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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 2Issue 1PP: 38-46 • 2020

Some Results on Single Valued Neutrosophic (Weak) Polygroups

Madeleine Al- Tahan 1*
1Lebanese International University, Bekaa, Lebanon
* Corresponding Author.

Abstract

Polygroups are a generalized concept of groups and  the concept of single valued neutrosophic set is a generalization of the classical notion of a set. The objective of this paper is to combine the innovative concept of single valued neutrosophic sets and polygroups. In this regard, we introduce the concepts of single valued neutrosophic polygroups and anti- single valued neutrosophic polygroups. Moreover, we investigate their properties and study the relation between level sets of single valued neutrosophic polygroups and (normal) subpolygroups.

 

Keywords

Polygroup Weak polygroup Single valued neutrosophic set Single valued neutrosophic polygroup Anti- single valued neutrosophic polygroup

References

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[2] 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.

[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., 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.

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

[6] Davvaz, B. and Cristea, I., Fuzzy Algebraic Hyperstructures, Studies in Fuzziness and Soft Computing 321, Springer International Publishing (2015)

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

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

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

 

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

 

[11] Wang, H., Smarandache ,F., Vasantha Kandasamy W.B., and Smarandache, F., Some neutrosophic algebraic structures and neutrosophic N-algebraic structures, Hexis, Phoenix, Arizona, (2006).

 

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

 

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

 

 

 

 

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Tahan, Madeleine Al-. "Some Results on Single Valued Neutrosophic (Weak) Polygroups." International Journal of Neutrosophic Science, vol. Volume 2, no. Issue 1, 2020, pp. 38-46. DOI: https://doi.org/10.54216/IJNS.020102
Tahan, M. (2020). Some Results on Single Valued Neutrosophic (Weak) Polygroups. International Journal of Neutrosophic Science, Volume 2(Issue 1), 38-46. DOI: https://doi.org/10.54216/IJNS.020102
Tahan, Madeleine Al-. "Some Results on Single Valued Neutrosophic (Weak) Polygroups." International Journal of Neutrosophic Science Volume 2, no. Issue 1 (2020): 38-46. DOI: https://doi.org/10.54216/IJNS.020102
Tahan, M. (2020) 'Some Results on Single Valued Neutrosophic (Weak) Polygroups', International Journal of Neutrosophic Science, Volume 2(Issue 1), pp. 38-46. DOI: https://doi.org/10.54216/IJNS.020102
Tahan M. Some Results on Single Valued Neutrosophic (Weak) Polygroups. International Journal of Neutrosophic Science. 2020;Volume 2(Issue 1):38-46. DOI: https://doi.org/10.54216/IJNS.020102
M. Tahan, "Some Results on Single Valued Neutrosophic (Weak) Polygroups," International Journal of Neutrosophic Science, vol. Volume 2, no. Issue 1, pp. 38-46, 2020. DOI: https://doi.org/10.54216/IJNS.020102
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