Soft Sub Spaces and Soft b-Separation Axioms in Binary Soft Topological Spaces

Arif Mehmood Khattak; Zia Ullah; Fazli Amin; Saleem Abdullah; Shamoona Jabeen; Nasir Ahmad Khattak; Zaheer Anjum Khattak

Research Article

Soft Sub Spaces and Soft b-Separation Axioms in Binary Soft Topological Spaces

Year 2018, Issue: 23, 48 - 62, 01.06.2018

Arif Mehmood Khattak Zia Ullah Fazli Amin Saleem Abdullah Shamoona Jabeen Nasir Ahmad Khattak Zaheer Anjum Khattak

Abstract

In this article, we introduce binary soft pre-separation axioms in
binary soft topological space along with several properties of binary soft pre , i = 0; 1; 2, binary soft pre regular,
binary soft pre, binary soft pre normal and
binary soft axiom using binary soft points. We also
mention some binary soft invariance properties namely binary soft topological
property and binary soft hereditary property. We hope that these results will
be useful for the future study on binary soft topology to carry out general
background for the practical applications and to solve the thorny problems
containing doubts in different grounds.

Keywords

Binary soft topology, binary soft pre-open sets, binary soft pre closed sets, binary soft pre separation axioms

References

[1] A. Acikgöz, N. Tas, Binary Soft Set Theory, Eur. J. of Pure. And Appl. Math., Vol. 9, No. 4, 2016, 452- 463.
[2] S. S. Benchalli, G. Patil, On Binary Soft Separation Axioms in Binary Soft Topological Spaces, Global journal and Applied Mathematics,Vol 13,No.9,2017,5393-5412.
[3] D. Molodtsov, Soft Set Theory First Results. Comput. Math. Appl., 37, 1999, 9 - 31.
[4] D.Molodtsov, V. Y. Leonov and D. V. Kovkov, Soft sets technique and itsApplication, Nechetkie Sistemy i Myagkie Vychisleniya 1 (1), 2006, 8-39.
[5] M. Shabir, M. Naz, On Some New Operations in Soft Set Theory, Computers and Math. With Appl., 57, 2011, 1786-1799.
[6] S. S. Benchalli, G. Patil, A. S. Dodamani and J. P. Kumar, On Binary Soft Topological Spaces, International Journal of Applied Mathematics 30 (6) (2017), 437-453.
[7] A. Kalaichelvi and P.H. Malini, Application of Fuzzy Soft Sets to Investment Decision Making Problem, International Journal of Mathematical Sciences and Applications 1 (3) (2011) 1583-1586.
[8] N. Y. Özgür and N. Taş, A Note on “Application of Fuzzy Soft Sets to Investment Decision Making Problem”, Journal of New Theory 7 (2015) 1-10.
[9] N. Taş, N. Y. Özgür and P. Demir, An Application of Soft Set and Fuzzy Soft Set Theories to Stock Management, Süleyman Demirel University Journal of Natural and Applied Sciences 21 (2) (2017), 791-196.
[10] J. C. R. Alcantud, S. C. Rambaud and M. J. M. Torrecillas, Valuation Fuzzy Soft Sets: A Flexible Fuzzy Soft Set Based Decision Making Procedure for the Valuation of Assets, Symmetry 2017, 9(11), 253; doi:10.3390/sym9110253
[11] N. Çağman, S. Enginoğlu, Soft Matrix Theory and its Decision Making, Computers and Mathematics with Applications 59 (2010) 3308-3314.

Year 2018, Issue: 23, 48 - 62, 01.06.2018

Arif Mehmood Khattak Zia Ullah Fazli Amin Saleem Abdullah Shamoona Jabeen Nasir Ahmad Khattak Zaheer Anjum Khattak

Abstract

References

[1] A. Acikgöz, N. Tas, Binary Soft Set Theory, Eur. J. of Pure. And Appl. Math., Vol. 9, No. 4, 2016, 452- 463.
[2] S. S. Benchalli, G. Patil, On Binary Soft Separation Axioms in Binary Soft Topological Spaces, Global journal and Applied Mathematics,Vol 13,No.9,2017,5393-5412.
[3] D. Molodtsov, Soft Set Theory First Results. Comput. Math. Appl., 37, 1999, 9 - 31.
[4] D.Molodtsov, V. Y. Leonov and D. V. Kovkov, Soft sets technique and itsApplication, Nechetkie Sistemy i Myagkie Vychisleniya 1 (1), 2006, 8-39.
[5] M. Shabir, M. Naz, On Some New Operations in Soft Set Theory, Computers and Math. With Appl., 57, 2011, 1786-1799.
[6] S. S. Benchalli, G. Patil, A. S. Dodamani and J. P. Kumar, On Binary Soft Topological Spaces, International Journal of Applied Mathematics 30 (6) (2017), 437-453.
[7] A. Kalaichelvi and P.H. Malini, Application of Fuzzy Soft Sets to Investment Decision Making Problem, International Journal of Mathematical Sciences and Applications 1 (3) (2011) 1583-1586.
[8] N. Y. Özgür and N. Taş, A Note on “Application of Fuzzy Soft Sets to Investment Decision Making Problem”, Journal of New Theory 7 (2015) 1-10.
[9] N. Taş, N. Y. Özgür and P. Demir, An Application of Soft Set and Fuzzy Soft Set Theories to Stock Management, Süleyman Demirel University Journal of Natural and Applied Sciences 21 (2) (2017), 791-196.
[10] J. C. R. Alcantud, S. C. Rambaud and M. J. M. Torrecillas, Valuation Fuzzy Soft Sets: A Flexible Fuzzy Soft Set Based Decision Making Procedure for the Valuation of Assets, Symmetry 2017, 9(11), 253; doi:10.3390/sym9110253
[11] N. Çağman, S. Enginoğlu, Soft Matrix Theory and its Decision Making, Computers and Mathematics with Applications 59 (2010) 3308-3314.

There are 11 citations in total.

Details

Primary Language	English
Journal Section	Research Article
Authors	Arif Mehmood Khattak Zia Ullah This is me Fazli Amin This is me Saleem Abdullah This is me Shamoona Jabeen This is me Nasir Ahmad Khattak This is me Zaheer Anjum Khattak This is me
Publication Date	June 1, 2018
Submission Date	February 23, 2018
Published in Issue	Year 2018 Issue: 23

Cite

APA	Khattak, A. M., Ullah, Z., Amin, F., Abdullah, S., et al. (2018). Soft Sub Spaces and Soft b-Separation Axioms in Binary Soft Topological Spaces. Journal of New Theory(23), 48-62.
AMA	Khattak AM, Ullah Z, Amin F, Abdullah S, Jabeen S, Khattak NA, Khattak ZA. Soft Sub Spaces and Soft b-Separation Axioms in Binary Soft Topological Spaces. JNT. June 2018;(23):48-62.
Chicago	Khattak, Arif Mehmood, Zia Ullah, Fazli Amin, Saleem Abdullah, Shamoona Jabeen, Nasir Ahmad Khattak, and Zaheer Anjum Khattak. “Soft Sub Spaces and Soft B-Separation Axioms in Binary Soft Topological Spaces”. Journal of New Theory, no. 23 (June 2018): 48-62.
EndNote	Khattak AM, Ullah Z, Amin F, Abdullah S, Jabeen S, Khattak NA, Khattak ZA (June 1, 2018) Soft Sub Spaces and Soft b-Separation Axioms in Binary Soft Topological Spaces. Journal of New Theory 23 48–62.
IEEE	A. M. Khattak, “Soft Sub Spaces and Soft b-Separation Axioms in Binary Soft Topological Spaces”, JNT, no. 23, pp. 48–62, June 2018.
ISNAD	Khattak, Arif Mehmood et al. “Soft Sub Spaces and Soft B-Separation Axioms in Binary Soft Topological Spaces”. Journal of New Theory 23 (June 2018), 48-62.
JAMA	Khattak AM, Ullah Z, Amin F, Abdullah S, Jabeen S, Khattak NA, Khattak ZA. Soft Sub Spaces and Soft b-Separation Axioms in Binary Soft Topological Spaces. JNT. 2018;:48–62.
MLA	Khattak, Arif Mehmood et al. “Soft Sub Spaces and Soft B-Separation Axioms in Binary Soft Topological Spaces”. Journal of New Theory, no. 23, 2018, pp. 48-62.
Vancouver	Khattak AM, Ullah Z, Amin F, Abdullah S, Jabeen S, Khattak NA, Khattak ZA. Soft Sub Spaces and Soft b-Separation Axioms in Binary Soft Topological Spaces. JNT. 2018(23):48-62.