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International Journal of Neutrosophic Science
Volume 4 , Issue 1, PP: 08-15 , 2020 | Cite this article as | XML | Html |PDF


On Neutro-BE-algebras and Anti-BE-algebras

Authors Names :   Akbar Rezaei   1 *     Florentin Smarandache   2  

1  Affiliation :  Department of Mathematics, Payame Noor University, P.O..Box. 19395-3697, Tehran, IRAN

    Email :  rezaei@pnu.ac.ir

2  Affiliation :  Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA

    Email :  smarand@unm.edu

Doi   :   https://doi.org/10.54216/IJNS.040101

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.

Cite this Article as :
Akbar Rezaei , Florentin Smarandache, On Neutro-BE-algebras and Anti-BE-algebras, International Journal of Neutrosophic Science, Vol. 4 , No. 1 , (2020) : 08-15 (Doi   :  https://doi.org/10.54216/IJNS.040101)