Subgrup Normal Multi-Fuzzy, Subgrup Normal Multi-Anti Fuzzy, dan Teorema Korespondensi

https://doi.org/10.22146/jmt.52857

Amaluddin Amaluddin(1*), Budi Surodjo(2)

(1) Universitas Gadjah Mada
(2) Universitas Gadjah Mada
(*) Corresponding Author

Abstract


Pada sebarang grup dapat dibentuk subgrup normal multi-fuzzy dan subgrup normal multi-anti fuzzy. Pada tulisan ini, dikaji sifat-sifat subgrup normal multi-fuzzy dan subgrup normal multi-anti fuzzy. Berdasarkan struktur tersebut, dikonstruksi grup faktor relatif terhadap subgrup normal multi-fuzzy atau subgrup normal multi-anti fuzzy. Lebih lanjut, dibuktikan bahwa jika f : G1 → G2 merupakan epimorfisma grup, maka terdapat korespondensi satu-satu antara subgrup-subgrup normal multi-anti fuzzy pada G2 dan pada G1 yang bernilai konstan pada kernel f. Terakhir, dengan menggunakan epimorfisma f, diberikan suatu isomorfisma grup antara dua grup faktor relatif terhadap subgrup normal multi-anti fuzzy.


Keywords


Multi-fuzzy subgroup; multi-anti fuzzy subgroup; normal multi-fuzzy sub-group; normal multi-anti fuzzy subgroup; multi-fuzzy coset

Full Text:

PDF Amaluddin


References

[1] Biswas, R., Fuzzy subgroups and anti fuzzy subgroups, Fuzzy Sets and Systems, 35 ( 1990), 121-124.
[2] Liu, Y. L., Quotient groups induced by fuzzy subgroups, Quasigroups and Related Systems, 11 (2004), 71-78.
[3] Mukherjee, N. P., dan Bhattacharya, P., Fuzzy normal subgroups and fuzzy cosets, Information Sciences, 34 (1984), 225-239.
[4] Muthuraj, R., dan Balamurugan, S., Multi-fuzzy group and its level subgroups, Gen. Math. Notes, 17 (2013), 74-81.
[5] Muthuraj, R., dan Balamurugan, S., Multi-anti fuzzy group and its lower level subgroups, Inter- national Journal of Engineering Research and Applications, 3 (2013), 1498-1501.
[6] Muthuraj, R., dan Balamurugan, S., Some characterization of normal multi-fuzzy and normal multi-anti fuzzy subgroup, IOSR Journal of Mathematic, 10 (2014), 116-122.
[7] Muthuraj, R., dan Balamurugan, S., Correspondence theorem for normal multi-anti fuzzy sub- groups, Discovery, 21 (2014), 113-117.
[8] Muthuraj, R., dan Balamurugan, S., A study on multi-fuzzy cosets, International Journal of Engineering Associates, 5 (2016), 1-7.
[9] Rosenfeld, A., Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.

[10] Sabu, S., dan Ramakrishnan, T. V., Multi-fuzzy sets, International Mathematical Forum, 50 (2010), 2471-2476.

[11] Sabu, S., dan Ramakrishnan, T. V., Multi-fuzzy subgroups, Int. J. Contemp. Math. Sciences,6 (2011), 365-372.

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



DOI: https://doi.org/10.22146/jmt.52857

Article Metrics

Abstract views : 2202 | views : 2415

Refbacks



Copyright of Jurnal Matematika Thales ISSN 2715-1891 (Print).

Jumlah Kunjungan: View My Stats


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

JMT Indexed by: