Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33090
k-Fuzzy Ideals of Ternary Semirings
Authors: Sathinee Malee, Ronnason Chinram
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
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1057241
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1812References:
[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.