Generalized Fuzzy Right h-Ideals of Hemirings Redefined by Fuzzy Sums and Fuzzy Products


  • G. Mohanraj
  • E. Prabu


In this paper, we redene the concepts of (; )-fuzzy right [left]
ideals of hemirings by using the notions of fuzzy sum and fuzzy product. And also the notions of (; )-fuzzy right [left] h-ideals of hemirings are redened by fuzzy sum, fuzzy closure and fuzzy product. Further, using the notions of fuzzy h-sum and fuzzy h-product, we characterize (; )-fuzzy right [left] h-ideals. In particular, we investigate (; )-fuzzy right [left] h-ideals by using
fuzzy h-sum and fuzzy h-intrinsic product.


[1] S. K. Bhakat and P. Das. (2;2 _q)-fuzzy group, Fuzzy Sets and Systems, 80(1996), 359-368.

[2] S. K. Bhakat and P. Das. Fuzzy subrings and ideals redened, Fuzzy Sets and Systems, 81(1996), 383-393.

[3] P. Dheena and G. Mohanraj. (landa; mi)-fuzzy ideals in Semirings, Advances in Fuzzy Mathemat-ics, 6(2)(2011), 183-192.

[4] P. Dheena and G. Mohanraj. On (landa, mi)-fuzzy Prime ideals of semirings, J. Fuzzy Math., 20(4)(2012), 889-898.

[5] Y. B. Jun, M. A. Ozturk and S.Z. Song. On fuzzy h-ideals in hemirings, Information Science, 162(3-4)(2004), 211-226.

[6] D. R. La Torre. On h-ideals and k-ideals in hemirings, Publ. Math. Debrecen, 12(1965), 219-226.

[7] X. Ma and J. Zhan. Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings, Information Sciences, 179(9)(2009), 1249-1268.

[8] G. Mohanraj and E. Prabu. Weakly fuzzy prime ideals of hemiring, International Conference on Mathematical Sciences (ICMS2014), Sathyabama University, Chennai, Conference,
Tamil Nadu, July 17-19 2014, (Vol. 1, pp. 480-483), Elsevier, ISBN-978-93-5107-261-4

[9] G. Mohanraj and E. Prabu. Generalized Fuzzy Right h-Ideals of Hemirings, Inter. J. Fuzzy Math. Archive, 7(2)(2015), 147-155.

[10] G. Mohanraj and E. Prabu. Redefined T-fuzzy right h-ideals of hemirings, Global Journal of Pure and Applied Mathematics, Print ISSN 0973-1768, Volume 12, Number 4, (2016),

[11] G. Mohanraj and E. Prabu. Redefined generalized L-h-bi-ideals of hemirings, (to appear in Fuzzy Information and Engineering).

[12] G. Mohanraj and E. Prabu. Characterizations of generalized fuzzy h-bi-ideals of hemirings by fuzzy sums and products. (to appear in Journal of Fuzzy Mathematics).

[13] G. Mohanraj, D. Krishnasamy and R. Hema. On generalized fuzzy weakly interior ideals of ordered semigroups, Ann. Fuzzy Math. Infor., 8(5)(2014), 803-814.

[14] A. Rosenfeld. Fuzzy groups, J. Math. Anal. Appl., 35(3) (1971), 512-517.

[15] Y. B. Jun, W. A. Dudek, M. Shabir and M. S. Kang. General types of (alfa, beta)-fuzzy ideals of hemirings, Honam Math. J., 32(3)(2010), 413-439.

[16] W.A. Dudek, M. Shabir and R. Anjum. Characterizations of hemirings by their h-ideals, Comput. Math. Appl., 59(9)(2010), 3167-3179.

[17] X. Ma, Y. Yin and J. Zhan. Characterizations of h-intra- and h-quasi-hemiregular hemirings, Comput. Math. Appl., 63(4)(2012), 783-793.

[18] B. Yao. (landa, mi)-fuzzy normal subgroups and (landa, mi)-fuzzy quotients subgroup, J. Fuzzy Math., 13(3)(2005), 695-705.

[19] B. Yao. (lamda, mi)-fuzzy subrings and (landa, mi)-fuzzy ideals, J. Fuzzy Math., 15(4)(2007), 981-987.

[20] L. A. Zadeh. Fuzzy sets, Information and Control, 8(3)(1965), 338-353.

[21] J. Zhan and W. A. Dudek. Fuzzy h-ideals of hemirings, Information Science, 177(3)(2007),