430 235
Full Length Article
Volume 3 , Issue 1, PP: 44-53 , 2020


Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra

Authors Names :   Madeleine Al- Tahan   1 *     Bijan Davvaz   2  

1  Affiliation :  Department of Mathematics, Lebanese International University, Bekaa, Lebanon

    Email :  madeline.tahan@liu.edu.lb

2  Affiliation :  Department of Mathematics Yazd University, Yazd, Iran

    Email :  davvaz@yazd.ac.ir

Doi   :  10.5281/zenodo.3738737

Abstract :

The connection between neutrosophy and algebra has been of great interest with respect to many researchers. The objective of this paper is to provide a connection between neutrosophic −structures and subtraction algebras. In this regard, we introduce the concept of neutrosophic −ideals in subtraction algebra. Moreover, we study its properties and find a necessary and sufficient condition for a neutrosophic −structure to be a neutrosophic −ideal.

Keywords :

Subtraction algebra ,  −structure , Neutrosophic −ideal , Level set

References :

[1] Al- Tahan, M., “Some results on single valued neutrosophic (weak) polygroups”, International Journal of Neutrosophic Science (IJNS), vol 2, no.1, pp. 38-46, 2020. 


[2] Al- Tahan, M. and  Davvaz, B., "Refined neutrosophic quadruple (po-)hypergroups and their fundamental group, Neutrosophic Sets and Systems, vol 27, pp. 138-153, 2019.


[3] Ibrahim, M.A., Agboola, A.A.A., Adeleke, E.O., Akinleye, S.A., “Introduction to neutrosophic subtraction algebra and neutrosophic subtraction semigroup”, International journal of neutrosophic science (IJNS) vol 2 , no. 1, pp. 47-62 ,2020.


[4] Jun, Y. B., Kim, H. S, Roh, E. H., “Ideal theory of subtraction algebras”, Sci. Math. Jpn., vol 61, no. 3, pp. 459–464, 2005.


[5] Jun, Y. B.,  Lee, K. J. , Song, S. Z., “N-ideals of BCK/BCI-algebras”, J. Chungcheong Math. Soc., vol. 22, pp. 417-437, 2009.


[6] Jun, Y. B., Smarandache. F.,  Bordbar, H., “Neutrosophic N-structures applied to BCK/BCI-Algebras”, Information, vol.8, no.128, 2017.


[7] Khan, M., Anis, S., Smarandache, F., Jun, Y. B.,  “Neutrosophic N-structures and their applications in semigroups”, Annals of Fuzzy Mathematics and Informatics, vol. 14, no. 6, pp. 583-598, 2017.


[8] Park, C.H., “Neutrosophic ideal of subtraction algebras”, Neutrosophic Sets and Systems, vol. 24, pp. 36-45, 2019.


[9] Schein, B. M., “Difference Semigroups”, Comm. in Algebra, vol. 20, pp. 2153–2169, 1992. 


[10] Smarandache. F., Neutrosophy: Neutrosophic Probability, Set and logic, Ann Arbor, Michigan, USA, 105 (2002). 


[11] Smarandache. F., “Neutrosophic set- A generalization of the intuitionistic fuzzy set”. Int. J. Pure Appl. Math., vol 24, pp. 287-297, 2005.


[12] Smarcrandach, F., “NeutroAlgebra is a generalization of partial algebra”, International Journal of Neutrosophic Science,(IJNS), vol. 2, no. 1, pp. 08-17, 2020 


[13] Smarcrandach, F., “(t, i, f)-Neutrosophic Structures & I-Neutrosophic Structures (Revisited)”, Neutrosophic Sets and Systems, vol 8, pp. 3-9, 2015.


[14] Zadeh, L., “Fuzzy sets”, Inform and Control, vol. 8, pp. 338-353, 1965. 


[15] Zelinka, B., “Subtraction semigroups”, Math. Bohemica, vol.120, pp. 445–447, 1995.