Volume 10 • Issue 2 • PP: 73-83 • 2020
A Note on Single Valued Neutrosophic Sets in Ordered Groupoids
View PDF 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
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
Choose your preferred format