Advanced Studies in Contemporary Mathematics

Jangjeon Mathematical Society (장전수학회)
권호 표지

INTERSECTIONAL SOFT SETS APPLIED TO SUBALGEBRAS/IDEALS IN BCK/BCI-ALGEBRAS

  • Song, Seok Zun (Department of Mathematics, Jeju National University) ;
  • Lee, Kyoung Ja (Department of Mathematics Education, Hannam University) ;
  • Jun, Young Bae (Department of Mathematics Education (and RINS), Gyeongsang National University)
  • Published : 2013.07.01
⟨ Previous Next ⟩

Abstract

Basic properties on intersectional soft BCK/BCI-algebras/ideals are considered. The notion of supports of soft sets is introduced, and its basic properties are investigated. Using this notion, characterizations of an intersectional soft BCK/BCI-algebras/ideals are discussed. The problem of classifying intersectional soft BCK/BCI-algebras/ideals by their supporting subalgerbas/ideals will be solved.

Keywords

References

  1. U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl. 59, (2010) 3458-3463. https://doi.org/10.1016/j.camwa.2010.03.034
  2. H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci. 177(2007) 2726-2735. https://doi.org/10.1016/j.ins.2006.12.008
  3. A. O. AtagUun and A. Sezgin, Soft substructures of rings, Fields and modules, Comput. Math. Appl. 61 (2011) 592-601. https://doi.org/10.1016/j.camwa.2010.12.005
  4. D. Chen, E. C. C. Tsang, D. S. Yeung and X. Wang, The parametrization reduction of soft sets and its applications, Comput. Math. Appl. 49 (2005) 757-763. https://doi.org/10.1016/j.camwa.2004.10.036
  5. F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl. 56 (2008) 2621-2628. https://doi.org/10.1016/j.camwa.2008.05.011
  6. Y. Huang, BCI-algebra, Science Press, Beijing 2006.
  7. Y. B. Jun, Soft BCK=BCI-algebras, Comput. Math. Appl. 56 (2008) 1408-1413. https://doi.org/10.1016/j.camwa.2008.02.035
  8. Y. B. Jun, H. S. Kim and J. Neggers, Pseudo d-algebras, Inform. Sci. 179 (2009) 1751-1759. https://doi.org/10.1016/j.ins.2009.01.021
  9. Y. B. Jun, K. J. Lee and C. H. Park, Soft set theory applied to ideals in d-algebras, Comput. Math. Appl. 57 (2009) 367-378. https://doi.org/10.1016/j.camwa.2008.11.002
  10. Y. B. Jun, K. J. Lee and E. H. Roh, Intersectional soft BCK=BCI-ideals, Ann. Fuzzy Math. Inform. 4(1) (2012) 1-7.
  11. Y. B. Jun, K. J. Lee and J. Zhan, Soft p-ideals of soft BCI-algebras, Comput. Math. Appl. 58 (2009) 2060-2068. https://doi.org/10.1016/j.camwa.2009.07.072
  12. Y. B. Jun, K. J. Lee and A. Khan, Soft ordered semigroups, Math. Logic Q. 56 (2010) 42-50. https://doi.org/10.1002/malq.200810030
  13. Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI- algebras, Inform. Sci. 178 (2008) 2466-2475.
  14. 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
  15. 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
  16. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa Co. Seoul 1994.
  17. D. Molodtsov, Soft set theory - First results, Comput. Math. Appl. 37 (1999) 19-31.
  18. C. H. Park, Y. B. Jun and M. A. OztUurk, Soft WS-algebras, Commun. Korean Math. Soc. 23 (2008) 313-324. https://doi.org/10.4134/CKMS.2008.23.3.313
  19. L. A. Zadeh, From circuit theory to system theory, Proc. Inst. Radio Eng. 50 (1962) 856-865.
  20. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  21. L. A. Zadeh, Toward a generalized theory of uncertainty (GTU) - an outline, Inform. Sci. 172 (2005) 1-40. https://doi.org/10.1016/j.ins.2005.01.017
  22. J. Zhan and Y. B. Jun, Soft BL-algebras based on fuzzy sets, Comput. Math. Appl. 59 (2010) 2037-2046. https://doi.org/10.1016/j.camwa.2009.12.008