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FSI-IDEALS AND FSC-IDEALS OF BCI-ALGEBRAS

  • Liu, Yong-Lin (Department of Applied Mathematics, Xidian University) ;
  • Liu, San-Yang (Department of Applied Mathematics, Xidian University) ;
  • Meng, Jie (Department of Mathematics, Northwest University)
  • Published : 2004.02.01

Abstract

The notions of FSI-ideals and FSC-ideals in BCI-algebras are introduced. The characterization properties of FSI-ideals and FSC-ideals are obtained. We investigate the relations between FSI-ideals (resp. FSC-ideals) and other fuzzy ideals, between FSI-ideals (resp. FSC-ideals) and BCI-algebras, and show that a fuzzy subset of a BCI-algebra is an FSI-ideal if and only if it is both an FSC-ideal and a fuzzy BCI-positive implicative ideal.

Keywords

BCI-algebra;FSI-ideal;FSC-ideal;fuzzy ideal

References

  1. Math. Japon v.38 no.3 Positive implicative BCK-algebras R.Barbacioru
  2. J. Fuzzy Math. v.4 no.3 Fuzzy quasi-associative ideals in BCI-algebras Y.B.Jun
  3. Fuzzy Set and Systems v.89 no.2 Fuzzy implicative ideals of BCK-algebras J.Meng;Y.B.Jun;H.S.Kim https://doi.org/10.1016/S0165-0114(96)00096-6
  4. Information and Control v.8 Fuzzy sets L.A.Zadeh https://doi.org/10.1016/S0019-9958(65)90241-X
  5. J. Math. Anal. Appl. v.84 no.1 Fuzzy groups and level subgroups P.S.Das https://doi.org/10.1016/0022-247X(81)90164-5
  6. Fuzzy Sets and System v.123 no.2 Fuzzy ideals in BCI-algebras https://doi.org/10.1016/S0165-0114(00)00047-6
  7. Math. Japon v.37 no.3 Commutative BCI-algebras J.Ment;X.L.Xin
  8. Fuzzy Commutative Algebra J.N.Mordeson;D.S.Malik
  9. Math. Japon. v.23 no.1 An introduction to the theory of BCK-algebras K.Iseki:S.Tanaka
  10. Fuzzy Sets and Systems v.64 no.3 Fuzzy commutative ideals of BCK-algevras Y.B.Jun;E.H.Roh https://doi.org/10.1016/0165-0114(94)90163-5
  11. Math. Japon v.36 no.5 Fuzzy BCK-algebras O.G.Xi
  12. Math. Japon v.40 no.2 Fuzzy p-ideals in BCI-algebras Y.B.Jun;J.Meng
  13. Adv. Math. (China) v.31 no.1 Fuzzy a-ideals of BCI-algebras Y.L.Liu;X.H.Zhang
  14. Pure Appl. Math. v.8 no.2 Implicative BCI-algebras
  15. Math. Japon v.31 no.6 MV-algebras are categorically equivalent to bounded commutative BCK-algebras D.Mundici
  16. Commun. Korean Math. Soc. v.9 no.1 Fuzzy commutative ideals in BCI-algebras
  17. J. Han-zhong Teachers College (1) Characterization of weakly positive implicative BCI-algebras
  18. Math. Japon v.40 no.3 Characterizations of fuzzy positive implicative ideals in BCK-algebras Y.B.Jun;S.M.Hong;J.Meng;X.L.Xin
  19. Soochow J. Math. v.26 no.4 Sub-implicative ideals and sub-commutative ideals of BCI-algevras Y.L.Liu;J.Meng
  20. Math. Sem. v.8 no.1 On BCI-algevras K.Iseki

Cited by

  1. On characterizations of generalized fuzzy ideals of BCI-algebras vol.86, pp.12, 2009, https://doi.org/10.1080/00207160902795601
  2. BCI-implicative ideals of BCI-algebras vol.177, pp.22, 2007, https://doi.org/10.1016/j.ins.2007.07.003
  3. Non-commutative residuated lattices based on soft sets vol.29, pp.5, 2015, https://doi.org/10.3233/IFS-151702
  4. Some kinds of (∈,∈∨q)-interval-valued fuzzy ideals of BCI-algebras vol.178, pp.19, 2008, https://doi.org/10.1016/j.ins.2008.06.006