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International Journal of Neutrosophic Science
Volume 8 , Issue 1, PP: 34-43 , 2020 | Cite this article as | XML | Html |PDF


Weakly b-Closed Sets and Weakly b-Open Sets based of Fuzzy Neutrosophic bi-Topological Spaces

Authors Names :   Fatimah M. Mohammed   1 *     Sarah W. Raheem   2  

1  Affiliation :  Department of Mathematics, College of Education for Pure Sciences, Tikrit University, Tikrit, IRAQ

    Email :  dr.fatimahmahmood@tu.edu.iq

2  Affiliation :  Department of Mathematics, College of Education for Pure Sciences, Tikrit University, Tikrit, IRAQ

    Email :  sarahraheem@tu.edu.iq

Doi   :   https://doi.org/10.54216/IJNS.080103

Abstract :

   In this paper,  we present and study some of the basic properties of the new class of sets called weakly b-closed sets and weakly b- open sets in fuzzy neutrosophic bi-topological spaces. We referred to some results related to the new definitions, which we taked the case of equal in the definition of b-sets instead of subset. Then, we discussed the relations between the new defined sets by hand and others fuzzy neutrosophic sets which were studied before us on the other hand on fuzzy neutrosophic bi-topological spaces. Then, we have studied some of characteristics and some relations are compared with necessary examples

Keywords :

Fuzzy neutrosophic sets , Fuzzy neutrosophic bi-topology , Fuzzy neutrosophic weakly b-closed sets , Fuzzy neutrosophic weakly b-open sets.

References :

[1]  L. Zadeh, “Fuzzy sets”, Information and control, 8, pp. 338-353, 1965.

[2]  K. Atanassov, S. Stoeva, "Intuitionistic Fuzzy Sets", in: Polish Syrup. On Interval and Fuzzy Mathematics, Poznan, pp. 23-26, 1983.

[3]  K. Atanassov, " Review and New Results on Intuitionistic Fuzzy Sets", Preprint IM- MFAIS, Sofia, pp.1-88, 1988.

[4]  K. Atanassov, "Intuitionistic fuzzy sets. Fuzzy Sets and Systems", 20(1), pp. 87-96, 1986.

[5]  F. Smarandache, "Neutrosophic set- a generalization of intuitionistic fuzzy sets", International Journal of Pure and Applied Mathematics,  24(3), pp. 287-297, 2005.

[6]  F. Smaradache, "Neutrosophic Set A Generalization of Intuitionistic Fuzzy set", Journal of Defense Resourses Management, vol. 1, pp.107-114, 2010.

[7]  A. A. Salama and S. Alblowi, "Generalized Neutrosophic Sets and Generalized Neutrosophic Topological Spaces", Journal Compiter Sci. Engineering, 2(7), pp. 12-23, 2012.

[8]  Y. Veereswari, "An  Introduction  to  Fuzzy  Neutrosophic  Topological Spaces", IJMA, vol. 8, pp. 144-149, 2017.

[9]  F. M. Mohammed, A. A. Hijab and Sh. F. Matar , "Fuzzy Neutrosophic Weakly- Generalized closed set in Fuzzy Neutrosophic Topological Spaces", University of Anbar for Pure Science, vol. 12, pp. 63-73, 2018.

[10]          F. M. Mohammed, "Generalized b Closed Sets and Generalized b Open Sets in Fuzzy Neutrosophic bi-Topological Spaces" (submitted)

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

[12]          R. K. Al-Hamido, T. Gharibah, S. Jafari and F. Smarandache, “On Neutrosophic Crisp Topology via N-Topology”, Neutrosophic Sets and Systems, vol. 21, pp. 96-109, 2018. 

[13]          R. K. Al-Hamido, "On Neutrosophic Crisp Supra Bi-Topological Spaces”, International Journal of Neutrosophic Science, 4 (1), pp.36-46, 2020. 

[14]          E. Ebenanjar, J. Immaculate and C. Bazil Wilfred, "On Neutrosophic b-open sets in Neutrosophic topological space" Journal of Physics Conference Series, 1139(1), pp.1-6, 2018

[15]          P. Indhumathi and D. Jayanthi, “On Fuzzy b# Closed Sets”, international Journal of Mathematics Trends and Technology – Special issue ICRMIT, pp.108-11, 2018.

[16]          W. Al-Omeri and F. Smarandache, "New Neutrosophic Sets via Neutrosophic Topological Spaces", Neutrosophic Operational Research; Pons Editions: Brussels, Belgium, vol. I, pp. 189–209, 2017.

[17]          W. Al-Omeri, "Neutrosophic crisp sets via neutrosophic crisp topological spaces", Neutrosophic Sets Syst., vol.13, pp.96–104, 2016.

[18]          S. Thakur and R. Dhavaseelan, “Nowhere dense sets in intuitionistic fuzzy topological spaces”, Proceedings of  National Seminar on Recent Developments in topology, vol. 52, pp.17-21, 2015.

[19]          M. Parimala , M. Karthika , F. Smarandache and S. Broumi, “On αω-closed sets and its connectedness in terms of neutrosophic topological spaces”, International Journal of Neutrosophic Science,  vol. 2(2), pp. 82-88 , 2020.

[20]          V. Christianto, F. Smarandache and M. Aslam, “How we can extend the standard deviation notion with neutrosophic interval and quadruple neutrosophic numbers”, International Journal of Neutrosophic Science, vol. 2(2), pp.72-76 , 2020.


[21]          W. Al-Omeri, S. Jafari, "On generalized closed sets and generalized pre-closed sets in neutrosophic topological spaces", Mathematics, vol.(7)1: pp.1-12, 2019.

Cite this Article as :
Fatimah M. Mohammed , Sarah W. Raheem, Weakly b-Closed Sets and Weakly b-Open Sets based of Fuzzy Neutrosophic bi-Topological Spaces, International Journal of Neutrosophic Science, Vol. 8 , No. 1 , (2020) : 34-43 (Doi   :  https://doi.org/10.54216/IJNS.080103)