ASPG Menu
search

American Scientific Publishing Group

verified Journal

International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
Frequency

Continuous publication

Publication Model

Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 14Issue 1PP: 47-56 • 2021

Neutrosophic Soft Bitopological Spaces

Ahmed B. AL-Nafee 1* ,
Said Broumi 2 ,
Florentin Smarandache 3
1Ministry of Education Open Educational College, Department of Mathematics, Babylon, Iraq.
2Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, B.P 7955, Morocco.
3Deparment of Mathematics ,University of New Mexico 705 AVE Gallup, NM 87301, USA.
* Corresponding Author.
November 20, 2020 Accepted: March 25, 2021

Abstract

 

In this paper, we built bitopological space on the concept of neutrosophic soft set, we defined the basic topological concepts of this spaces which are N3-(bi)*-open set, N3-(bi)*-closed set, (bi)*-neutrosophic soft interior, (bi)neutrosophic soft closure, (bi)*-neutrosophic soft boundary, (bi)*-neutrosophic soft exterior and we introduced their properties. In addition, we investigated the relations of these basic topological concepts with their counterparts in neutrosophic soft topological spaces and we introduced many examples.

 

Keywords

Neutrosophic soft bitopological Spaces star bineutrosophic soft open set star bi neutrosophic soft closed set.

References

 

[1]     D. Molodtsov, "Soft set theory-First results", Computers & Mathematics with Applications37, pp.19–31,  1999.

 

[2]     F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Re- search Press, Rehoboth, NM, 1999.

 

[3]     L. Zadeh, "Fuzzy sets", Inform and Control, 8, pp.338353, 1965.

 

[4]     K.Atanassov, "Intuitionistic Fuzzy Sets", Fuzzy Sets and Systems, 20 , pp. 87-96, 1986.

 

[5]     P. Maji, "Neutrosophic soft set", Annals of Fuzzy Mathematics and Informatics, 5(1), pp.157-168, 2013.

 

[6]     F. Karaasla, "Neutrosophic soft sets with applications in decision making", International Journal of information science and Intelligent system, 4(2), pp.1-20, 2015.

 

[7]     I. Deli and S. Broumi, "Neutrosophic soft relations and some properties", Annals of Fuzzy Mathematics and Informatics, 9(1), pp.169 – 182, 2015.

 

[8]     T. Bera and N.Mahapatra, "Introduction to neutrosophic soft topological space", Opsearch, 54(4), pp. 841- 867, 2017.

 

[9]     A. B. AL-Nafee, "New Family of Neutrosophic Soft Sets", Neutrosophic Sets and Systems, 38, pp. 482 - 496, 2020.

 

[10]   Y. Taha, G. A. Cigdem and B. Sadi,"A New Approach to Operations on Neutrosophic Soft Sets and to Neutrosophic Soft Topological Spaces", Communications in Mathematics and Applications, vol. 10(3) , pp. 481493, 2019.

 

[11]   A. B. AL-Nafee, R. Al-Hamido and F. Smarandache, “ Separation Axioms in Neutrosophic Crisp Topological Spaces”, Neutrosophic Sets and Systems, 25 , pp. 25 - 33, 2019.

 

[12]   A. B. AL-Nafee, A. A. Salama, & F. Smarandache, "New Types of Neutrosophic Crisp Closed Sets"Neutrosophic Sets and Systems36, pp. 175 -183, 2020.

 

[13]   A. B. AL-Nafee, “On *Soft Turing Point with Separation Axioms”, JUBPAS, vol. 26, no. 7, pp. 200 - 209, May 2018.  

 

[14]   A. Al-nafee and L. Al-swidi , "Separation Axioms Using Soft Turing Point of a Soft Ideal in Soft Topological Space", Journal of New Theory, no. 25, pp. 29-37, Oct. 2018.

 

[15]    A. B. AL-Nafee and R. D. Ali. On Idea of Controlling Soft Gem-Set in Soft Topological Space, Jour of Adv Research in Dynamical & Control Systems, Vol. 10, 13-Special Issue, 606-615, 2018. http://jardcs.org/backissues/abstract.php?archiveid=6022.

 

[16]   E. P Evanzalin, I. H Jude and .K. Sivaranjani, "Introduction to neutrosophic soft topological spatial region", Neutrosophic Sets and Systems, vol. 31 , pp. 297304, 2020.

 

[17]   A. A. Salama and S. Alblowi, “Neutrosophic set and neutrosophic topological spaces”, ISOR J. Mathematicsvol. 3, no. 3, pp.31 – 35, 2012.

 

[18]   D. R. Narmada, R. Dhavaseelan and S. Jafari, On Separation Axioms in an Ordered Neutrosophic Bitopological Space, Neutrosophic Sets and Systems, vol. 18, pp. 27-36, 2017.

 

[19]   D. N. Georgiou, A. C. Megaritis and V. I. Petropoulos, On soft topological spaces, Appl. Math. Inf. Sci, 7(2) 1889-1901. 2013.

 

[20]   N.Cageman and S.Enginolgu, Contributions to the Theory of Soft Sets, Journal of New Results in Science, 4 ,33-41, 2014.

 

[21]   J. C. Kelly,Bitopological spaces, Proceedings of the London Mathematical Society, 3(1), 71-89, 1963.

 

[22]   B. M. Ittanagi, “Soft bitopological spaces“. International Journal of Computer Applications, 107(7), 1-4, 2014.

 

[23]   A. Kandil, A. A. Nouh & S. A El-Sheikh, “On fuzzy bitopological spaces“, Fuzzy sets and systems, 74(3), 353-363, 1995.

 

[24]   Y. O.Taha, O.Alkan Neutrosophic Bitopological Spaces, Neutrosophic Sets and Systems, vol. 30, pp.88-97, 2019.

 

[25]   R. Al-Hamido,“Neutrosophic Crisp Bi-Topological Spaces”, Neutrosophic Sets and Systems, vol. 21, 66-73. 2018.

 

[26]   F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Inter. J.Pure Appl. Math. 24, 287-297, 2005.

 

[27]   I. D. Jaleel and L. A. Al-Swidi, d-OPEN SET IN BITOPOLOGICAL SPACE . M.sc. thesis University of Babylon, 2003.

 

Cite This Article

Choose your preferred format

format_quote
AL-Nafee, Ahmed B., Broumi, Said, Smarandache, Florentin. "Neutrosophic Soft Bitopological Spaces." International Journal of Neutrosophic Science, vol. Volume 14, no. Issue 1, 2021, pp. 47-56. DOI: https://doi.org/10.54216/IJNS.140104
AL-Nafee, A., Broumi, S., Smarandache, F. (2021). Neutrosophic Soft Bitopological Spaces. International Journal of Neutrosophic Science, Volume 14(Issue 1), 47-56. DOI: https://doi.org/10.54216/IJNS.140104
AL-Nafee, Ahmed B., Broumi, Said, Smarandache, Florentin. "Neutrosophic Soft Bitopological Spaces." International Journal of Neutrosophic Science Volume 14, no. Issue 1 (2021): 47-56. DOI: https://doi.org/10.54216/IJNS.140104
AL-Nafee, A., Broumi, S., Smarandache, F. (2021) 'Neutrosophic Soft Bitopological Spaces', International Journal of Neutrosophic Science, Volume 14(Issue 1), pp. 47-56. DOI: https://doi.org/10.54216/IJNS.140104
AL-Nafee A, Broumi S, Smarandache F. Neutrosophic Soft Bitopological Spaces. International Journal of Neutrosophic Science. 2021;Volume 14(Issue 1):47-56. DOI: https://doi.org/10.54216/IJNS.140104
A. AL-Nafee, S. Broumi, F. Smarandache, "Neutrosophic Soft Bitopological Spaces," International Journal of Neutrosophic Science, vol. Volume 14, no. Issue 1, pp. 47-56, 2021. DOI: https://doi.org/10.54216/IJNS.140104
Digital Archive Ready