The notion of k-fuzzy ideals of semirings was introduced
by Kim and Park in 1996. In 2003, Dutta and Kar introduced
a notion of ternary semirings. This structure is a generalization of
ternary rings and semirings. The main purpose of this paper is to
introduce and study k-fuzzy ideals in ternary semirings analogous to
k-fuzzy ideals in semirings considered by Kim and Park.
[1] M. Akram and W. A. Dudek, Intuitionistic fuzzy left k-ideals of semirings,
Soft Computing 12 (2008), 881-890.
[2] T. K. Dutta and B. K. Biswas, Fuzzy k-ideals of semirings, Bulletin of
the Calcutta Mathematical Society 87 (1995), 91-96.
[3] T. K. Dutta and S. Kar, On regular ternary semirings, Advances in
Algebra, Proceedings of the ICM Satellite Conference in Algebra and
Related Topics, World Sciencetific, 343-355, 2003.
[4] T. K. Dutta and S. Kar, On the Jacoson radical of a ternary semiring,
Southeast Asian Bulletin of Mathematics 28 (2004), 1-13.
[5] T. K. Dutta and S. Kar, A note on the Jacoson radical of a ternary
semiring, Southeast Asian Bulletin of Mathematics 29 (2005), 321-331.
[6] T. K. Dutta and S. Kar, Two types Jacoson radicals of ternary semirings,
Southeast Asian Bulletin of Mathematics 29 (2005), 677-687.
[7] T. K. Dutta and S. Kar, A note on regular ternary semirings, Kyungpook
Mathematical Journal 46 (2006), 357-365.
[8] S. Ghosh, Fuzzy k-ideals of semirings, Fuzzy Sets and Systems 95 (1998),
103-108.
[9] H. Hedayati, Generalized fuzzy k-ideals of semirings with interval-valued
membership functions, Bulletin of the Malaysian Mathematical Sciences
Society 32 (2009), 409-424.
[10] Y. B. Jun, J. Neggers and H. S. Kim, On L-fuzzy ideals in semirings I,
Czechoslovak Mathematical Journal 48 (1998), 669-675.
[11] S. Kar, On quasi-ideals and bi-ideals in ternary semirings, International
Journal of Mathematics and Mathematical Sciences 2005 (2005), 3015-
3023.
[12] J. Kavikumar and A. B. Khamis, Fuzzy ideals and fuzzy quasi-ideals in
ternary semirings, IAENG International Journal of Applied Mathematics
37 (2007), 102-106.
[13] J. Kavikumar, A. B. Khamis and Y. B. Jun, Fuzzy bi-ideals in ternary
semirings, International Journal of Computational and Mathematical
sciences 3 (2009), 164-168.
[14] C. B. Kim, M. A. Park, k-Fuzzy ideals in semirings, Fuzzy Sets and
Systems 81 (1996), 281-286.
[15] D. H. Lehmer, A ternary analogue of abelian groups, American Journal
of Mathematics 54 (1932), 329-388.
[16] W. G. Lister, Ternary rings, Transaction of American Mathematical
Society 154 (1971), 37-55.
[17] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
[1] M. Akram and W. A. Dudek, Intuitionistic fuzzy left k-ideals of semirings,
Soft Computing 12 (2008), 881-890.
[2] T. K. Dutta and B. K. Biswas, Fuzzy k-ideals of semirings, Bulletin of
the Calcutta Mathematical Society 87 (1995), 91-96.
[3] T. K. Dutta and S. Kar, On regular ternary semirings, Advances in
Algebra, Proceedings of the ICM Satellite Conference in Algebra and
Related Topics, World Sciencetific, 343-355, 2003.
[4] T. K. Dutta and S. Kar, On the Jacoson radical of a ternary semiring,
Southeast Asian Bulletin of Mathematics 28 (2004), 1-13.
[5] T. K. Dutta and S. Kar, A note on the Jacoson radical of a ternary
semiring, Southeast Asian Bulletin of Mathematics 29 (2005), 321-331.
[6] T. K. Dutta and S. Kar, Two types Jacoson radicals of ternary semirings,
Southeast Asian Bulletin of Mathematics 29 (2005), 677-687.
[7] T. K. Dutta and S. Kar, A note on regular ternary semirings, Kyungpook
Mathematical Journal 46 (2006), 357-365.
[8] S. Ghosh, Fuzzy k-ideals of semirings, Fuzzy Sets and Systems 95 (1998),
103-108.
[9] H. Hedayati, Generalized fuzzy k-ideals of semirings with interval-valued
membership functions, Bulletin of the Malaysian Mathematical Sciences
Society 32 (2009), 409-424.
[10] Y. B. Jun, J. Neggers and H. S. Kim, On L-fuzzy ideals in semirings I,
Czechoslovak Mathematical Journal 48 (1998), 669-675.
[11] S. Kar, On quasi-ideals and bi-ideals in ternary semirings, International
Journal of Mathematics and Mathematical Sciences 2005 (2005), 3015-
3023.
[12] J. Kavikumar and A. B. Khamis, Fuzzy ideals and fuzzy quasi-ideals in
ternary semirings, IAENG International Journal of Applied Mathematics
37 (2007), 102-106.
[13] J. Kavikumar, A. B. Khamis and Y. B. Jun, Fuzzy bi-ideals in ternary
semirings, International Journal of Computational and Mathematical
sciences 3 (2009), 164-168.
[14] C. B. Kim, M. A. Park, k-Fuzzy ideals in semirings, Fuzzy Sets and
Systems 81 (1996), 281-286.
[15] D. H. Lehmer, A ternary analogue of abelian groups, American Journal
of Mathematics 54 (1932), 329-388.
[16] W. G. Lister, Ternary rings, Transaction of American Mathematical
Society 154 (1971), 37-55.
[17] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51582", author = "Sathinee Malee and Ronnason Chinram", title = "k-Fuzzy Ideals of Ternary Semirings", abstract = "The notion of k-fuzzy ideals of semirings was introduced
by Kim and Park in 1996. In 2003, Dutta and Kar introduced
a notion of ternary semirings. This structure is a generalization of
ternary rings and semirings. The main purpose of this paper is to
introduce and study k-fuzzy ideals in ternary semirings analogous to
k-fuzzy ideals in semirings considered by Kim and Park.", keywords = "k-ideals, k-fuzzy ideals, fuzzy k-ideals, ternarysemirings", volume = "4", number = "7", pages = "802-5", }
