379 232
Full Length Article
Volume 7 , Issue 2, PP: 97-109 , 2020

Title

On Refined Neutrosophic Vector Spaces I

Authors Names :   M.A. Ibrahim   1 *     A.A.A. Agboola   2     B.S. Badmus   3     S.A. Akinleye   4  

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

    Email :  muritalaibrahim40@gmail.com


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

    Email :  agboolaaaa@funaab.edu.ng


3  Affiliation :  Department of Physics, Federal University of Agriculture, Abeokuta, Nigeria

    Email :  badmusbs@yahoo.com


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

    Email :  sa akinleye@yahoo.com



Doi   :  10.5281/zenodo.3884059


Abstract :

The objective of this paper is to present the concept of a refined neutrosophic vector space. Weak(strong) refined neutrosophic vector spaces and subspaces, and, strong refined neutrosophic quotient vector spaces are studied. Several interesting results and examples are presented. It is shown that every weak (strong) refined neutrosophic vector space is a vector space and it is equally shown that every strong refined neutrosophic vector space is a weak refined neutrosophic vector space.

Keywords :

Neutrosophy , neutrosophic vector space , neutrosophic vector subspace , refined neutrosophic vector space , refined neutrosophic vector subspace , refined neutrosophic quotient vector space.

References :

[1] Adeleke, E.O, Agboola, A.A.A and Smarandache, F. Refined Neutrosophic Rings I, International Journalof Neutrosophic Science (IJNS), Vol. 2(2), pp. 77-81, 2020.[2] 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.[3] Agboola, A.A.A., Ibrahim, A.M. and Adeleke, E.O, Elementary Examination of NeutroAlgebras andAntiAlgebras Viz-a-Viz the Classical Number Systems, Vol. 4, pp. 16-19, 2020.[4] Agboola, A.A.A. On Refined Neutrosophic Algebraic Structures, Neutrosophic Sets and Systems, Vol.10, pp 99-101, 2015.[5] 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.[6] 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.[7] 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.[8] Agboola, A.A.A. and Akinleye, S.A., Neutrosophic Vector Spaces, Neutrosophic Sets and Systems Vol.4,pp. 9-18. 2014.[9] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, pp. 87-96, 1986.[10] 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.[11] Bera, T. and Mahapatra, N.K., On neutrosophic normal soft groups, International Journal of Applied andComputational Mathematics., Vol. 3, pp 3047-3066, 2017. DOI 10.1007/s40819-016-0284-2.[12] Bera, T. and Mahapatra, N.K., On neutrosophic soft rings, OPSEARCH, Vol. 54, pp. 143-167, 2017. DOI10.1007/ s12597-016-0273-6.[13] Bera, T and Mahapatra, N. K., On neutrosophic soft linear spaces, Fuzzy Information and Engineering,Vol. 9, pp 299-324, 2017.[14] Bera, T and Mahapatra, N. K., On neutrosophic soft field, IJMTT, Vol. 56(7), pp. 472-494, 2018.[15] Hashmi, M.R., Riaz, M. and Smarandache,F., m-polar Neutrosophic Topology with Applications toMulti-Criteria Decision-Making in Medical Diagnosis and Clustering Analysis, International Journal ofFuzzy Systems, Vol.22(1), pp. 273-292, 2020. https://doi.org/10.1007/s40815-019-00763-2.[16] Ibrahim, M.A., Agboola, A.A.A, Adeleke, E.O, Akinleye, S.A., Introduction to Neutrosophic SubtractionAlgebra and Neutrosophic Subtraction Semigroup,International Journal of Neutrosophic Science (IJNS),Vol. 2(2), pp. 47-62, 2020.[17] Riaz, M. and Hashmi,M.R., Linear Diophantine Fuzzy Set and its Applications towards Multi-AttributeDecision Making Problems, Journal of Intelligent and Fuzzy Systems, Vol.37(4),pp. 5417-5439 2019.[18] Riaz, M., Nawa, I. and Sohail, M., Novel Concepts of Soft Multi Rough Sets with MCGDM for Selectionof Humanoid Robot, Punjab University Journal of Mathematics, Vol.52(2), pp.111-137, 2020

[19] Riaz,M. Smarandache,F., Firdous, A, and Fakhar,A., On Soft Rough Topology with Multi-AttributeGroup Decision Making, Mathematics Vol.7(1),pp,1-18, 2019. Doi:10.3390/math7010067[20] Smarandache, F., A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set,Neutrosophic Probability, American Research Press, Rehoboth, 2003.[21] Smarandache, F., n-Valued Refined Neutrosophic Logic and Its Applications in Physics, Progress inPhysics, Vol. 4, pp. 143-146, 2013.[22] Smarandache, F., (T,I,F)- Neutrosophic Structures, Neutrosophic Sets and Systems, Vol.8, pp.3-10, 2015.[23] Vasantha Kandasamy, W.B and Smarandache,F., Basic Neutrosophic Algebraic Structuresand Their Applications to Fuzzy and Neutrosophic Models, Hexis, Church Rock, (2004),http://fs.unm.edu/ScienceLibrary.htm[24] Vasantha Kandasamy, W.B. and Florentin Smarandache, Some Neutrosophic AlgebraicStructures and Neutrosophic N-Algebraic Structures, Hexis, Phoenix, Arizona, (2006),http://fs.unm.edu/ScienceLibrary.htm[25] Vasantha Kandasamy, W.B., Neutrosophic Rings, Hexis, Phoenix, Arizona,(2006)http://fs.unm.edu/ScienceLibrary.htm[26] Wadei Al-Omeri and Smarandache, F., New Neutrosophic Set via Neutrosophic Topological Spaces.Excerpt from Neutrosophic Operation Research Vol I, Pons Editions: Brussels, Belgium, pp. 189-209,2017.[27] Wadei Al-Omeri, Neutrosophic crisp Sets Via Neutrosophic crisp Topological Spaces, Neutrosophic Setand Systems Vol 13, pp 96- 104, 2016.[28] Wadei Al-Omeri and Saeid Jafari, On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces, Mathematics, Vol 7, pp 1- 12, 2019. Doi: doi.org/10.3390/math/7010001.[29] Zadeh, L.A., Fuzzy Sets, Information and Control, Vol. 8, pp. 338-353, 1965.