1
Department of Mathematics, Payame Noor University, P.O..Box. 19395-3697, Tehran, IRAN
(rezaei@pnu.ac.ir)
2
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
(smarand@unm.edu)
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 :
BE-algebra; Neutro-sophication; Neutro-BE-algebra; Anti-sophication; Anti-BE-algebra.
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.
| Style | # |
|---|---|
| MLA | Akbar Rezaei , Florentin Smarandache. "On Neutro-BE-algebras and Anti-BE-algebras." International Journal of Neutrosophic Science, Vol. 4, No. 1, 2020 ,PP. 08-15 (Doi : https://doi.org/10.54216/IJNS.040101) |
| APA | Akbar Rezaei , Florentin Smarandache. (2020). On Neutro-BE-algebras and Anti-BE-algebras. Journal of International Journal of Neutrosophic Science, 4 ( 1 ), 08-15 (Doi : https://doi.org/10.54216/IJNS.040101) |
| Chicago | Akbar Rezaei , Florentin Smarandache. "On Neutro-BE-algebras and Anti-BE-algebras." Journal of International Journal of Neutrosophic Science, 4 no. 1 (2020): 08-15 (Doi : https://doi.org/10.54216/IJNS.040101) |
| Harvard | Akbar Rezaei , Florentin Smarandache. (2020). On Neutro-BE-algebras and Anti-BE-algebras. Journal of International Journal of Neutrosophic Science, 4 ( 1 ), 08-15 (Doi : https://doi.org/10.54216/IJNS.040101) |
| Vancouver | Akbar Rezaei , Florentin Smarandache. On Neutro-BE-algebras and Anti-BE-algebras. Journal of International Journal of Neutrosophic Science, (2020); 4 ( 1 ): 08-15 (Doi : https://doi.org/10.54216/IJNS.040101) |
| IEEE | Akbar Rezaei, Florentin Smarandache, On Neutro-BE-algebras and Anti-BE-algebras, Journal of International Journal of Neutrosophic Science, Vol. 4 , No. 1 , (2020) : 08-15 (Doi : https://doi.org/10.54216/IJNS.040101) |