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ON (α, β)-FUZZY SUBALGEBRAS OF BCK/ BCI-ALGEBRAS

  • Published : 2005.11.01

Abstract

Using the belongs to relation ($\in$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (${\alpha},\;{\beta}$)-fuzzy subalgebras where ${\alpha},\;{\beta}$ are any two of $\{\in,\;q,\;{\in}\;{\vee}\;q,\;{\in}\;{\wedge}\;q\}$ with $\;{\alpha}\;{\neq}\;{\in}\;{\wedge}\;q$ is introduced, and related properties are investigated.

Keywords

belong to;quasi-coincident with

References

  1. S. A. Bhatti, M. A. Chaudhry, and B. Ahmad, On classification of BCI-algebras, Math. Jpn. 34 (1989), no. 6, 865-876
  2. S. K. Bhakat and P. Das, ($\in,\in \bigvee$q)-fuzzy subgroup, Fuzzy Sets and Systems 80 (1996), 359-368 https://doi.org/10.1016/0165-0114(95)00157-3
  3. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa Co., Korea, 1994
  4. P. M. Pu and Y. M. Liu, Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980), 571-599 https://doi.org/10.1016/0022-247X(80)90048-7

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