449 227
Full Length Article
Volume 3 , Issue 2, PP: 108-117 , 2020

Title

On single valued neutrosophic sets and neutrosophic א-structures: Applications on algebraic structures (hyperstructures)

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.3750220


Abstract :

In this paper, we find a relationship between SVNS and neutrosophic N-structures and study it. Moreover, we apply our results to algebraic structures (hyperstructures) and prove that the results on  neutrosophic N-substructure (subhyperstructure) of a given algebraic structure (hyperstructure) can be deduced from single valued neutrosophic algebraic structure (hyperstructure) and vice versa.

Keywords :

Neutrosophic א-structures , SVNS , (α , β , γ)-level set , neutrosophic א-ideals , neutrosophic א-substructures (subhypertsructures)

References :

[1] Al- Tahan, M. and Davvaz, B., “Commutative single power cyclic hypergroups of order three and period two”, Discrete Mathematics, Algorithms and Applications, vol. 9, no. 5, pp. 1750070-1750084, 2017.

[2] Al- Tahan, M., Hoskova-Mayerova, S., and Davvaz, B., “An overview of topological hypergroupoids”, Journal of Intelligent and Fuzzy Systems, vol. 34, pp. 1907–1916, 2018.

[3] 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.

 [4] Al- Tahan, M. and Davvaz, B., “Complex fuzzy and generalized complex fuzzy subpolygroups of a polygroup”, Jordan Journal of Mathematics and Statistics, vol 12, no 2, pp. 151-173, 2019.

[5] 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.

[6] Al- Tahan, M., Hoskova-Mayerova, S. and Davvaz, B., “Fuzzy multi-polygroups”, Journal of Intelligent & Fuzzy Systems Journal of Intelligent & Fuzzy Systems, vol 38, pp. 2337–2345, 2020.

[7] Al- Tahan, M., Davvaz, B., “Neutrosophic N–Ideals (N-Subalgebras) of Subtraction Algebra”, International Journal of Neutrosophic Science (IJNS), vol. 3, no. 1, pp. 44-53, 2020.

[8] Atanassov, K.T, “Intuitionistic fuzzy sets”, Fuzzy sets and systems, vol. 20, no. 1, pp. 87-96, 1986.

[9] Comer, S.D., “Polygroups derived from cogroups”, J. Algebra, vol 89, pp. 397-405, 1984.

[10] Corsini, P., Leoreanu, V., Applications of Hyperstructures Theory, Advances in Mathematics, Kluwer Academic Publisher, 2003.

[11] Davvaz, B., Polygroup Theory and Related Systems, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2013)

[12] Hoskova-Mayerova, S., Al- Tahan, M., Davvaz, B., ”Fuzzy multi-hypergroups”, Mathematics, vol. 8, 2020.

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

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

[15] 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.

[16] Marty, F. , “Sur une generalization de la notion de group”, In 8th Congress Math. Scandenaves, pp. 45-49, 1934.

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

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

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

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

[21] Ulucay, V., Sahin, M., “Neutrosophic multigroups and applications”, Mathematics, vol. 7, no. 1, 2019.

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

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

[24] Zhang, Y., Sunderraman, R., Single Valued Neutrosophic Sets, Technical Sciences and Applied Mathematics.

     

[1] Al- Tahan, M. and Davvaz, B., “Commutative single power cyclic hypergroups of order three and period two”, Discrete Mathematics, Algorithms and Applications, vol. 9, no. 5, pp. 1750070-1750084, 2017.

[2] Al- Tahan, M., Hoskova-Mayerova, S., and Davvaz, B., “An overview of topological hypergroupoids”, Journal of Intelligent and Fuzzy Systems, vol. 34, pp. 1907–1916, 2018.

[3] 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.

 [4] Al- Tahan, M. and Davvaz, B., “Complex fuzzy and generalized complex fuzzy subpolygroups of a polygroup”, Jordan Journal of Mathematics and Statistics, vol 12, no 2, pp. 151-173, 2019.

[5] 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.

[6] Al- Tahan, M., Hoskova-Mayerova, S. and Davvaz, B., “Fuzzy multi-polygroups”, Journal of Intelligent & Fuzzy Systems Journal of Intelligent & Fuzzy Systems, vol 38, pp. 2337–2345, 2020.

[7] Al- Tahan, M., Davvaz, B., “Neutrosophic N–Ideals (N-Subalgebras) of Subtraction Algebra”, International Journal of Neutrosophic Science (IJNS), vol. 3, no. 1, pp. 44-53, 2020.

[8] Atanassov, K.T, “Intuitionistic fuzzy sets”, Fuzzy sets and systems, vol. 20, no. 1, pp. 87-96, 1986.

[9] Comer, S.D., “Polygroups derived from cogroups”, J. Algebra, vol 89, pp. 397-405, 1984.

[10] Corsini, P., Leoreanu, V., Applications of Hyperstructures Theory, Advances in Mathematics, Kluwer Academic Publisher, 2003.

[11] Davvaz, B., Polygroup Theory and Related Systems, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2013)

[12] Hoskova-Mayerova, S., Al- Tahan, M., Davvaz, B., ”Fuzzy multi-hypergroups”, Mathematics, vol. 8, 2020.

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

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

[15] 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.

[16] Marty, F. , “Sur une generalization de la notion de group”, In 8th Congress Math. Scandenaves, pp. 45-49, 1934.

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

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

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

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

[21] Ulucay, V., Sahin, M., “Neutrosophic multigroups and applications”, Mathematics, vol. 7, no. 1, 2019.

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

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

[24] Zhang, Y., Sunderraman, R., Single Valued Neutrosophic Sets, Technical Sciences and Applied Mathematics.