426 217
Full Length Article
Volume 1 , Issue 2, PP: 64-73 , 2020

Title

Multiplicative Interpretation of Neutrosophic Cubic Set on B-Algebra

Authors Names :   Mohsin Khalid   1 *     Neha Andaleeb Khalid   2     Hasan Khalid   3     Said Broumi   4  

1  Affiliation :  Dept. of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

    Email :  mk4605107@gmail.com


2  Affiliation :  Dept. of Mathematics, Lahore Collage For Women University, Lahore, Pakistan

    Email :  nehakhalid97@gmail.com


3  Affiliation :  Dep.t of Mathematics,National College of Business Administration Economics, Lahore, 54000, Pakistan

    Email :  hasaikhan31@gmail.com


4  Affiliation :   Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco

    Email :  s.broumi@flbenmsik.ma



Doi   :  10.5281/zenodo.3679517


Abstract :

The purpose of this paper is to interpret the multiplication of neutrosophic cubic set. Here we define the notation of ɤ-multiplication of neutrosophic cubic set and study it with the help of neutrosophic cubic M-subalgebra, neutrosophic cubic normal ideal and neutrosophic cubic closed normal ideal. We also study ɤ-multiplication under homomorphism and cartesian product through significant characteristics.

Keywords :

B-algebra , Neutrosophic cubic set , ɤ-Multiplication , Cartesian product , Homomorphism

References :

[1] Zadeh, L. A. (1965). Fuzzy sets, Information and control, 8, 338-353.[2] Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning, Information science, 8, 199-249.

[3] Jun, Y. B. Kim, C. S. and Yang, K. O. (2012). Cubic sets, Annuals of Fuzzy Mathematics and Informatics, 4, 83-98.

[4] Senapati, T. Kim, C. H. Bhowmik, M., and Pal, M. (2015). Cubic subalgebras and cubic closed ideals of B-algebras, Fuzzy Information and Engineering, 7, 209-220.

[5] Imai, Y. and Iseki, K. (1966). On Axiom systems of Propositional calculi XIV, Proc. Japan Academy, 42, 19-22.[6] Iseki, K. (1966). An algebra related with a propositional calculus, Proc. Japan Academy, 42, 26-29. 

[7] Jun, Y. B. Kim, C. S. and Kang, M. S. (2010). Cubic subalgebras and ideals of BCK = BCI-algebra, Far East Journal of Mathematical Sciences, 44, 239-250. 

[8] Jun, Y. B. Kim, C. S. and Kang, J. G. (2011). Cubic q-Ideal of BCI-algebras, Annals of Fuzzy Mathematics and Informatics, 1, 25-34. 

[9] Khalid, M. Khalid, H. and Khalid, N. A., Neutrosophic cubic normal ideal and neutrosophic cubic closed normal ideal of PS-algebra.(submitted)

[10] Senapati, T. Bhowmik, M. and Pal, M. (2011). Fuzzy closed ideals of B-algebras, International Journal of Computer Science, Engineering and Tech- nology, 1, 669-673.[11] Senapati, T. Bhowmik, M. and Pal, M. (2013). Fuzzy closed ideals of B-alg-ebras, with interval-valued membership function, International Journal of Fuzzy Mathematical Archive, 1, 79-91.[12] Smarandache, F. (2005). Neutrosophic set a generalization of the intuitionistic fuzzy set, International Journal of Pure and Applied Mathematics, 24 (3), 287-297.

[13] Smarandache, F. (1999). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set and Neutrosophic Probability, (American Heserch Press, Rehoboth, NM).[14] Jun, Y. B. Smarandache, F. and Kim, C. S. (2015). Neutrosophic cubic sets, New Mathematics and Natural Computation, 8-41.

[15] Gulistan, M. Khan, M, Jun, Y. B. Smarandache, F. and Yaqoob, N. (2015). Neutrosophic cubic ideals in semigroups, 

[16] Khalid, M. Khalid, N. A. and Khalid, H. Neutrosophic soft cubic M Subalgebras of B-algebras. (submitted)

[17] Jun, Y. B. Smarandache, F. and Kim, C. S. (2016). R-union and R-intersection of neutrosophic cubic sets, IEEE International Conference on Fuzzy Systems (FUZZ).[18] Priya, T. and Ramachandran, T.( 2014). A note on fuzzy PS-ideals in PS-algebra and its level subsets, International Journal of Advanced Mathematical Sciences, Vol. 2, No. 2, 101-106.

[19] Khalid, M. Iqbal, R., Zafar, S. and Khalid, H. (2019). Intuitionistic Fuzzy Translation and Multiplication of G-algebra, The Journal of Fuzzy Mathematics, Vol. 27, No. 3, 543-559.

[20] Biwas, R. (1994). Rosenfeld’s fuzzy subgroup with interval valued membership function, Fuzzy Sets and Systems, 63, 87-90.

[21] Neggers, J. and Kim, H. S. (2002). A fundamental theorem of B-homomo rphism for B-algebras, Int. Math. J., 2 (3), 207-214.

[22] Khalid, M. Iqbal, R. and B, Said. (2019). Neutrosophic soft cubic Subalgebras of G-algebras. 28. 259-272. 10.5281/zenodo.3382552.

[23] Neggers, J. and Kim, H. S. (2002). On B-algebras, Matematichki Vesnik 54, 21-29.

[24] Khalid, M. Khalid, N. A. and Broumi, S. T-Neutrosophic Cubic Set on BF-Algebra, Neutrosophic Sets and Systems, vol. 31, (2020),  pp. 127-147. DOI: 10.5281/zenodo.3639470.