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MIGHTY FILTERS IN BE-ALGEBRAS

  • LEE, HYE RAN ;
  • AHN, SUN SHIN
  • Received : 2015.02.16
  • Accepted : 2015.03.15
  • Published : 2015.06.25

Abstract

The notion of a mighty (vague) filter in a BE-algebra is introduced, and the relation between a (vague) filter and a mighty (vague) filter are given. We investigate an equivalent condition for a (vague) filter to be mighty, and state an extension property for mighty filter. Also we define the notion of an n-fold mighty filter which is an extended notion of a mighty filter in a BE-algebra. Characterizations of an n-fold mighty filter are given. Extension property for an n-fold mighty filter are provided.

Keywords

BE-algebra;filter;mighty (vague) filter

References

  1. S. S. Ahn, Y. U. Cho and C. H. Park, Vague quick ideals of BCK/BCI-algebras, Honam Math. J. 30 (2008), 65-74. https://doi.org/10.5831/HMJ.2008.30.1.065
  2. S. S. Ahn and J. M. Ko, On Vague filters in BE-algebras, Commun. Korean Math. Soc. 26 (2011), 417-425. https://doi.org/10.4134/CKMS.2011.26.3.417
  3. R. Biswas, Vague groups, Internat. J. Comput. Cognition 4 (2006), 20-23.
  4. W. L. Gau and D. J. Buehrer, Vague setsd, IEEE Transactions on Systems, Man and Cybernetics 23 (1993), 610-614. https://doi.org/10.1109/21.229476
  5. K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Sci. Math. Jpn. 23 (1978), 1-26.
  6. K. Iseki, On BCI-algebras, Math. Seminar Notes 8 (1980), 125-130.
  7. Y. B. Jun and C. H. Park, Vague ideals of subtraction algebra, Int. Math. Forum. 2 (2007), 2919-2926. https://doi.org/10.12988/imf.2007.07266
  8. H. S. Kim and Y. H. Kim, On BE-algebras, Sci. Math. Jpn. 66 (2007), 113-116.
  9. K. L. Lee, K. S. So and K. S. Bang, Vague BCK/BCI-algebras, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 15 (2008), 297-308.
  10. B. L. Meng, On filters in BE-algebras, Sci. Math. Japn. 71(2010), 201-207.
  11. C. H. Park, Vague deductive systems of subtraction algebras, J. Appl. Math. Informatics 26 (2008), 427-436.
  12. L. A. Zadeh, Fuzzy sets, Inform. Control 56 (2008), 338-353.

Cited by

  1. INT-SOFT MIGHTY FILTERS IN BE-ALGEBRAS vol.34, pp.5_6, 2016, https://doi.org/10.14317/jami.2016.527