1
Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria
(muritalaibrahim40@gmail.com)
2
Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria
(agboolaaaa@funaab.edu.ng)
3
Department of Physics, Federal University of Agriculture, Abeokuta, Nigeria
(badmusbs@yahoo.com)
4
Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria
(sa akinleye@yahoo.com)
Abstract :
The concept of refined neutrosophic vector spaces was introduced by Ibrahim et al. in [20] and the present paper is the continuation of the work. In the present paper, further studies on neutrosophic vector spaces are presented. Specifically, linear dependence, independence, bases and dimensions of refined neutrosophic vector spaces are studied with several results and examples presented. Also, refined neutrosophic homomorphisms of refined neutrosophic vector spaces are studied and existence of linear maps between weak refined Neutrosophic vector spaces and weak neutrosophic vector spaces are established.
Keywords :
Neutrosophy , neutrosophic vector space , refined neutrosophic vector space , refined neutrosophic vector space homomorphism.
References :
[1] Abobala, M., On some Special Substructures of Neutrosophic Rings and their Properties, International Journal of Neutrosophic Science, Vol. 4 (2), pp. 72-81, 2020.
[2] Abobala, M., On some Special Substructures of Refined Neutrosophic Rings, International Journal of Neutrosophic Science, Vol. 5 (1), pp. 59-66, 2020.
[3] Abobala, M., Classical Homomorphisms between Refined Neutrosophic Rings and Neutrosophic Rings, International Journal of Neutrosophic Science, Vol. 5 (2), pp. 72-75, 2020.
[4] Adeleke, E.O, Agboola, A.A.A and Smarandache, F. Refined Neutrosophic Rings I, International Journal of Neutrosophic Science (IJNS), Vol. 2(2), pp. 77-81, 2020.
[5] Adeleke, E.O, Agboola, A.A.A and Smarandache, F. Refined Neutrosophic Rings II, International Journal of Neutrosophic Science (IJNS), Vol. 2(2), pp. 89-94, 2020.
[6] Agboola, A.A.A., On Refined Neutrosophic Quotient Groups, International Journal of Neutrosophic Science, vol. 5 (2), pp. 76-82, 2020. DOI:10.5281/zenodo.3828609.
[7] Agboola, A.A.A., Ibrahim, A.M. and Adeleke, E.O, Elementary Examination of NeutroAlgebras and AntiAlgebras Viz-a-Viz the Classical Number Systems, Vol. 4, pp. 16-19, 2020.
[8] Agboola, A.A.A. On Refined Neutrosophic Algebraic Structures, Neutrosophic Sets and Systems, Vol. 10, pp 99-101, 2015.
[9] Agboola, A.A.A., Akinola, A.D. and Oyebola, O.Y., Neutrosophic Rings I, Int. J. of Math. Comb. Vol 4, pp. 1-14, 2011.
[10] Agboola, A.A.A., Adeleke, E.O. and Akinleye, S.A., Neutrosophic Rings II, Int. J. of Math. Comb. Vol. 2, pp 1-8, 2012.
[11] Agboola, A.A.A. Akwu, A.O., and Oyebo, Y.T., Neutrosophic Groups and Neutrosopic Subgroups, Int. J. of Math. Comb. Vol. 3, pp. 1-9, 2012.
[12] Agboola, A.A.A. and Akinleye, S.A., Neutrosophic Vector Spaces, Neutrosophic Sets and Systems Vol. 4, pp. 9-18. 2014.
[13] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, pp. 87-96, 1986.
[14] Bera, T. and Mahapatra,N.K., Introduction to neutrosophic soft groups, Neutrosophic Sets and Systems,Vol. 13, pp, 118-127, 2016, doi.org/10.5281/zenodo.570845.
[15] Bera, T. and Mahapatra, N.K., On neutrosophic normal soft groups, International Journal of Applied and Computational Mathematics., Vol. 3, pp 3047-3066, 2017. DOI 10.1007/s40819-016-0284-2.
[16] Bera, T. and Mahapatra, N.K., On neutrosophic soft rings, OPSEARCH, Vol. 54, pp. 143-167, 2017. DOI 10.1007/ s12597-016-0273-6.
[17] Bera, T and Mahapatra, N. K., On neutrosophic soft linear spaces, Fuzzy Information and Engineering, Vol. 9, pp 299-324, 2017.
[18] Bera, T and Mahapatra, N. K., On neutrosophic soft field, IJMTT, Vol. 56(7), pp. 472-494, 2018.
[19] Deli, I., Broumi, S. and Smarandache, F., On neutrosophic refined sets and their applications in medical diagnosis, Journal of New Theory, Vol. 6, pp. 88-98, 2015.
[20] Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S, Akinleye, S.A., On Refined Neutrosophic Vector Spaces I, (submitted for publication) in International Journal of Neutrosophic Science.
[21] Ibrahim, M.A., Agboola, A.A.A, Adeleke, E.O, Akinleye, S.A., Introduction to Neutrosophic Subtraction Algebra and Neutrosophic Subtraction Semigroup, International Journal of Neutrosophic Science (IJNS), Vol. 2(2), pp. 47-62, 2020.
[22] Ibrahim, M.A., Agboola, A.A.A, Adeleke, E.O, Akinleye, S.A., On Neutrosophic Quadruple Hypervector Spaces, International Journal of Neutrosophic Science (IJNS), Vol. 4(1), pp. 20-35, 2020.
[1] Abobala, M., On some Special Substructures of Neutrosophic Rings and their Properties, International Journal of Neutrosophic Science, Vol. 4 (2), pp. 72-81, 2020.
[2] Abobala, M., On some Special Substructures of Refined Neutrosophic Rings, International Journal of Neutrosophic Science, Vol. 5 (1), pp. 59-66, 2020.
[3] Abobala, M., Classical Homomorphisms between Refined Neutrosophic Rings and Neutrosophic Rings, International Journal of Neutrosophic Science, Vol. 5 (2), pp. 72-75, 2020.
[4] Adeleke, E.O, Agboola, A.A.A and Smarandache, F. Refined Neutrosophic Rings I, International Journal of Neutrosophic Science (IJNS), Vol. 2(2), pp. 77-81, 2020.
[5] Adeleke, E.O, Agboola, A.A.A and Smarandache, F. Refined Neutrosophic Rings II, International Journal of Neutrosophic Science (IJNS), Vol. 2(2), pp. 89-94, 2020.
[6] Agboola, A.A.A., On Refined Neutrosophic Quotient Groups, International Journal of Neutrosophic Science, vol. 5 (2), pp. 76-82, 2020. DOI:10.5281/zenodo.3828609.
[7] Agboola, A.A.A., Ibrahim, A.M. and Adeleke, E.O, Elementary Examination of NeutroAlgebras and AntiAlgebras Viz-a-Viz the Classical Number Systems, Vol. 4, pp. 16-19, 2020.
[8] Agboola, A.A.A. On Refined Neutrosophic Algebraic Structures, Neutrosophic Sets and Systems, Vol. 10, pp 99-101, 2015.
[9] Agboola, A.A.A., Akinola, A.D. and Oyebola, O.Y., Neutrosophic Rings I, Int. J. of Math. Comb. Vol 4, pp. 1-14, 2011.
[10] Agboola, A.A.A., Adeleke, E.O. and Akinleye, S.A., Neutrosophic Rings II, Int. J. of Math. Comb. Vol. 2, pp 1-8, 2012.
[11] Agboola, A.A.A. Akwu, A.O., and Oyebo, Y.T., Neutrosophic Groups and Neutrosopic Subgroups, Int. J. of Math. Comb. Vol. 3, pp. 1-9, 2012.
[12] Agboola, A.A.A. and Akinleye, S.A., Neutrosophic Vector Spaces, Neutrosophic Sets and Systems Vol. 4, pp. 9-18. 2014.
[13] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, pp. 87-96, 1986.
[14] Bera, T. and Mahapatra,N.K., Introduction to neutrosophic soft groups, Neutrosophic Sets and Systems, Vol. 13, pp, 118-127, 2016, doi.org/10.5281/zenodo.570845.
[15] Bera, T. and Mahapatra, N.K., On neutrosophic normal soft groups, International Journal of Applied and Computational Mathematics., Vol. 3, pp 3047-3066, 2017. DOI 10.1007/s40819-016-0284-2.
[16] Bera, T. and Mahapatra, N.K., On neutrosophic soft rings, OPSEARCH, Vol. 54, pp. 143-167, 2017. DOI 10.1007/ s12597-016-0273-6.
[17] Bera, T and Mahapatra, N. K., On neutrosophic soft linear spaces, Fuzzy Information and Engineering, Vol. 9, pp 299-324, 2017.
[18] Bera, T and Mahapatra, N. K., On neutrosophic soft field, IJMTT, Vol. 56(7), pp. 472-494, 2018.
[19] Deli, I., Broumi, S. and Smarandache, F., On neutrosophic refined sets and their applications in medical diagnosis, Journal of New Theory, Vol. 6, pp. 88-98, 2015.
[20] Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S, Akinleye, S.A., On Refined Neutrosophic Vector Spaces I, (submitted for publication) in International Journal of Neutrosophic Science.
[21] Ibrahim, M.A., Agboola, A.A.A, Adeleke, E.O, Akinleye, S.A., Introduction to Neutrosophic Subtraction Algebra and Neutrosophic Subtraction Semigroup, International Journal of Neutrosophic Science (IJNS), Vol. 2(2), pp. 47-62, 2020.
[22] Ibrahim, M.A., Agboola, A.A.A, Adeleke, E.O, Akinleye, S.A., On Neutrosophic Quadruple Hypervector Spaces, International Journal of Neutrosophic Science (IJNS), Vol. 4(1), pp. 20-35, 2020.
| Style | # |
|---|---|
| MLA | M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. "On Refined Neutrosophic Vector Spaces II." International Journal of Neutrosophic Science, Vol. 9, No. 1, 2020 ,PP. 22-36 (Doi : https://doi.org/10.54216/IJNS.090102) |
| APA | M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. (2020). On Refined Neutrosophic Vector Spaces II. Journal of International Journal of Neutrosophic Science, 9 ( 1 ), 22-36 (Doi : https://doi.org/10.54216/IJNS.090102) |
| Chicago | M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. "On Refined Neutrosophic Vector Spaces II." Journal of International Journal of Neutrosophic Science, 9 no. 1 (2020): 22-36 (Doi : https://doi.org/10.54216/IJNS.090102) |
| Harvard | M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. (2020). On Refined Neutrosophic Vector Spaces II. Journal of International Journal of Neutrosophic Science, 9 ( 1 ), 22-36 (Doi : https://doi.org/10.54216/IJNS.090102) |
| Vancouver | M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. On Refined Neutrosophic Vector Spaces II. Journal of International Journal of Neutrosophic Science, (2020); 9 ( 1 ): 22-36 (Doi : https://doi.org/10.54216/IJNS.090102) |
| IEEE | M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye, On Refined Neutrosophic Vector Spaces II, Journal of International Journal of Neutrosophic Science, Vol. 9 , No. 1 , (2020) : 22-36 (Doi : https://doi.org/10.54216/IJNS.090102) |