945 519
Full Length Article
International Journal of Neutrosophic Science
Volume 14 , Issue 2, PP: 72-81 , 2021 | Cite this article as | XML |PDF


Introduction to Neutrosophic Soft Bitopological Spaces

Authors Names :   Hasan Dadas   1 *     Sibel Demiralp   2  

1  Affiliation :  Department of Mathematics, Faculty of Arts and Sciences, Kastamonu University, Turkey

    Email :  Sibel Demiralp

2  Affiliation :  Department of Mathematics, Faculty of Arts and Sciences, Kastamonu University, Turkey

    Email :  sdemiralp@kastamonu.edu.tr

Doi   :   https://doi.org/10.54216/IJNS.140201

December 09, 2020 Accepted: March 28, 2021

Abstract :

In this study, the concept of neutrosophic soft bitopological space is defined and it is one of the few studies that have dealt with this concept. In addition, pairwise neutrosophic soft open (closed) set on neutrosophic soft bitopological spaces are studied. Supra neutrosophic soft topology is defined by pairwise neutrosophic soft open sets. Important theorems related to the subject supported with many examples for better understanding of the subject are given.


Keywords :

Neutrosophic set; Neutrosophic soft set; Soft bitopological space; Neutrosophic soft bitopological space; Neutrosophic soft pairwise open (closed) set.

References :


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


[2]  S. Bayramov and C. Gunduz Aras "On intuitionistic fuzzy soft topological spaces"TWMS J. Pure Appl. Math: 5(1), pp.  66–79. 2014.


[3]  T. Bera and N. K. Mahapatra " On neutrosophic soft function", Ann. Fuzzy Math. Inform. ,12(1), pp. 101–119. 2016


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


[5]  N. Cagman, S. Karatas and S. Enginoglu "Soft topology", Comput. Math Appl, 62, pp. 351–358. 2011.


[6]  C. L. Chang "Fuzzy topological spaces" J. Math. Anal.Appl., 24(1), pp.  182–190. 1968.


[7]  D. Coker"A note on intuitionistic sets and intuitionistic points", J. Math, 20, pp. 343-351. 1996.


[8]  I. Deli and S. Broumi "Neutrosophic soft relations and some properties", Ann. Fuzzy Math. Inform. 9(1), pp. 169–182. 2015.


[9]  C. Gunduz Aras, T. Y. Öztürk and S. Bayramov " Separation axioms on neutrosophic soft" topological spaces. Turk. J. Math,43, pp.  498-510. 2019.


[10]   B. M. Ittanagi "Soft bitopological spaces", Int. J. Comput. Appl, 107(7), pp. 1-4. 2014.


[11]  G. Jayaparthasarathy, V. F. Flower and M. A. Dasan, " supra topological applications in data mining process ", Neutrosophic Sets & Systems, 27, pp.80-97. 2019.


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


[13]  J. C Kelly, "Bitopological spaces". Proc. London Math. Soc, 3(1), pp. 71-89. 1963.


[14]P. K. Maji "Neutrosophic soft set". Ann. Fuzzy Math. Inform., 5(1), pp. 157–168. 2013.


[15]   K, Mohana, V. Christy and F. Smarandache: " multi-criteria decision-making problem via bipolar single-valued neutrosophic settings "Neutrosophic Sets and Systems, pp.125-135. 2019. DOI: 10.5281/zenodo.2631512.


[16]D. Molodtsov" set theory-First results ". Comput. Math. Appl. 37, pp.  19-31. 1999.


[17] N. A. Nabeeh, M. Abdel-Basset, H. A. El-Ghareeb and A. Aboelfetouh, "Neutrosophic multicriteria decision making approach for iot-based enterprises". IEEE Access, 7, pp. 59559-59574. 2019.


[18]  N. A. Nabeeh, F. Smarandache, M. Abdel-Basset, H. A. El-Ghareeb and A. Aboelfetouh, "An integrated neutrosophic-topsis approach and its application to personnel selection: A new trend in brain processing and analysis". IEEE Access, 7, pp. 29734-29744. 2019.


[19]   R. Narmada Devi, R. Dhavaseelan and S. Jafari, " separation axioms in an ordered neutrosophic bitopological space ", Neutrosophic Sets and Systems, 27-36. 2017. http://doi.org/10.5281/zenodo.1175170


[20] R. Al-Hamido, " Neutrosophic crisp bitopological spaces", Neutrosophic Sets and Systems, pp. 66-73. 2018. https://doi.org/10.5281/zenodo.1408695


[21]  A. Saha and S. Broumi " operators on interval valued neutrosophic sets ", Neutrosophic Sets and Systems, vol. 28, pp. 128-137. 2019. DOI: 10.5281/zenodo.3382525


[22]A. A. Salma and S.A. Alblowi "Neutrosophic set and neutrosophic topological spaces". IOSR J.Math., 3(4), pp.   31–35. 2012.


[23]  F. Smarandache, "Neutrosophic set, a generalisation of the intuitionistic fuzzy sets". Int. J. Pure Appl. Math., 24, pp.  287–297. 2005.


[24]  M. Shabir and M. Naz "On soft topological spaces". Comput. Math. Appl, 61, pp. 1786–1799. 2011.


[25]  L. A. Zadeh "Fuzzy Sets". Inform. Control, 8, pp. 338-353. 1965.


[26]T. Ozturk, C. Gunduz Aras and S. Bayramov, "A new approach to operations on neutrosophic soft sets and to neutrosophic soft topological spaces". Comput. Math. Appl. 10(3), pp.  481–493. 2019.


[27] Y. O. Taha, G. A. Cigdem and B. Sadi. "Separation axioms on neutrosophic soft topological spaces". Turk. J. Math, 43, pp.  498-510. 2019.


Cite this Article as :
Hasan Dadas , Sibel Demiralp, Introduction to Neutrosophic Soft Bitopological Spaces, International Journal of Neutrosophic Science, Vol. 14 , No. 2 , (2021) : 72-81 (Doi   :  https://doi.org/10.54216/IJNS.140201)