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Coincidences of different types of fuzzy ideals in ordered Gamma-semigroups

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The notion of Gamma-semigroups was introduced by Sen in 1981 and that of fuzzy sets by Zadeh in 1965. Any semigroup can be reduced to a Gamma-semigroup but a Gamma-semigroup does not necessarily reduce to a semigroup. In this paper, we study the coincidences of fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy ideals in regular, left regular, right regular, intra-regular, semisimple ordered Gamma-semigroups.

Abstract

The notion of Gamma-semigroups was introduced by Sen in 1981 and that of fuzzy sets by Zadeh in 1965. Any semigroup can be reduced to a Gamma-semigroup but a Gamma-semigroup does not necessarily reduce to a semigroup. In this paper, we study the coincidences of fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy ideals in regular, left regular, right regular, intra-regular, semisimple ordered Gamma-semigroups.

참고문헌 (33)

  1. S. Abdullah, "A note on ordered semigroups characterized by their ({∈,∈νq∈,∈νq)-fuzzy bi-ideals", UPB Scientific Bulletin, Series A, 75, pp.41~44 (2013)
  2. S. Bashir, "Prime fuzzy bi-ideals of ΓΓ-semigroups", Ann. Fuzzy Math. Inform, 5, pp.115~128 (2013)
  3. R. Chinram, "L-fuzzy ternary subsemirings and L-fuzzy ideals in ternary semirings", IAENG Int. J. Appl. Math, 40 (2010)
  4. R. Chinram, "Fuzzy ideals and fuzzy filters of ordered ternary semi-groups", J. Math. Res, 2, pp.93~97 (2010)
  5. 전인흥, "On fuzzy bi-ideals in semigroups", 한국수학논문집, 19(3), pp.321~330 (2011), 강원경기수학회
  6. P. Dheena, "Quasiideals of a P-regular near-rings", Internat. J. Algebra, 5, pp.1005~1010 (2011)
  7. A. Iampan, "Characterizing fuzzy sets in ordered ΓΓ-semigroups", J. Math. Res, 2, pp.52~56 (2010)
  8. N. Kehayopulu, "A note on fuzzy sets in semigroups", Sci. Math, 2, pp.411~413 (1999)
  9. N. Kehayopulu, "Fuzzy sets in ordered groupoids", Semigroup Forum, 65, pp.128~132 (2002)
  10. N. Kehayopulu, "Green's relations in ordered groupoids in terms of fuzzy subsets", Soochow J. Math, 33, pp.383~397 (2007)
  11. F. M. Khan, "New types of generalized fuzzy bi ΓΓ-ideals in ordered ΓΓ-semigroups", Science International (Lahore), 25, pp.411~418 (2013)
  12. K. H. Kim, "Intuitionistic fuzzy sets in ordered semigroups", International Mathematical Forum, 4, pp.2259~2268 (2009)
  13. N. Kuroki, "Fuzzy bi-ideals in semigroups", Comment. Math. Univ. St. Pauli, 27, pp.17~21 (1979)
  14. N. Kuroki, "On fuzzy ideals and fuzzy bi-ideals in semigroups", Fuzzy Sets and Systems, 5, pp.203~215 (1981)
  15. N. Kuroki, "On fuzzy semigroups", Informing Science, 53, pp.203~236 (1991)
  16. N. Kuroki, "Fuzzy semiprime quasi-ideals in semigroups", Informing Science, 75, pp.201~211 (1993)
  17. S. K. Majumder, "On fuzzy weakly completely prime ideal in ΓΓ-semigroups", SDU Journal of Science (E-Journal), 5, pp.230~238 (2010)
  18. S. K. Majumder, "Fuzzy generalized bi-ideals of ΓΓ-semigroups", Fuzzy Information and Engineering, 4, pp.389~399 (2012)
  19. S. K. Majumder, "On properties of fuzzy ideals in po-semigroup", Armen. J. Math, 2, pp.2009~2065 (2009)
  20. A. Rosenfeld, "Fuzzy groups", J. Math. Anal. Appl, 35, pp.512~517 (1971)
  21. S. Saelee, "A study on rough, fuzzy and rough fuzzy bi-ideals of ternary semigroups", IAENG Int. J. Appl. Math, 41 (2011)
  22. N. K. Saha, "On ΓΓ-semigroup II", Bull. Calcutta Math. Soc, 79, pp.331~335 (1987)
  23. N. K. Saha, "On ΓΓ-semigroup III", Bull. Calcutta Math. Soc, 80, pp.1~12 (1988)
  24. S. K. Sardar, "On generalized fuzzy interior ideals in ΓΓ-semigroups", Hacet. J. Math. Stat, 41, pp.231~241 (2012)
  25. S. K. Sardar, "Characteristic ideals and fuzzy characteristic ideals of ΓΓ-semigroups", Mathematica Aeterna, 2, pp.189~201 (2012)
  26. M. K. Sen, "On ΓΓ-semigroups", Proceedings of the International conference on Algebra and its application, pp.301~308 (1981), Decker Publication
  27. M. K. Sen, "On ΓΓ-semigroup I", Bull. Calcutta Math. Soc, 78(3), pp.180~186 (1986)
  28. M. K. Sen, "On po-ΓΓ-semigroups", Bull. Calcutta Math. Soc, 85, pp.445~450 (1993)
  29. M. Shabir, "Fuzzy filters in ordered semigroups", Lobachevskii J. Math, 29, pp.82~89 (2008)
  30. T. Shah, "On ΓΓ-ideals and ΓΓ-bi-ideals in ΓΓ-AG-groupoids", International Journal of Algebra, 4, pp.267~276 (2010)
  31. D. R. Prince Williams, "Fuzzy bi-ΓΓ-ideals in ΓΓ-semigroups", Hacet. J. Math. Stat, 38, pp.1~15 (2009)
  32. L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
  33. J. M. Zhan, "On fuzzy interior ideals in semigroups", J. Math. Res. Exposition, 28, pp.103~110 (2008)

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