Research Article

Some Notes on Soft Topological Concepts and an Application Method

Volume: 8 Number: 1 March 20, 2020
EN

Some Notes on Soft Topological Concepts and an Application Method

Abstract

In this paper, using the concept of soft topology given in \cite{Mbk} i.e. with our new perspective of soft topology, we give some basic topological concepts such as open soft set, closed soft set, interior and closure of a soft set. We then give the concept of soft continuity of a given function between soft topological spaces, and from here we also define the concept of soft homeomorphism and argue the all obtained results. At the end of the article, we propose a decision-making method using soft topological concepts.

Keywords

Soft set,Soft topological space,continuity,interior,closure

References

  1. Acar, U. and Koyuncu, F. and Tanay, B., Soft sets and soft rings. Comput. Math. Appl. 59 (11) (2010) 3458-3463.
  2. Aktaş, H. and Çağman, N., Soft sets and soft groups. Inform. Sci. 177 (13) (2007) 2726-2735.
  3. Ali, M.I. and Feng, F. and Liu, X. and Min, W.K. and Shabir, M., On some new operations in soft set theory. Comput. Math. Appl. 57 (2009) 1547-1553.
  4. Aygüoğlu, A. and Aygün, H., Some notes on soft topological spaces, Neural Comput. & Applic. 21 (1) (2012) 113-119.
  5. Çağman, N. and Enginoğlu, S., Soft set theory and $uni-int$ decision making, European J. Oper. Res. 207 (2) (2010) 848-855.
  6. Çetkin, V. and Aygüoğlu, A. and Aygün, H., A new approach in handling soft decision making problems, J. Nonlinear Sci. Appl. 9 (2016) 231-239.
  7. Hussain, S. and Ahmad, B., Some properties of soft topological spaces, Comput. Math. Appl. 62 (11) (2011) 4058-4067.
  8. Kandemir, M.B., A new perspective on soft topology. Hittite J. Sci. Eng. 5 (2) (2018) 105-113.
  9. Kandemir, M.B., The concept of $\sigma$-algebraic soft set, Soft Comput. 22 (13) (2018) 4353-4360.
  10. Kandemir, M.B., Monotonic soft sets and its applications, Ann. Fuzzy Math. Inform. 12 (2) (2016) 295-307.
APA
Kandemir, M. B. (2020). Some Notes on Soft Topological Concepts and an Application Method. Mathematical Sciences and Applications E-Notes, 8(1), 105-116. https://doi.org/10.36753/mathenot.632024
AMA
1.Kandemir MB. Some Notes on Soft Topological Concepts and an Application Method. Math. Sci. Appl. E-Notes. 2020;8(1):105-116. doi:10.36753/mathenot.632024
Chicago
Kandemir, Mustafa Burç. 2020. “Some Notes on Soft Topological Concepts and an Application Method”. Mathematical Sciences and Applications E-Notes 8 (1): 105-16. https://doi.org/10.36753/mathenot.632024.
EndNote
Kandemir MB (March 1, 2020) Some Notes on Soft Topological Concepts and an Application Method. Mathematical Sciences and Applications E-Notes 8 1 105–116.
IEEE
[1]M. B. Kandemir, “Some Notes on Soft Topological Concepts and an Application Method”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 105–116, Mar. 2020, doi: 10.36753/mathenot.632024.
ISNAD
Kandemir, Mustafa Burç. “Some Notes on Soft Topological Concepts and an Application Method”. Mathematical Sciences and Applications E-Notes 8/1 (March 1, 2020): 105-116. https://doi.org/10.36753/mathenot.632024.
JAMA
1.Kandemir MB. Some Notes on Soft Topological Concepts and an Application Method. Math. Sci. Appl. E-Notes. 2020;8:105–116.
MLA
Kandemir, Mustafa Burç. “Some Notes on Soft Topological Concepts and an Application Method”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, Mar. 2020, pp. 105-16, doi:10.36753/mathenot.632024.
Vancouver
1.Mustafa Burç Kandemir. Some Notes on Soft Topological Concepts and an Application Method. Math. Sci. Appl. E-Notes. 2020 Mar. 1;8(1):105-16. doi:10.36753/mathenot.632024