Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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FUZZY IDEALS GENERATED BY FUZZY SUBSETS IN SEMIGROUPS

  • Received : 2011.04.18
  • Published : 2012.07.31
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Abstract

We characterize the fuzzy ideal generated by a fuzzy subset in a semigroup and the fuzzy interior ideal generated by a fuzzy subset in a semigroup. Our work generalizes the characterizations ([8]) of those fuzzy ideals generated by fuzzy subsets in semigroups with an identity element.

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References

  1. J. M. Anthony and H. Sherwood, Fuzzy groups redefined, J. Math. Anal. Appl. 69 (1979), no. 1, 124-130. https://doi.org/10.1016/0022-247X(79)90182-3
  2. N. Kuroki, Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Paul. 28 (1980), no. 1, 17-21.
  3. N. Kuroki, On fuzzy ideals and bi-ideals in semigroups, Fuzzy Sets and Systems 5 (1981), no. 2, 203-215. https://doi.org/10.1016/0165-0114(81)90018-X
  4. N. Kuroki, Fuzzy semiprime ideals in semigroups, Fuzzy Sets and Systems 8 (1982), no. 1, 71-79. https://doi.org/10.1016/0165-0114(82)90031-8
  5. N. Kuroki, On fuzzy semigroups, Inform. Sci. 53 (1991), no. 3, 203-236. https://doi.org/10.1016/0020-0255(91)90037-U
  6. N. Kuroki, Fuzzy semiprime quasi-ideals in semigroups, Inform. Sci. 75 (1993), no. 3, 201-211. https://doi.org/10.1016/0020-0255(93)90054-P
  7. W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982), no. 2, 133-139. https://doi.org/10.1016/0165-0114(82)90003-3
  8. Z.-W. Mo and X.-P. Wang, Fuzzy ideals generated by fuzzy sets in semigroups, Inform. Sci. 86 (1995), no. 4, 203-210. https://doi.org/10.1016/0020-0255(95)00096-8
  9. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
  10. S. Sessa, On fuzzy subgroups and fuzzy ideals under triangular norms, Fuzzy Sets and Systems 13 (1984), no. 1, 95-100. https://doi.org/10.1016/0165-0114(84)90028-9
  11. X.-P. Wang, Fuzzy regular subsemigroups in semigroups, Inform. Sci. 68 (1993), no. 3, 225-231. https://doi.org/10.1016/0020-0255(93)90106-V
  12. X.-Y. Xie, Fuzzy ideals in semigroups, J. Fuzzy Math. 7 (1999), no. 2, 357-365.
  13. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X