Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 125614, 15 pages
http://dx.doi.org/10.1155/2012/125614
Research Article

Closed Int Soft -Ideals and Int Soft c- -Ideals

1Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Republic of Korea
2Department of Mathematics Education, Hannam University, Daejeon 306-791, Republic of Korea
3Department of Mathematics Education, Chinju National University of Education, Chinju 660-756, Republic of Korea

Received 18 July 2012; Accepted 10 November 2012

Academic Editor: Nazim Idrisoglu Mahmudov

Copyright © 2012 Young Bae Jun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. A. Zadeh, “From circuit theory to system theory,” Proceedings of the Institute of Radio Engineers, vol. 50, pp. 856–865, 1962. View at Google Scholar
  2. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Google Scholar · View at Zentralblatt MATH
  3. L. A. Zadeh, “Toward a generalized theory of uncertainty (GTU)—an outline,” Information Sciences, vol. 172, no. 1-2, pp. 1–40, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. D. Molodtsov, “Soft set theory—first results,” Computers & Mathematics with Applications, vol. 37, no. 4-5, pp. 19–31, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. P. K. Maji, A. R. Roy, and R. Biswas, “An application of soft sets in a decision making problem,” Computers & Mathematics with Applications, vol. 44, no. 8-9, pp. 1077–1083, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. P. K. Maji, R. Biswas, and A. R. Roy, “Soft set theory,” Computers & Mathematics with Applications, vol. 45, no. 4-5, pp. 555–562, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. H. Aktaş and N. Çağman, “Soft sets and soft groups,” Information Sciences, vol. 177, no. 13, pp. 2726–2735, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Y. B. Jun and C. H. Park, “Applications of soft sets in ideal theory of BCK/BCI-algebras,” Information Sciences, vol. 178, no. 11, pp. 2466–2475, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. Y. B. Jun, K. J. Lee, and M. S. Kang, “Intersectional soft sets and applications to BCK/BCI-algebras,” Communications of the Korean Mathematical Society. In press.
  10. Y. B. Jun, K. J. Lee, and E. H. Roh, “Intersectional soft BCK/BCI-ideals,” Annals of Fuzzy Mathematics and Informatics, vol. 4, no. 1, pp. 1–7, 2012. View at Google Scholar
  11. N. Çağman and F. Çitak, “Soft int-group and its applications to group theory,” Neural Computing & Applications, vol. 21, Supplement 11, pp. S151–S158, 2012. View at Google Scholar
  12. Y. B. Jun, “Union soft sets with applications in BCK/BCI-algebras,” Submitted to Bulletin of the Korean Mathematical Society.
  13. U. Acar, F. Koyuncu, and B. Tanay, “Soft sets and soft rings,” Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3458–3463, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. A. O. Atagün and A. Sezgin, “Soft substructures of rings, fields and modules,” Computers & Mathematics with Applications, vol. 61, no. 3, pp. 592–601, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. N. Çağman, F. Çitak, and S. Enginoglu, “FP-soft set theory and its applications,” Annals of Fuzzy Mathematics and Informatics, vol. 2, no. 2, pp. 219–226, 2011. View at Google Scholar
  16. F. Feng, “Soft rough sets applied to multicriteria group decision making,” Annals of Fuzzy Mathematics and Informatics, vol. 2, no. 1, pp. 69–80, 2011. View at Google Scholar
  17. F. Feng, Y. B. Jun, and X. Zhao, “Soft semirings,” Computers & Mathematics with Applications, vol. 56, no. 10, pp. 2621–2628, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. Y. B. Jun, “Soft BCK/BCI-algebras,” Computers & Mathematics with Applications, vol. 56, no. 5, pp. 1408–1413, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. Y. B. Jun, H. S. Kim, and J. Neggers, “Pseudo d-algebras,” Information Sciences, vol. 179, no. 11, pp. 1751–1759, 2009. View at Publisher · View at Google Scholar
  20. Y. B. Jun, K. J. Lee, and A. Khan, “Soft ordered semigroups,” Mathematical Logic Quarterly, vol. 56, no. 1, pp. 42–50, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. Y. B. Jun, K. J. Lee, and C. H. Park, “Soft set theory applied to ideals in d-algebras,” Computers & Mathematics with Applications, vol. 57, no. 3, pp. 367–378, 2009. View at Publisher · View at Google Scholar
  22. Y. B. Jun, K. J. Lee, and J. Zhan, “Soft p-ideals of soft BCI-algebras,” Computers & Mathematics with Applications, vol. 58, no. 10, pp. 2060–2068, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. Y. B. Jun and J. Zhan, “Soft ideals of BCK/BCI-algebras based on fuzzy set theory,” International Journal of Computer Mathematics, vol. 88, no. 12, pp. 2502–2515, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. C. H. Park, Y. B. Jun, and M. A. Öztürk, “Soft WS-algebras,” Communications of the Korean Mathematical Society, vol. 23, no. 3, pp. 313–324, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. S. Z. Song, K. J. Lee, and Y. B. Jun, “Intersectional soft sets applied to subalgebras/ideals in BCK/BCI-algebras,” Submitted to Knowledge-Based Systems.
  26. J. Zhan and Y. B. Jun, “Soft BL-algebras based on fuzzy sets,” Computers & Mathematics with Applications, vol. 59, no. 6, pp. 2037–2046, 2010. View at Publisher · View at Google Scholar
  27. J. Meng and X. L. Xin, “Commutative BCI-algebras,” Mathematica Japonica, vol. 37, no. 3, pp. 569–572, 1992. View at Google Scholar · View at Zentralblatt MATH
  28. J. Meng, “An ideal characterization of commutative BCI-algebras,” Pusan Kyongnam Mathematical Journal, vol. 9, no. 1, pp. 1–6, 1993. View at Google Scholar
  29. Y. Huang, BCI-Algebra, Science Press, Beijing, China, 2006.
  30. J. Meng and Y. B. Jun, BCK-algebras, KyungMoon Sa, Seoul, South Korea, 1994.
  31. N. Çağman and S. Enginoğlu, “Soft set theory and uni-int decision making,” European Journal of Operational Research, vol. 207, no. 2, pp. 848–855, 2010. View at Publisher · View at Google Scholar
  32. J. Meng and S. M. Wei, “Periods of elements in BCI-algebras,” Mathematica Japonica, vol. 38, no. 3, pp. 427–431, 1993. View at Google Scholar · View at Zentralblatt MATH