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A COUPLED 𝒩-STRUCTURE WITH AN APPLICATION IN A SUBTRACTION ALGEBRA

  • Received : 2014.10.15
  • Accepted : 2014.10.28
  • Published : 2014.12.25

Abstract

In this paper, we introduce a coupled $\mathcal{N}$-structure which is the generalization of $\mathcal{N}$-structure. Using this coupled $\mathcal{N}$-structure, we have applied in a subtraction algebra and have introduced the notion of a coupled $\mathcal{N}$-subalgebra, a coupled $\mathcal{N}$-ideal. Also the characterization of coupled $\mathcal{N}$-ideal is presented.

Keywords

$\mathcal{N}$-subalgebras;$\mathcal{N}$-ideals;coupled $\mathcal{N}$-subalgebras;coupled $\mathcal{N}$-ideals

References

  1. J. C. Abbott, Sets, Lattices and Boolean Algebra, Allyn and Bacon, Boston, 1969.
  2. K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems. 1 (1986), 87-96.
  3. K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems. 61 (1994), 137-142. https://doi.org/10.1016/0165-0114(94)90229-1
  4. Y. Ceven and M. A Ozturk, Some results on subtraction algebras, Hacettepe Journal of Mathematics and Statistics 38 (2009), 299-304.
  5. Y. B. Jun, H. S. Kim and E. H. Roh, Ideal theory of subtraction algebras, Sci. Math. Jpn. 61 (2005), 459-464.
  6. Y. B. Jun and H. S. Kim, On ideals in subtraction algebras, Sci. Math. Jpn. 65 (2007), 129-134.
  7. Y. B. Jun, K. J. Lee and S. Z. Song, $\aleph$-ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc. 22 (2009), 417-437.
  8. Y. B. Jun, J. Kavikumar and K. S. So, N-ideals of subtraction algebras, Commun. Korean Math. Soc. 25 (2010), 173-184. https://doi.org/10.4134/CKMS.2010.25.2.173
  9. A. Khan, Y. B. Jun and M. Shabir, N-fuzzy ideals in ordered semigroups, International Journal of Mathematics and Mathematical Sciences. 1 (2009), 1-4.
  10. Y. B. Jun, S. S. Ahn and D. R. Prince Williams, Coupled N-structures and its application in BCK/BCI-algebras, (in press).
  11. A. Khan, Y. B. Jun and M. Shabir, N-fuzzy filters in ordered semigroups, Mohu Xitong yu Shuxue 24 (2010), 28-32.
  12. K. J. Lee and C. H. Park, Some questions on fuzzifications of ideals in subtraction algebras, Commun. Korean Math. Soc. 22 (2007), 359-363. https://doi.org/10.4134/CKMS.2007.22.3.359
  13. B. M. Schein, Difference Semigroups, Comm. Algebra 20 (1992), 2153-2169. https://doi.org/10.1080/00927879208824453
  14. L. A. Zadeh, Fuzzy sets, Information Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  15. L. A. Zelinka, Subtraction semigroup, Math. Bohemica 120 (1995), 445-447.

Acknowledgement

Supported by : Ministry of Higher Education