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

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

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