DOI QR코드

DOI QR Code

Soft Hemirings Related to Fuzzy Set Theory

Wu, Hua-Jun;Zhan, Jianming

  • Received : 2010.12.20
  • Accepted : 2011.04.25
  • Published : 2012.03.23

Abstract

In this paper, we investigate soft hemirings by fuzzy theory. Some characterizations of hemirings are introduced by means of soft sets. In particular, the $h$-hemiregular hemirings and $h$-intra-hemiregular hemirings are also characterized.

Keywords

$h$-idealistic soft hemiring;$h$-bi-idealistic soft hemiring;$h$-quasi-idealistic soft hemirng;$h$-hemiregular-hemiring;$h$-intra-hemiregular hemiring

References

  1. H. Aktas, N. Cagman, Soft sets and soft groups, Inform. Sci., 177(2007), 2726-2735. https://doi.org/10.1016/j.ins.2006.12.008
  2. M.I. Ali, M. Shabir, K.P. Shum, On soft ideals over semigroups, Southeast Asian Bull. Math., 34(2010), 595-611.
  3. A.O. Atagun, A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl., 61(3)(2011), 592-601. https://doi.org/10.1016/j.camwa.2010.12.005
  4. S.K. Bhakat, P. Das, ($\in$, $\in$ Vq)-fuzzy subgroups, Fuzzy Sets Syst., 80(1996), 359-368. https://doi.org/10.1016/0165-0114(95)00157-3
  5. D. Chen, E. C. C. Tsang, D. S. Yeung, X. Wang, The parametrization reduction of soft sets and its applications, Comput. Math. Appl., 49(2005), 757-763. https://doi.org/10.1016/j.camwa.2004.10.036
  6. F. Feng, C. Li, B. Davvaz, M.I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Comput., 14(2010), 899-911. https://doi.org/10.1007/s00500-009-0465-6
  7. F. Feng, X.Y. Liu, v. Leoreanu-Fotea, Y.B. Jun, Soft sets and soft rough sets, Inform. Sci., 181(6)(2011), 1125-1137. https://doi.org/10.1016/j.ins.2010.11.004
  8. F. Feng, Y.B. Jun, X. Zhao, Soft semirings, Comput. Math. Appl., 56(2008), 2621- 2628. https://doi.org/10.1016/j.camwa.2008.05.011
  9. K. Gong, Z. Xiao, X. Zhang, The bijective soft set with its operations, Comput. Math. Appl., 60(2010), 2270-2278. https://doi.org/10.1016/j.camwa.2010.08.017
  10. M. Henriksen, Ideals in semirings with commutative addtion, Amer. Math. Soc. Notices, 6(1958), 321.
  11. K. Iizuka, On the Jacobson radial of a semiring, Tohoku Math. J., 11(1959), 409-421. https://doi.org/10.2748/tmj/1178244538
  12. Y.B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56(2008), 1408-1413. https://doi.org/10.1016/j.camwa.2008.02.035
  13. Y.B. Jun, M.A. Ozturk, 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
  14. Y.B. Jun, C.H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci., 178(2008), 2466-2475.
  15. X. Liu, Normal soft groups, Journal of Hubei University for Nationalities(Natural Science Edition), 27(2)(2009), 168-170.
  16. X. Liu, D. Xiang, J. Zhan, Soft rings related to fuzzy set theory, submitted.
  17. X. Ma, J. Zhan, Generalized fuzzy h-bi-ideals and fuzzy h-quasi-ideals of hemirings, Inform. Sci., 179(2009), 1249-1268. https://doi.org/10.1016/j.ins.2008.12.014
  18. X. Ma, 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
  19. P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl., 45(2003), 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
  20. P.K. Maji, A.R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44(2002), 1077-1083. https://doi.org/10.1016/S0898-1221(02)00216-X
  21. P. Majumdar, S.K. Samanta, On soft mappings, Comput. Math. Appl., 60(9)(2010), 2666-2672. https://doi.org/10.1016/j.camwa.2010.09.004
  22. D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37(1999), 19-31.
  23. A. Sezgin, A.O. Atagun, On operations of soft sets, Comput. Math. Appl., 61(5)(2011), 1457-1467. https://doi.org/10.1016/j.camwa.2011.01.018
  24. M. Shabir, M.Naz, On soft topological spaces, Comput. Math. Appl., 61(2011), 1786- 1799. https://doi.org/10.1016/j.camwa.2011.02.006
  25. D. Xiang, X. Liu, Summary report of soft set theory, Journal of Hubei University for Nationalities (Natural Science Edition), 27(4)(2009), 361-365.
  26. Y. Yin, X. Huang, D. Xu, H. Li, The characterizations of h-semisimple hemirings, Int. J. Fuzzy Syst., 11(2009), 116-122.
  27. Y. Yin, H. Li, The characterizations 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
  28. L.A. Zadeh, Fuzzy sets, Inform. Control, 8(1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  29. L.A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Inform. Sci., 172(2005), 1-40. https://doi.org/10.1016/j.ins.2005.01.017
  30. J. Zhan, B. Davvaz, L-fuzzy h-ideals with operators in hemirings, Northeast. Math. J., 23(2007), 1-14.
  31. J. Zhan, On properties of fuzzy left h-ideals in hemirings, Int. J. Math. Math. Sci., 19(2005), 3127-3144.
  32. J. Zhan, W.A. Dudek, Fuzzy h-ideals of hemirings, Inform. Sci., 177(2007), 876-886. https://doi.org/10.1016/j.ins.2006.04.005
  33. J. Zhan, K.P. Shum, Intuitionistic M-fuzzy h-ideals in M-hemirings, J. Fuzzy Math., 14(2006), 929-945.
  34. J. Zhan, Z. Tan, T-fuzzy k-ideals of semirings, Sci. Math. Japon., 58(2003), 597-601.