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QUOTIENT B-ALGEBRA-S VIA FUZZY NORMAL B-ALGEBRAS

  • Kim, Young-Hee (Department of Mathematics Institute for Basic Science, Chungbuk National University) ;
  • Yoem, Sung-Jun (Department of Mathematics Institute for Basic Science, Chungbuk National University)
  • Received : 2007.09.06
  • Accepted : 2008.01.21
  • Published : 2008.03.25

Abstract

We introduce some notions and results which have been discussed, and we define the notion of fuzzy normal B-algebra and obtain the structure of quotient B-algebra via fuzzy normal B-algebra. Moreover, we generalize a fundamental theorem of B-homomorphism for B-algebras via fuzzy normal B-algebras.

Keywords

References

  1. J. R. Cho and H. S. Kim, On B-algebras and Quasigroups, Quasigroups Related Systems 8(2001), 1-6.
  2. Qing Ping Hu and Xin Li, On BCH-algebras, Math. Seminar Notes 11 (1983), 313-320.
  3. Qing Ping Hu and Xin Li, On proper BCH-algebras, Math. Japonica 30 (1985), 659-661.
  4. K. Iseki, On BCI-algebras, Math. Seminar Notes 8 (1980), 125-130.
  5. K. Iseki and S. Tanaka, An introduction to theory of BC K-algebras, Math. Japonica 23 (1978), 1-26.
  6. T. E. Jeong, K. Y. Kim and Y. H. Kim, Quotient structure of product BCK-algebra via Fuzzy ideals, Korea Fuzzy Logic and Intelligent Systems Society Vol.12, No.2 (2002), 182-186. https://doi.org/10.5391/JKIIS.2002.12.2.182
  7. Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Sci. Mathematicae Vol. 11, No.3 (1998), 347-354.
  8. Y. B. Jun and E. H. Roh, Fuzzy commutative ideals of BCK-algebras, Fuzzy Sets and Systems 64 (1994), 401-405. https://doi.org/10.1016/0165-0114(94)90163-5
  9. Y. B. Jun, E. H. Roh and H. S. Kim, On Fuzzy B-algebras, Czech. Math. J. 52(127). no.2 (2002), 375-384. https://doi.org/10.1023/A:1021739030890
  10. J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa Co., Seoul (1994).
  11. J. Meng and Y. B. Jun, Fuzzy p-ideal in BCK-algebras, Math. Japonica 40 (1994), 271-282.
  12. J. Meng, Y. B. Jun and H. S. Kim, Fuzzy implicative ideals of BCK-algebras, Fuzzy Sets and Systems 89 (1997), 243-248. https://doi.org/10.1016/S0165-0114(96)00096-6
  13. J. Meng, X. L. Xin and Y. S. Pu, Quotient BCK-algebra induced by a fuzzy ideal, Southeast Asian Bulletin of Mathematics 23, No. 2(1999), 243-251.
  14. J. Neggers and H. S. Kim, On B-algebras,Mate. Vesnik 54, No.1-2(2002), 21-29.
  15. J. Neggers and H. S. Kim, A fundamental theorem of B-homomorphism for B-algebras,Int. Math. J. 2, No.3(2002), 207-214.