399 214
Full Length Article
Volume 4 , Issue 1, PP: 20-35 , 2020


On Neutrosophic Quadruple Hypervector Spaces

Authors Names :   M.A. Ibrahim, A.A.A. Agboola , E.O. Adeleke, S.A. Akinleye   1 *  

1  Affiliation :  Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria

    Email :  muritalaibrahim40@gmail.com, agboolaaaa@funaab.edu.ng, yemi376@yahoo.com, sa akinleye@yahoo.com

Doi   :  10.5281/zenodo.3752906

Abstract :

The objective of this paper is to study Neutrosophic Quadruple Hypervector Spaces and present some of their basic definitions and properties. This paper generalizes the concept of Neutrosophic Hypervector spaces by presenting their Neutrosophic Quadruple forms. Some notions such as Neutrosphic hypersubspaces, linear combination, linearly dependence and linearly independence are generalized. Some interesting results and examples to illustrate the new concepts introduced are presented.

Keywords :

Neutrosophic Quadruple (NQ) , Neutrosophic Quadruple set , NQ Hypervector spaces , Super strong NQ Hypervector spaces , strong NQ Hypervector spaces , Weak NQ Hypervector spaces , NQ field , Neutrosophic field , NQ Hypersubspaces , NQ bases.

References :

[1]     Agboola, A.A.A. and Akinleye, S.A., Neutrosophic Hypervector Spaces, ROMAI Journal, vol. 11(1),pp. 1-16, 2015.

[2]     Agboola, A.A.A. and Akinleye, S.A., Neutrosophic Vector Spaces, Neutrosophic Set and Systems, vol. 4, pp. 9-18, 2012.

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

[4]     Akinleye, S.A., Smarandache, F., Agboola, A.A.A. On neutrosophic quadruple algebraic structures.Neu- trosophic Sets System. vol. 12, pp. 122-126, 2016.

[5]     Ameri, R. Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems.vol. 2, pp. 37-42, 2005.

[6]     Ameri, R. Fuzzy (co-) norm hypervector spaces, Proceeding of the 8th International Congress in Alge- braic Hyperstructures and Applications,Samotraki, Greece, pp.71-79, 2002.

[7]     Ameri, R., Dehghan,O.R., On dimension of hypervector spaces, European Journal of Pure and Applied Mathematics, Vol. 1(2),pp. 32-50, 2008.

[8]     Ameri, R., Dehghan,O.R., Fuzzy hypervector spaces, Advances in Fuzzy Systems, Article ID 295649, 2008.

[9]     Broumi, S., Bakali, A., Talea, M., Smarandache, F.,Singh, P. K., Uluc¸ay, V., and Khan, M., Bipolarcom- plex neutrosophic sets and its application in decision making problem. In Fuzzy Multi-criteriaDecision- Making Using Neutrosophic Sets. Springer, Cham. pp. 677-710, 2019.

[10]     Ibrahim M.A, Agboola,A.A.A, Adeleke, E.O. and Akinleye, S.A, Introduction to NeutrosophicSubtrac- tion Algebra and Neutrosophic Subtraction Semigroup, International Journal of Neutrosophic Science, vol.2, pp. 47-62, 2020.

[11]     Jun, Y.B., Song, S.Z., Kim, S.J. Neutrosophic Quadruple BCI-Positive Implicative Ideals. Mathematics vol. 7, pp. 385, 2019.

[12]     Jun,Y., Song,S.Z., Smarandache,F., Bordbar, H., Neutrosophic quadruple BCK/BCI-algebras. Axioms, vol.7, pp. 41, 2018.

[13]     Krasner,M. A class of hyperrings and hyperfields, Intern. J.Math. and Math. Sci., Vol 6, no.2, pp. 307- 312, 1983.

[14]     Li, Q., Ma, Y., Zhang, X., Zhang, J. Neutrosophic Extended Triplet Group Based on Neutrosophic Quadruple Numbers. Symmetry, vol. 11, pp. 696. 2019.