Volume 4 • Issue 2 • PP: 93-103 • 2020
A STUDY OF NEUTROSOPHIC CUBIC MN SUBALGEBRA
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© 2020 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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In this paper, we present the new kind of MN-subalgebra for neutrosophic cubic set which is called neutrosophic cubic MN-subalgebra where M represents the initial of author’s first name Mohsin and N represents the initial of second author’s first name Neha. We investigate this neutrosophic cubic MN-subalgebra on BF-algebra through some significant properties of BF-algebra. We also use R-intersection, p-intersection, p-union upper bound, lower bound and some important characteristics to study the behaviour of neutrosophic cubic MN-subalgebra [NCMNSU] on BF-algebra.
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References
[1] S. S. Ahn, K. Bang, “On fuzzy subalgebras in B-algebra”, Communications of the Korean Mathematical Society 18, pp. 429-437, 2003.
[2] R. Biswas, “Rosenfeld’s fuzzy subgroup with interval valued membership function”, Fuzzy Sets and Systems, 63, pp. 87-90, 1994.
[3] Y. B. Jun, C. S. Kim, K. O Yang, “Cubic sets”, Annuals of Fuzzy Mathematics and Informatics, 4, pp. 83-98, 2012.
[4] Y. B. Jun, S. T. Jung, M. S. Kim, “Cubic subgroup”, Annals of Fuzzy Mathematics and Infirmatics, 2, pp. 9-15, 2011.
[5] Y. B. Jun, F. Smarandache, C. S. Kim, “Neutrosophic cubic sets”, New Math. and Natural Comput., 8, 41, 2015.
[6] C. B. Kim, H. S. Kim, “On BG-algebra”, Demonstration Mathematica, 41, pp. 497-505, 2008.
[7] W. Andrzej, “On BF-algebras”, Mathematica Slovaca, 57, 2007.
[8] J. Neggers, H. S. Kim, “A fundamental theorem of B-homomorphism for B-algebras”, International Mathematical Journal, 2, pp. 215-219, 2002.
[9] S. S. Ahn, J. M. Ko, “Structure of BF-algebras”, Applied Mathematical Sciences, pp. 6369–6374, 2015.
[10] A. B. Saeid, “Interval-valued fuzzy B-algebras”, Iranian Journal of Fuzzy System, 3, pp. 63-73, 2006.
[11] F. Smarandache, “Neutrosophic set a generalization of the intuitionistic fuzzy set”, International Journal of Pure and Applied Mathematics. 24, 3, pp. 287-297, 2005.
[12] F. Smarandache, “A unifying field in logics, Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability”, American Reserch Press, Rehoboth, NM, 1999.
[13] T. Senapati, M. Bhowmik, M. Pal, “Fuzzy dot subalgebras and fuzzy dot ideals of B-algebra”, Journal of Uncertain System, 8, pp. 22-30, 2014.
[14] T. Senapati, M. Bhowmik, M. Pal, “Interval-valued intuitionistic fuzzy BG-subalgebras”, The Journal of Fuzzy Mathematics, 20, pp. 707-720, 2012.
[15] M. Khalid, R. Iqbal, S. Broumi, “Neutrosophic soft cubic subalgebras of G-algebras”, Neutrosophic Sets and Systems, 28, pp. 259-272, 2019.
[16] M. Khalid, B. Y. Jun, M. M. Takallo, N. A. Khalid, “Magnification of MBJ-Neutrosophic translation on G-Algebra”, International Journal of Neutrosophic Science, 2, 1, pp. 27–37, 2020.
[17] M. Khalid, A. N. Khalid, R. Iqbal, “MBJ-neutrosophic T-ideal on B-algebra”, International Journal of Neutrosophic Science, 1, 1, pp. 24-33, 2020.
[18] M. Khalid, A. N. Khalid, H. Khalid, S. Broumi, “Multiplicative interpretation of neutrosophic cubic set on B-Algebra”, International Journal of Neutrosophic Science, 1, 1, pp. 58-67, 2020.
[19] A. Walendziak, “Some axiomation of B-algebras”, Mathematics Slovaca, 56, pp. 301-306, 2006.
[20] L.A Zadeh, “Fuzzy sets”, Information and control, 8, pp. 338-353, 1965.
[21] L.A Zadeh, “The concept of a linguistic variable and its application to approximate reasoning”, Information science, 8, pp. 199-249, 1975.
[22] T. Senapati, C. H. Kim, M. Bhowmik, M. Pal, “Cubic subalgebras and cubic closed ideals of B-algebras”, Fuzzy Information and Engineering, 7, pp. 129-149, 2015.
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