) 310 - 314.
  • D. Molodtsov, Soft sets- rst results, Comput. Math. Appl. 37 (1999) 19 - 31.
  • D. Patrick, E. Wepsic, Cyclicizers, centralizers and normalizers, RoseHulman Institute of Technology, Indiana, USA, Technical Reprot MS-TR 91-05, (1991).
  • D. Pei, D. Miao, From soft sets to information systems, Proceedings of IEEE International Conference on Granular Computing 2 (2005) 617 - 621.

Year 2018, Volume: 1 Issue: 3 - To memory of Prof. RNDr. Beloslav Rieˇcan, DrSc., 283 - 292, 24.10.2018

Mustafa Burç Kandemir

Abstract

References

  • H. Aktaş, N. Çağman, Soft sets and soft groups, Inform. Sci. 177 (2007) 2726 - 2735.
  • H. Aktaş, Ş. Özlü, Cyclic soft groups and their applications on groups, The Scienti c World Journal Vol. 2014 (2014), Article ID 437324, 5 pages.
  • M. I. Ali, F. Feng, X. Y. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009) 1547 - 1553.
  • J. B. Fraleigh, A rst course in abstract algebra-4th Ed., Addison-Wesley Publishing Company (1989), pp. 518.
  • K. Gong, Z. Xiao, X. Zhang, The bijective soft set with applications, Comput. Math. Appl. 60 (2010) 2270 - 2278.
  • M. B. Kandemir, Monotonic soft sets and its applications, Ann. Fuzzy Math. Inform. 12 (2) (2016) 295 - 307.
  • Y. K. Kim, W. K. Min, Full soft sets and full soft decision systems, Journal of Intelligent &Fuzzy Systems 26 (2014) 925 - 933.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math.Appl. 45 (2003) 555 - 562.
  • W. K. Min, Similarity in soft set theory, Appl. Math. Let. 25 (2012) 310 - 314.
  • D. Molodtsov, Soft sets- rst results, Comput. Math. Appl. 37 (1999) 19 - 31.
  • D. Patrick, E. Wepsic, Cyclicizers, centralizers and normalizers, RoseHulman Institute of Technology, Indiana, USA, Technical Reprot MS-TR 91-05, (1991).
  • D. Pei, D. Miao, From soft sets to information systems, Proceedings of IEEE International Conference on Granular Computing 2 (2005) 617 - 621.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Mustafa Burç Kandemir

Publication Date October 24, 2018
Submission Date October 14, 2018
Acceptance Date October 24, 2018
Published in Issue Year 2018 Volume: 1 Issue: 3 - To memory of Prof. RNDr. Beloslav Rieˇcan, DrSc.

Cite

APA Kandemir, M. B. (2018). SOFT STRUCTURES DERIVED FROM GROUPS. Journal of Universal Mathematics, 1(3), 283-292.
AMA Kandemir MB. SOFT STRUCTURES DERIVED FROM GROUPS. JUM. October 2018;1(3):283-292.
Chicago Kandemir, Mustafa Burç. “SOFT STRUCTURES DERIVED FROM GROUPS”. Journal of Universal Mathematics 1, no. 3 (October 2018): 283-92.
EndNote Kandemir MB (October 1, 2018) SOFT STRUCTURES DERIVED FROM GROUPS. Journal of Universal Mathematics 1 3 283–292.
IEEE M. B. Kandemir, “SOFT STRUCTURES DERIVED FROM GROUPS”, JUM, vol. 1, no. 3, pp. 283–292, 2018.
ISNAD Kandemir, Mustafa Burç. “SOFT STRUCTURES DERIVED FROM GROUPS”. Journal of Universal Mathematics 1/3 (October 2018), 283-292.
JAMA Kandemir MB. SOFT STRUCTURES DERIVED FROM GROUPS. JUM. 2018;1:283–292.
MLA Kandemir, Mustafa Burç. “SOFT STRUCTURES DERIVED FROM GROUPS”. Journal of Universal Mathematics, vol. 1, no. 3, 2018, pp. 283-92.
Vancouver Kandemir MB. SOFT STRUCTURES DERIVED FROM GROUPS. JUM. 2018;1(3):283-92.
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