591 424
Full Length Article
International Journal of Neutrosophic Science
Volume 10 , Issue 2, PP: 73-83 , 2020 | Cite this article as | XML | Html |PDF


A Note on Single Valued Neutrosophic Sets in Ordered Groupoids

Authors Names :   M. Al-Tahan   1     B. Davvaz   2     M. Parimala   3  

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

3  Affiliation :  Department of Mathematics, Bannari Amman Institute of Technology, India

    Email :  rishwanthpari@gmail.com

Doi   :   https://doi.org/10.54216/IJNS.0100201

Received: April 15, 2020 Accepted: August 10, 2020

Abstract :


The aim of this paper is to combine the notions of ordered algebraic structures and neutrosophy. In this regard, we define for the first time single valued neutrosophic sets in ordered groupoids. More precisely, we study single valued neutrosophic subgroupoids of ordered groupoids, single valued neutrosophic ideals of ordered groupoids, and single valued neutrosophic filters of ordered groupoids. Finally, we present some remarks on single valued neutrosophic subgroups (ideals) of ordered groups.


Keywords :



SVNS , ( , )-level set , ordered groupoid , single valued neutrosophic subgroupoid , single valued neutrosophic ideal , single valued neutrosophic filter.



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., “Neutrosophic N–Ideals (N-Subalgebras) of Subtraction Algebra”, International Journal of Neutrosophic Science (IJNS), Vol 3, No. 1, pp. 44-53, 2020.


[3]   Al-Tahan, M. and Davvaz, B., “On Single Valued Neutrosophic Sets and Neutrosophic N-Structures: Applications on Algebraic Structures (Hyperstructures)”, International Journal of Neutrosophic Science (IJNS), Vol 3, No. 2, pp. 108-117, 2020.Atanassov, K.T, “Intuitionistic Fuzzy Sets”, Fuzzy Sets and Systems, Vol 20, No. 1, pp. 87-96, 1986.


[4]   Clifford, A.H and Preston, G.B, “The Algebraic Theory of Semigroups”, Vol 1, Amer. Math. Soc., Math. Surveys 7, Providence, Rhode Island, 1977.


[5]   Fuchs, L., “Partially Ordered Algebraic Systems”, Int. Ser. of Monographs on Pure and Appl. Math. 28, Pergamon Press, Oxford, 1963.


[6]   Kehayopulu, N. and Tsingelis, M., “Fuzzy sets in Ordered Groupoids”, Semigroup Forum, Vol 65, pp.128-132, 2002.


[7]   Khan, M., Anis, S., Smarandache, and 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]   Rezaei, A. and Smarandache. F., “On Neutro-BE-algebras and Anti-BE-algebras”, International Journal of Neutrosophic Science (IJNS), Vol 4, No. 1, pp. 8-15, 2020.


[9]   Smarandache. F., “Neutrosophy: Neutrosophic Probability, Set and logic”, Ann Arbor, Michigan, USA, Vol 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]    Smarandache. F., “NeutroAlgebra is a Generalization of Partial Algebra”, International Journal of Neutrosophic Science (IJNS), Vol 2, No. 1, pp. 8-17, 2020.


[12]    Ulucay and V., Sahin, M., “Neutrosophic Multigroups and Applications”, Mathematics, Vol 7, 95, 2019.


[13]    Wang, H., Smarandache, F., Zhang, Y. and Sunderraman, R., “Single Valued Neutrosophic Sets”, Multispace and Multi-structure, Vol 4, pp. 410-413, 2010.


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





Cite this Article as :
M. Al-Tahan , B. Davvaz , M. Parimala, A Note on Single Valued Neutrosophic Sets in Ordered Groupoids, International Journal of Neutrosophic Science, Vol. 10 , No. 2 , (2020) : 73-83 (Doi   :  https://doi.org/10.54216/IJNS.0100201)