Volume 17 • Issue 1 • PP: 61-67 • 2021
Neutrosophic Bi-topological Group
Open Access & Copyright
© 2021 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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
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.
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