N-SUBALGEBRAS OF TYPE (∈, ∈ ∨ q) BASED ON POINT N-STRUCTURES IN BCK/BCI-ALGEBRAS

Title & Authors
N-SUBALGEBRAS OF TYPE (∈, ∈ ∨ q) BASED ON POINT N-STRUCTURES IN BCK/BCI-ALGEBRAS
Lee, Kyoung-Ja; Jun, Young-Bae; Zhang, Xiaohong;

Abstract
Characterizations of $\small{\mathcal{N}}$-subalgebra of type ($\small{{\in}}$, $\small{{\in}{\vee}q}$) are provided. The notion of $\small{\mathcal{N}}$-subalgebras of type ($\small{\bar{\in}}$, $\small{\bar{\in}{\vee}\bar{q}}$) is introduced, and its characterizations are discussed. Conditions for an $\small{\mathcal{N}}$-subalgebra of type ($\small{{\in}}$, $\small{{\in}{\vee}q}$) (resp. ($\small{\bar{\in}}$, $\small{\bar{\in}{\vee}\bar{q}}$) to be an $\small{\mathcal{N}}$-subalgebra of type ($\small{{\in}}$, $\small{{\in}}$) are considered.
Keywords
point $\small{\mathcal{N}}$-structure;closed (resp. open) support;q-support;$\small{{\in}{\vee}q}$-support;$\small{\mathcal{N}}$-subalgebra of types ($\small{{\in}}$, $\small{{\in}{\vee}q}$);($\small{\bar{\in}}$, $\small{\bar{\in}{\vee}\bar{q}}$);
Language
English
Cited by
References
1.
Y. S. Huang, BCI-algebra, Science Press, Beijing, 2006.

2.
Y. B. Jun, M. S. Kang, and C. H. Park, N-subalgebras in BCK/BCI-algebras based on point N-structures, Int. J. Math. Math. Sci. 2010 (2010), Article ID 303412, 9 pages.

3.
Y. B. Jun and M. Kondo, On transfer principle of fuzzy BCK/BCI-algebras, Sci. Math. Jpn. 59 (2004), no. 1, 35-40.

4.
Y. B. Jun and K. J. Lee, The essence of subtraction algebras based on N-structures, Commun. Korean Math. Soc. (to appear).

5.
Y. B. Jun, K. J. Lee, and S. Z. Song, N-ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc. 22 (2009), 417-437.

6.
Y. B. Jun, M. A. Ozturk, and E. H. Roh, N-structures applied to closed ideals in BCH-algebras, Int. J. Math. Math. Sci. 2010 (2010), Article ID 943565, 9 pages.

7.
M. Kondo and W. A. Dudek, On the transfer principle in fuzzy theory, Mathware Soft Comput. 12 (2005), no. 1, 41-55.

8.
J. Meng and Y. B. Jun, BCK-Algebras, Kyungmoon Sa Co., Seoul, 1994.