Image dan Pre-Image Anti-Homomorfisma Pada Subgrup Fuzzy

Miftah Sigit Rahmawati, Dr. Budi Surodjo, M.Si

2012 | Tesis | S2 Matematika

Himpunan X yang dikenai suatu fungsi karakteristik dikenal dengan istilah subset fuzzy. Pada grup X, konsep subset fuzzy berkembang menjadi subgrup fuzzy yang memenuhi dua aksioma. Dalam subgrup fuzzy dikenal level subgrup yang mempunyai sifat tertentu. Berdasarkan kesamaan sifat yang dimiliki oleh homomorfisma grup dan anti-homomorfisma grup, dalam tesis ini diselidiki sifatsifat yang ada pada subgrup fuzzy terkait dengan image dan pre-image antihomomorfisma subgrup fuzzy. Diawali dengan beberapa sifat homomorfisma dan anti-homomorfisma level subgrup dari subgrup fuzzy, selanjutnya diselidiki beberapa sifat anti-homomorfisma subgrup fuzzy normal dan subgrup Abel fuzzy.

For all arbitrary set X with characteristic functions, is known as fuzzy subsets. On group X, fuzzy subsets can be defined as fuzzy subgroups appropriate with some axioms. In fuzzy subgroup there is sub set with some properties that known as level subgroups of fuzzy subgroup. Of common properties on homomorphism and anti-homomorphism groups, we investigated that properties exist on fuzzy subgroups. The properties associated with the image and pre-image anti-homomorphism of fuzzy subgroups. We started from properties of homomorphism and anti-homomorphism level subgroups of fuzzy subgroups. Futhermore, we investigated some properties associated the image and pre-image an anti-homomorphism of normal fuzzy subgroups and fuzzy abelian subgroups.

Kata Kunci : image,pre-image,anti-hormomorisma,fussy