TRANSLATIONS AND MULTILICATIONS OF JUN’S CUBIC SETS IN  CUBIC SUBALGEBRAS AND CUBIC FILTERS OF CI-ALGEBRAS

S R Barbhuiya; A K Dutta

doi:10.48165/

Authors

S R Barbhuiya Department of Mathematics, Srikishan Sarda College, Hailakandi, Assam 788151, India.
A K Dutta Department of Mathematics, D.H.S.K. College, Dibrugarh, Assam 786001, India.

DOI:

https://doi.org/10.48165/

Keywords:

CI-algebra, Interval-valued fuzzy set, Cubic set, Cubic subalgebra, Cubic filters, Translation, Multiplication, Extension

Abstract

In this paper, we introduce the concept of translation and multiplication of cubic subalgebras and cubic filters of CI-algebras and investigate some of their basic properties. The notion of cubic extensions of cubic subalgebras and cubic filters is also introduced and several related properties are investigated.

References

. Ahn, S.S., Kim, Y.H. and Ko, J. Mi. (2014). Cubic subalgebras and filters of CI-algebras, Honam Mathematical Journal, 36(1), 43-54.

. Akram, M., Yaqoob, N. and Kavikumar J.(2014). Interval valued )~,~(θ δ -fuzzy KU-ideals of KU-algebras, Int. J. Pure Appl. Math., 92(3), 335-349.

. Atanassov, K.T. and Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31(1), 343-349.

. Atanassov, K.T. (1994). Operators over interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64, 159-174.

. Barbhuiya, S.R. (2016). Fuzzy translations and Fuzzy multiplications of Interval-Valued Doubt Fuzzy Ideals of BF-Algebras, Journal of Information and Optimization Sciences, 37(1), 23-36. [6]. Borzooei, R.A., Saeid, A.B., Rezaei, A. and Ameri, R. (2014). Anti fuzzy filters of CI-algebras, Afr. Mat., 25(4), 1197-1210.

. Dutta, T.K., Kar, S. and Purkait S. (2015). Interval-valued fuzzy prime and semiprime ideals of a hyper Semiring, Annals of Fuzzy Mathematics and Informatics, 9(2), 261-278.

. Hu, Q.P. and Li, X. (1983). On BCH-algebras, Math. Seminar Notes, 11(2) part 2, 313-320. [9]. Imai, Y. and Iseki, K. (1966). On Axiom systems of Propositional Calculi XIV, Proc. Japan Academy, 42, 19-22.

. Iseki, K. (1966). An algebra related with a Propositional Calculus (1966), Proc. Japan Academy, 42, 26-29.

. Iseki, K. (1975). On some ideals in BCK-algebras, Math.Seminar Notes, 3, 65-70. [12]. Jun, Y.B. (2000). Interval-valued fuzzy subalgebras/ideals in BCK-algebras, Scientiae Mathematicae, 3(3), 435-444.

. Jun, Y.B. (2011).Translation of fuzzy ideals in BCK/BCI-Algebras, Hacettepe Journal of Mathematics and Statistics, 40(3), 349-358.

. Jun, Y.B., Kim, C.S. and Yang, K.O. (2012). Cubic sets, Ann. Fuzzy Math. Inform., 4(1), 83-98. [15]. Jun, Y.B., Kim, C.S. and Kang, M.S.(2010). Cubic subalgebras and ideals of BCK/BCI-algebras, Far East J. Math Sci., 44, 239-250.

. Jun, Y.B., Lee, K.J. and Kang, M.S. (2011). Cubic structures applied to ideals of BCI-algebras, Comput Math. Appl., 62(9), 3334-3342.

. Jun, Y.B., Kim, C.S. and Kang, J.G. (2011). Cubic q-ideals of BCI-algebras, Ann. Fuzzy Math Inform. 1(1), 25-34.

. Jun, Y.B., Jung, S.T. and Kim, M.S. (2011). Cubic subgroups, Ann. Fuzzy Math Inform., 2(1), 9-15. [19]. Klaua, D. (1965). Ãœber einen Ansatz zur mehrwertigen Mengenlehre, Monatsberichte der Deutschen Akademie derWissenschaften zu Berlin, 7, 859-867.

. Klaua, D. (1966). Ãœber einen zweiten Ansatz zur mehrwertigen Mengenlehre, Monatsberichte der Deutschen Akademie der Wissenschaften zu Berlin, 8, 161-177.

. Kim, K.H. (2011). A Note on CI- algebras, International Mathematical Forum, 6(1), 1-5. [22]. Kim, K.H. and Yon, Y. H. (2007). Dual BCK-algebra and MV –algebra, Sci. Math. Jpn., 66, 247-253. [23]. Lee, K.J., Jun, Y.B. and Doh, M.I. (2009). Fuzzy translation and Fuzzy multiplications of BCK/BCI-algebras, Commun. Korean Math.Soc. , 24(3), 353-360.

. Majumder, S.K. and Sardar, S.K. (2008). Fuzzy Magnified translation on groups, Journal of Mathematics North Bengal University, 1(2), 117-124.

. Meng, B.L. (2009). CI-algebras, Sci. Math. Japo. Online. ( e-2009) , 695-701. [26]. Mostafa, S.M., Abdel Naby, M.A. and Elgendy, O.R. (2011). Fuzzy ideals in CI- algebras, Journal of American Science, 7(8), 485-488.

. Mostafa, S.M., Abd-Elnaby, M.A. and Elgendy, O.R. (2011). Interval-valued fuzzy KU-ideals in KU-algebras. Int.Math. Forum, 6(64), 3151-3159.

. Neggers, J. and Kim,H.S. (2002). On B-algebras, Math.Vensik. , 54, 21-29.

. Neggers, J. and Kim,H.S. (1999). On d-algebras, Math Slovaca, 40(1), 19-26.

. Rosenfeld, A. (1971). Fuzzy subgroups, J. Math. Anal. Appl., 35, 512-517.

. Saeid, A.B. (2006). Interval-valued fuzzy BG-algebras, Kangweon-Kyungki Math.Jour., 14(2), 203-215. [32]. Xi, O.G. (1991). Fuzzy BCK algebras, Math. Japonica, 36, 935-942.

. Yaqoob, N., Mostafa, S.M. and Ansari, M.A. (2013). On cubic KU-ideals of KU-algebras, ISRN Algebra, Article ID 935905, 10 pages.

. Zadeh, L.A. (1965). Fuzzy sets, Information and Control, 8, 338-353.

. Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning-I, Information Science, 8, 199-249.