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International Journal of Neutrosophic Science
Volume 2 , Issue 1, PP: 38-46 , 2020 | Cite this article as | XML | Html |PDF

Title

Some Results on Single Valued Neutrosophic (Weak) Polygroups

  Madeleine Al- Tahan 1 *

1  Lebanese International University, Bekaa, Lebanon
    (madeline.tahan@liu.edu.lb)


Doi   :   https://doi.org/10.54216/IJNS.020102


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 :

[1] Agboola, A. A. A., Davvaz, B. and Smarandache, F. “Neutrosophic quadruple algebraic hyperstructures”, Ann. Fuzzy Math. Inform, vol 14, pp. 29-42, 2017.

[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. 

 

 

 

 


Cite this Article as :
Style #
MLA Madeleine Al- Tahan. "Some Results on Single Valued Neutrosophic (Weak) Polygroups." International Journal of Neutrosophic Science, Vol. 2, No. 1, 2020 ,PP. 38-46 (Doi   :  https://doi.org/10.54216/IJNS.020102)
APA Madeleine Al- Tahan. (2020). Some Results on Single Valued Neutrosophic (Weak) Polygroups. Journal of International Journal of Neutrosophic Science, 2 ( 1 ), 38-46 (Doi   :  https://doi.org/10.54216/IJNS.020102)
Chicago Madeleine Al- Tahan. "Some Results on Single Valued Neutrosophic (Weak) Polygroups." Journal of International Journal of Neutrosophic Science, 2 no. 1 (2020): 38-46 (Doi   :  https://doi.org/10.54216/IJNS.020102)
Harvard Madeleine Al- Tahan. (2020). Some Results on Single Valued Neutrosophic (Weak) Polygroups. Journal of International Journal of Neutrosophic Science, 2 ( 1 ), 38-46 (Doi   :  https://doi.org/10.54216/IJNS.020102)
Vancouver Madeleine Al- Tahan. Some Results on Single Valued Neutrosophic (Weak) Polygroups. Journal of International Journal of Neutrosophic Science, (2020); 2 ( 1 ): 38-46 (Doi   :  https://doi.org/10.54216/IJNS.020102)
IEEE Madeleine Al- Tahan, Some Results on Single Valued Neutrosophic (Weak) Polygroups, Journal of International Journal of Neutrosophic Science, Vol. 2 , No. 1 , (2020) : 38-46 (Doi   :  https://doi.org/10.54216/IJNS.020102)