Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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FUZZY SEMIGROUPS IN REDUCTIVE SEMIGROUPS

  • Chon, Inheung (Department of Mathematics Seoul Women's University)
  • Received : 2013.03.21
  • Accepted : 2013.05.20
  • Published : 2013.06.30
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Abstract

We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ and find a faithful representation (or anti-representation) of S by transformations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ is isomorphic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup.

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References

  1. J.M. Anthony and H. Sherwood, Fuzzy groups redefined, J. Math. Anal. Appl. 69 (1979), 124-130. https://doi.org/10.1016/0022-247X(79)90182-3
  2. I. Chon, Fuzzy ideals generated by fuzzy subsets in semigroups, (To appear Commun. Korean Math. Soc.).
  3. A.H. Clifford and G.B. Preston, The algebraic theory of semigroups Vol. 1, American mathematical society, Providence, Rhode Island, 1961.
  4. P. Da, Fuzzy multiplication semigroup, Fuzzy Sets and Systems 105 (1999), 171-176. https://doi.org/10.1016/S0165-0114(97)00228-5
  5. N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems 5 (1981), 203-215. https://doi.org/10.1016/0165-0114(81)90018-X
  6. N. Kuroki, Fuzzy semiprime ideals in semigroups, Fuzzy Sets and Systems 8 (1982), 71-79. https://doi.org/10.1016/0165-0114(82)90031-8
  7. N. Kuroki, On Fuzzy semigroups, Information Sciences 53 (1991), 203-236. https://doi.org/10.1016/0020-0255(91)90037-U
  8. N. Kuroki, Fuzzy semiprime quasi-ideals in semigroups, Information Sciences 75 (1993), 201-211. https://doi.org/10.1016/0020-0255(93)90054-P
  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), 95-100. https://doi.org/10.1016/0165-0114(84)90028-9
  11. L.A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X