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International Journal of Neutrosophic Science
Volume 17 , Issue 1, PP: 61-67 , 2021 | Cite this article as | XML | Html |PDF


Neutrosophic Bi-topological Group

Authors Names :   Riad K. Al-Hamido   1 *  

1  Affiliation :  Department of Mathematics, College of Science, Al-Furat University, Deir-ez-Zor, Syria

    Email :  riad-hamido1983@hotmail.com

Doi   :   https://doi.org/10.54216/IJNS.170104

Received: September 27, 2021 Accepted: December 01, 2021

Abstract :

Neutrosophic topological groups are neutrosophic groups in an algebraic sense together with neutrosophic continuous group operations. In this article, we have presented neutrosophic bi-topological groups with illustrative examples. We have also defined eight new models of neutrosophic bi-topological groups. Neutrosophic bi-topological group that depends on two neutrosophic topologies group is more general than the neutrosophic topological group. Finally, Some basic properties of neutrosophic bi-topological groups were studied.

Keywords :

Neutrosophic topological groups , neutrosophic bi-topological groups , neutrosophic grups

References :

[1]   F. Smarandache; "A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability". American Research Press, Rehoboth, NM, 1999.

[2]   F. Smarandache; "Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics" University of New Mexico, Gallup, NM 87301, USA 2002.

[3]   L. A. Zadeh; "Fuzzy Sets". Inform. Control,Vol. 8, 338-353, 1965.

[4]   K. Atanassov; "intuitionistic fuzzy sets". fuzzy sets and systems, Vol. 20, 87-96, 1986.

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

[6]   A. A. A. Agboola; A.D. Akinola and O.Y. Oyebola; "Neutrosophic Rings I", Int. J. of Math. Comb., vol. 4, 1-14, 2011.

[7]    A. A. A. Agboola; Akwu A.O. and Y.T. Oyebo; "Neutrosophic Groups and Neutrosopic Subgroups", Int. J.of Math. Comb., vol. 3, 1-9, 2012.

[8]    A. A. A. Agboola; "On Refined Neutrosophic Algebraic Structures", Neutrosophic Sets and Systems, vol.10, 99-101, 2015.

[9]    E. O. Adeleke;  A.A.A. Agboola and F. Smarandache; "Refined Neutrosophic Rings I", International Journal

of Neutrosophic Science (IJNS), vol. 2(2), pp. 77-81, 2020. (DOI:10.5281/zenodo.3728222)

[10]       E.O. Adeleke;  A.A.A. Agboola and F. Smarandache; "Refined Neutrosophic Rings II", International Journal of Neutrosophic Science (IJNS), vol. 2(2), pp. 89-94, (2020). (DOI:10.5281/zenodo.3728235.

[11]      Q. H. Imran; A. H. Al-Obaidi; F. Smarandache; "On Some Types of Neutrosophic Topological Groups

with Respect to Neutrosophic Alpha Open Sets". Neutrosophic Sets Syst, Vol. 33, 426–433, 2020.

[12]      R. Sumathi; I. Arockiarani; "Topological Group Structure of Neutrosophic set". Journal of Advanced Studies in Topology, Vol. 7, 12-20, 2016. 

[13]      W. B. Vasantha Kandasamy; and F. Smarandache; "Neutrosophic Rings", Neutrosophic Sets and Systems, 2006.

[14]      A. A. Salama, F. Smarandache and V. Kroumov, Neutrosophic Closed Set and Neutrosophic Continuous Functions. Neutrosophic Sets and Systems, 4(2014), 2-8. 

[15]      I. Arokiarani, R. Dhavaseelan, S. Jafari and M. Parimala, On Some New Notions and Functions in Neutrosophic Topological Spaces, Neutrosophic Sets and Systems, Vol.16, 2017, pp.16-19.


Cite this Article as :
Riad K. Al-Hamido, Neutrosophic Bi-topological Group, International Journal of Neutrosophic Science, Vol. 17 , No. 1 , (2021) : 61-67 (Doi   :  https://doi.org/10.54216/IJNS.170104)