1722 1320
Full Length Article
International Journal of Neutrosophic Science
Volume 8 , Issue 1, PP: 50-71 , 2020 | Cite this article as | XML | Html |PDF

Title

On Refined Neutrosophic Hypervector Spaces

  M.A. Ibrahim 1 * ,   A.A.A. Agboola 2 ,   B.S. Badmus 3 ,   S.A. Akinleye 4

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)

Full Text Download


Doi   :   https://doi.org/10.54216/IJNS.080105


Abstract :

This paper presents the refinement of neutrosophic hypervector spaces and studies some of its basic properties. Some basic definitions and important results are presented. The paper also establishes the existence of a good linear transformation between a weak refined neutrosophic hypervector space V (I1; I2) and a weak neutrosophic hypervector space V (I).

Keywords :

Neutrosophy , neutrosophic hypervector space , neutrosophic subhypervector space , refined Neutrosophic hypervector space , refined neutrosophic subhypervector space , refined neutrosophic hypervector space homomorphism.

 

 

References :

[1] 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.

[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 and AntiAlgebras 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 10, pp 99-101, 2015.

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

[6] Agboola,A.A.A. and Akinleye, S.A., Neutrosophic Vector Spaces, Neutrosophic Sets and Systems 4, pp 9-18, 2014.

[7] Agboola, A.A.A. and Davvaz, B., Introduction to Neutrosophic Hypergroups, Romai J.,Vol. 9(2), pp. 1-10, 2013.

[8] Agboola, A.A.A and Davvaz, B., On Neutrosophic Canonical Hypergroups and Neutrosophic Hyperrings, Neutrosophic Sets and Systems. Vol. 2, pp.34-41, 2014.

[9] Asokkumar, A., Hyperlattice formed by the idempotents of a hyperring, Tamkang J. Math., Vol. 3(38), pp. 209-215, 2007.

[10] Asokkumar, A. and Veelrajan, M., Characterizations of regular hyperrings, Italian J. Pure and App. Math., Vol. 22, pp.115-124, 2007.

[11] Asokkumar, A. and Veelrajan, M., Hyperrings of matrices over a regular hyperring, Italian J. Pure and App. Math. Vol. 23, pp. 113-120, 2008.

[12] Ameri. R. and Dehghan, O.R., On Dimension of Hypervector Spaces, European Journal of Pure and Applied Mathematics, Vol. 1(2), pp. 32-50, 2008.

[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] Bonansinga, P., Quasicanonical hypergroups, (Italian), Atti Soc. Peloritana Sci. Fis. Mat. Natur., Vol. 27, pp. 9-17, 1981.

[20] Bonansinga, P.,Weakly quasicanonical hypergroups, (Italian), Atti Sem. Mat. Fis. Univ. Modena, Vol.30, pp. 286-298, 1981.

[21] Corsini, P., Prolegomena of Hypergroup Theory, Second edition, Aviani editor, (1993).

[22] Corsini, P., Finite canonical hypergroups with partial scalar identities, (Italian), Rend. Circ. Mat. Palermo (2), Vol.36, pp.205-219, 1987.

[23] Davvaz, B. and Leoreanu-Fotea, V., Hyperring Theory and Applications, International Academic Press,Palm Harber, USA, 2007.

[24] De Salvo, M., Hyperrings and hyperfields, Annales Scientifiques de l’Universite de Clermont-Ferrand II, Vol.22, pp. 89-107, 1984.

[25] Marty, F. Role de la notion dhypergroupe dans letude des groupes non abeliens, Comptes Renclus Acad. Sci. Paris Math, Vol. 201, pp 636-638, 1935.

[26] Krasner, M., A class of hyperrings and hyperfields, International Journal of Mathematics and Mathematical Science, Vol 6(2), pp. 307-312, 1983.

[27] Mittas, J., Hypergroupes canoniques, Math. Balkanica, Vol.2, pp. 165-179, 1972.

[28] Muthusamy Velrajan and Arjunan Asokkumar, Note on Isomophism Theorems of Hyperrings, Int. J. Math. Math. Sc., Hindawi Publishing Corporation, pp.1-12, 2010.

[29] Nakassis, A., Recent results in hyperring and hyperfield theory, Internat. J. Math.Math. Sci., Vol.11(2), pp. 209-220, 1988.

[30] Sanjay Roy and Samanta,T.K., A Note on Hypervector Spaces, Discussiones Mathematicae -General Algebra and Applications Vol. 31(1), pp. 75-99, 2011. 

[31] Scafati Tallini,M., Characterization of Remarkable Hypervector spaces, Proc. of 8th int. Congress on Algebraic Hyperstructures and Applications, Samotraki, Greece, Sept. 1-9-2002, Spanidis Press, Xanthi, Greece, ISBN 960-87499-5-6 , pp. 231-237, 2003.

[32] Serafimidis, K., Sur les hypergroups canoniques ordonne‘s et strictement ordonne‘s,(French) [Ordered and strictly ordered canonical hypergroups], Rend. Mat., Vol. 7(6), pp. 231-238. 1986.

[33] Serafimidis, K., Konstantinidou, M. and Mittas, J., Sur les hypergroups canoniques strictement re’ticule’s, (French) [On strictly lattice-ordered canonical hypergroups], Riv. Mat. Pura Appl., Vol. 2, pp 21-35, 1987.

[34] Spartalis, S., A class of hyperrings, Riv. Mat. Pura Appl., Vol. 4, pp.55-64, 1989.

[35] Smarandache, F., A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, Rehoboth, 2003.

[36] Smarandache, F., (T,I,F)- Neutrosophic Structures, Neutrosophic Sets and Systems, Vol. 8, pp. 3-10, 2015.

[37] Vasantha Kandasamy W.B and Smarandache,F., Basic Neutrosophic Algebraic Structures and Their Applications to Fuzzy and Neutrosophic Models, Hexis, Church Rock,(2004), http://fs.gallup.unm.edu/eBook-otherformats.htm

[38] Vasantha Kandasamy, W.B. and Florentin Smarandache, Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures, Hexis, Phoenix, Arizona, (2006), http://www.gallup.unm.edu/smarandache/eBooks-otherformats.htm.

[39] Vasantha Kandasamy, W.B., Neutrosophic Rings, Hexis, Phoenix, Arizona,(2006) http://www.gallup.unm.edu/ smarandache/eBooks-otherformats.htm. 

[40] 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.

[41] Wadei Al-Omeri, Neutrosophic crisp Sets Via Neutrosophic crisp Topological Spaces, Neutrosophic Set and Systems Vol 13, pp 96- 104, 2016.

[42] 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.

[43] Zadeh, L.A., Fuzzy Sets, Information and Control, Vol. 8, pp. 338-353, 1965.

 

Cite this Article as :
Style #
MLA M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. "On Refined Neutrosophic Hypervector Spaces." International Journal of Neutrosophic Science, Vol. 8, No. 1, 2020 ,PP. 50-71 (Doi   :  https://doi.org/10.54216/IJNS.080105)
APA M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. (2020). On Refined Neutrosophic Hypervector Spaces. Journal of International Journal of Neutrosophic Science, 8 ( 1 ), 50-71 (Doi   :  https://doi.org/10.54216/IJNS.080105)
Chicago M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. "On Refined Neutrosophic Hypervector Spaces." Journal of International Journal of Neutrosophic Science, 8 no. 1 (2020): 50-71 (Doi   :  https://doi.org/10.54216/IJNS.080105)
Harvard M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. (2020). On Refined Neutrosophic Hypervector Spaces. Journal of International Journal of Neutrosophic Science, 8 ( 1 ), 50-71 (Doi   :  https://doi.org/10.54216/IJNS.080105)
Vancouver M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye. On Refined Neutrosophic Hypervector Spaces. Journal of International Journal of Neutrosophic Science, (2020); 8 ( 1 ): 50-71 (Doi   :  https://doi.org/10.54216/IJNS.080105)
IEEE M.A. Ibrahim, A.A.A. Agboola, B.S. Badmus, S.A. Akinleye, On Refined Neutrosophic Hypervector Spaces, Journal of International Journal of Neutrosophic Science, Vol. 8 , No. 1 , (2020) : 50-71 (Doi   :  https://doi.org/10.54216/IJNS.080105)
↑