East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

ON INTERVAL VALUED (${\alpha}$, ${\beta}$)-FUZZY IDEA OF HEMIRINGS

  • Received : 2011.03.25
  • Accepted : 2011.05.07
  • Published : 2011.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we define interval valued (${\in}$, ${\in}{\vee}q$)-fuzzy hquasi-ideals, interval valued (${\in}$, ${\in}{\vee}q$)-fuzzy h-bi-ideals, interval valued ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$)-fuzzy h-ideals, interval valued ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$)-fuzzy h-quasi-ideals, interval valued ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$)-fuzzy h-bi-ideals and characterize different classes of hemirings by the properties of these ideals.

Keywords

References

  1. J. Ahsan, Semirings characterized by their fuzzy ideals, J. Fuzzy Math. 6 (1998), 181-192.
  2. W. A. Dudek, M. Shabir and M. Irfan Ali, ($\alpha,\;\beta$)-Fuzzy ideals of Hemirings, Comput. Math. Appl. 58 (2009), 310-321. https://doi.org/10.1016/j.camwa.2009.03.097
  3. S. Ghosh, Fuzzy k-ideals of semirings, Fuzzy Sets Syst. 95 (1998), 103-108. https://doi.org/10.1016/S0165-0114(96)00306-5
  4. J. S. Golan, Semirings and their applications, Kluwer Acad. Publ. 1999.
  5. M. Henriksen, Ideals in semirings with commutative addition, Amer. Math. Soc. Notices 6 (1958), 321.
  6. K. Iizuka, On Jacobson radical of a semiring, Tohoku Math. J. 11 (1959), 409-421. https://doi.org/10.2748/tmj/1178244538
  7. Y. B. Jun, M. A. Ozurk and S. Z. Song, On fuzzy h-ideals in hemirings, Inform. Sci. 162 (2004), 211-226. https://doi.org/10.1016/j.ins.2003.09.007
  8. X. Ma and J. Zhan, On fuzzy h-ideals of hemirings, J. Syst. Sci. Complexity 20 (2007), 470-478. https://doi.org/10.1007/s11424-007-9043-0
  9. X. Ma and J. Zhan, Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings, Inform. Sci. 179 (2009), 1249-1268. https://doi.org/10.1016/j.ins.2008.12.014
  10. M. Shabir and T. Mahmood, Characterizations of Hemirings by Interval Valued Fuzzy Ideals, Quasigroups and Related Systems 19 (2011), 101-113.
  11. G. Sun, Y. Yin and Y. Li, Interval valued fuzzy h-ideals of Hemirings, Int. Math. Forum 5 (2010) 545-556.
  12. H. S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40 (1934), 914-920. https://doi.org/10.1090/S0002-9904-1934-06003-8
  13. Y. Q. Yin and H. Li, The charatecrizations of h-hemiregular hemirings and h-intra-hemiregular hemirings, Inform. Sci. 178 (2008), 3451-3464. https://doi.org/10.1016/j.ins.2008.04.002
  14. L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  15. J. Zhan and W. A. Dudek, Fuzzy h-ideals of hemirings, Inform. Sci. 177 (2007), 876-886. https://doi.org/10.1016/j.ins.2006.04.005