DOI QR코드

DOI QR Code

Double-framed Soft Filters in CI-algebras

  • Al-Roqi, Abdullah M.
  • Received : 2013.09.21
  • Accepted : 2013.11.08
  • Published : 2014.03.23

Abstract

The notion of double-framed soft filters of a CI-algebra is introduced, and related properties are investigated. Further characterization of a double-framed soft filter is considered, and conditions for a double-framed soft set to be a double-framed soft filter are provided. Finally a new double-framed soft filter from old one is established.

Keywords

CI-algebra;Filter;Double-framed soft filter

References

  1. Y. B. Jun and S. S. Ahn, Double-framed soft sets with applications in BCK/BCI-algebras, J. Appl. Math., Volume 2012, Article ID 178159, 15 pages.
  2. S. S. Ahn and K. S. So, On ideals and upper sets in BE-algerbas, Sci. Math. Jpn., 68(2008), 279-285.
  3. Y. Imai and K iseki, On axiom systems of propositional calculi XIV, Proc. Japan Academy, 42(1966), 19-22. https://doi.org/10.3792/pja/1195522169
  4. K. Iseki, An algebra related with a propositional calculus, Proc. Japan Academy, 42(1966), 26-29. https://doi.org/10.3792/pja/1195522171
  5. Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci., 178(2008), 2466-2475.
  6. Y. B. Jun, G. Muhiuddin and A. M. Al-roqi, Ideal theory of BCK/BCI-algebras based on double-framed soft sets, Appl. Math. Inf. Sci., 7(5)(2013), 1879-1887. https://doi.org/10.12785/amis/070526
  7. K. H. Kim, A note on CI-algebras, Int. Math. Forum, 6(1)(2011), 1-5.
  8. H. S. Kim and Y. H. Kim, On BE-algerbas, Sci. Math. Jpn., 66(1)(2007), 113-116.
  9. P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl., 45(2003), 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
  10. P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44(2002), 1077-1083. https://doi.org/10.1016/S0898-1221(02)00216-X
  11. B. L. Meng, CI-algebras, Sci. Math. Jpn., 71(1)(2010), 11-17.
  12. B. L. Meng, Closed filters in CI-algebras, Sci. Math. Jpn., 71(3)(2010), 367-372.
  13. D. Molodtsov, Soft set theory - First results, Comput. Math. Appl., 37(1999), 19-31.
  14. B. Piekart and A. Walendziak, On filters and upper sets in CI-algebras, Algebra Discrete Math., 11(1)(2011), 109-115.