The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

A GENERALIZATION OF FUZZY SUBSEMIGROUPS IN SEMIGROUPS

  • Kang, Mee Kwang (Department of Mathematics, Dongeui University) ;
  • Ban, Hee Young (Department of Mathematics Education, Gyeongsang National University) ;
  • Yun, Sang Wook (Department of Mathematics Education, Gyeongsang National University)
  • Received : 2013.02.12
  • Accepted : 2013.04.22
  • Published : 2013.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

As a generalization of fuzzy subsemigroups, the notion of ${\varepsilon}$-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of ${\varepsilon}$-generalized fuzzy subsemigroups are established, and we show that the intersection of two ${\varepsilon}$-generalized fuzzy subsemigroups is also an ${\varepsilon}$-generalized fuzzy subsemigroup. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be ${\varepsilon}$-fuzzy idempotent is discussed. Using a given ${\varepsilon}$-generalized fuzzy subsemigroup, a new ${\varepsilon}$-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an ${\varepsilon}$-generalized fuzzy subsemigroup is considered.

Keywords

References

  1. K.A. Dib & N. Galhum: Fuzzy ideals and fuzzy bi-ideals in fuzzy semigroups. Fuzzy Sets and Systems 92 (1997), 103-111. https://doi.org/10.1016/S0165-0114(96)00170-4
  2. Y.B. Jun & S.Z. Song: Generalized fuzzy interior-ideals in semigroups. Inform. Sci. 176 (2006), no. 20, 3079-3093. https://doi.org/10.1016/j.ins.2005.09.002
  3. S.M. Hong, Y.B. Jun & J. Meng: Fuzzy interior-ideals in semigroups. Indian J. Pure Appl. Math. 26 (1995), 859-863.
  4. O. Kazanci & S. Yamak: Generalized fuzzy bi-ideals of semigroups. Soft Computing 12 (2008), 1119-1124. https://doi.org/10.1007/s00500-008-0280-5
  5. O. Kazanci & S. Yamak: Fuzzy ideals and semiprime fuzzy ideals in semigroups. Inform. Sci. 179 (2009), 3720-3731. https://doi.org/10.1016/j.ins.2009.06.026
  6. N. Kuroki: Fuzzy hi-ideals in semigroups. Comment. Math., Univ. St. Paul. 28 (1979), 17-21.
  7. N. Kuroki: On fuzzy ideals and fuzzy bi-ideals in semigroups. Fazzy Sets and Systems 5 (1981), 203-215 https://doi.org/10.1016/0165-0114(81)90018-X
  8. 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
  9. N. Kuroki: On fuzzy semigroups. Inform. Sci. 53 (1991), 203-236. https://doi.org/10.1016/0020-0255(91)90037-U
  10. 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
  11. Z.W. Mo & X.P. Wang: On pointwise depiction of fuzzy regularity of semigroups. Inform. Sci. 74 (1993), 265-274. https://doi.org/10.1016/0020-0255(93)90099-8
  12. J.N. Mordeson, D.S. Malik & N. Kuroki: Fuzzy semigroups. Springer-Verlag Berlin Heidelberg New York, 2003.
  13. X. Pan & Y. Xu: Lattice implication ordered semigroups. Inform. Sci. 178 (2008), no. 2, 403-413. https://doi.org/10.1016/j.ins.2007.08.017
  14. A. Rosenfeld: Fuzzy groups. J. Math. Anal. Appl. 35 (1971), 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
  15. X.Y. Xie: Fuzzy ideals in semigroups. J. Fuzzy Math. 7 (1999), no. 2, 357-365.
  16. L.A. Zadeh: Fuzzy sets. Inform. Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X