# FUZZY IDEALS GENERATED BY FUZZY SUBSETS IN SEMIGROUPS

Chon, In-Heung

• Published : 2012.07.31
• 33 7

#### 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.

#### Keywords

t-norm;fuzzy ideal;fuzzy interior ideal

#### 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

#### Acknowledgement

Supported by : Seoul Women's University