Volume 4 • Issue 1 • PP: 08-15 • 2020
On Neutro-BE-algebras and Anti-BE-algebras
Open Access & Copyright
© 2020 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Abstract
In this paper, the concepts of Neutro-BE-algebra and Anti-BE-algebra are introduced, and some related properties and four theorems are investigated. We show that the classes of Neutro-BE-algebra and Anti-BE-algebras are alternatives of the class of BE-algebras.
Keywords
References
[1] S.S. Ahn, K.S. So, “On ideals and upper sets in BE-algebras, Sci. Math. Jpn. 68 (2) pp.279-285, 2008.
[2] H.S. Kim, Y.H. Kim, “On BE-algebras,” Sci. Math. Jpn. 66 (2007), pp.113-116.
[3] A. Borumand Saeid, A. Rezaei, R.A. Borzooei, “Some types of filters in BE-algebras,” Math. Comput. Sci., 7, pp.341-352, 2013.
[4] A. Rezaei, A. Borumand Saeid, R.A. Borzooei, “Relation between Hilbert algebras and BE-algebras,” Applications and Applied Mathematics, 8 (2) pp.573-584, 2013.
[5] A. Rezaei, F. Smarandache, “The Neutrosophic Triplet of BI-algebras,” (submitted to Neutrosophic Sets and System, USA).
[6] F. Smarandache, “Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures, “in Advances of Standard and Nonstandard Neutrosophic Theories, Pons Publishing House Brussels, Belgium, Ch. 6, pp. 240-265, 2019.
[7] F. Smarandache, “NeutroAlgebra is a Generalization of Partial Algebra,” International Journal of Neutrosophic Science, 2 (1) pp. 8–17, 2020.
[8] F. Smarandache, “Neutrosophy / Neutrosophic probability, set, and logic,” American Research Press, 1998. See also: http://gallup.unm.edu/~smarandache/NeutLog.txt.
[9] S. A. Edalatpanah, “A Direct Model for Triangular Neutrosophic Linear Programming, “International Journal of Neutrosophic Science, Volume 1 , Issue 1, pp 19-28 , 2020
[10] S. Broumi, M.Talea, A. Bakali, F. Smarandache, D.Nagarajan, M. Lathamaheswari and M.Parimala, “Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview,” Complex & Intelligent Systems, 5, pp.371–378, 2019, https://doi.org/10.1007/s40747-019-0098-z
[11] S.Broumi,D. Nagarajan, A. Bakali, M. Talea, F. Smarandache, M. Lathamaheswari, “The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment,” Complex & Intelligent Systems, 5, 2019, pp.391–402, https://doi.org/10.1007/s40747-019-0092-5
[12] S. Broumi, D. Nagarajan, A. Bakali, M. Talea, F. Smarandache, M. Lathamaheswari and J. Kavikumar, “Implementation of Neutrosophic Function Memberships Using MATLAB Program,” Neutrosophic Sets and Systems, Vol. 27, 2019, 44-52. DOI: 10.5281/zenodo.3275355
[13] Philippe Schweizer, “Uncertainty: two probabilities for the three states of neutrosophy,” International Journal of Neutrosophic Science, Volume 2 , Issue 1, pp.18-26 , 2020.
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.