Semigrup Prima Fuzzy Penuh

ABDURAHIM, Dr. Yeni Susanti, M.Si.

2015 | Tesis | S2 Matematika

Fungsi keanggotaan fuzzy merupakan fungsi yang memetakan himpunan tak kosong X ke interval tertutup [0,1]. Selanjutnya, jika domain fungsi tersebut diganti dengan semigrup, maka fungsi tersebut dinamakan subhimpunan fuzzy. Subhimpunan fuzzy yang memetakan S ke 1 dinotasikan dengan C_S. Subhimpunan fuzzy f disebut ideal fuzzy jika memenuhi C_S o f subset f dan f o C_S subset f. Selanjutnya f disebut ideal prima fuzzy jika untuk setiap ideal fuzzy g dan h yang memenuhi g o h subset f berakibat g subset f atau h subset f. Lebih jauh, semigrup prima fuzzy penuh merupakan semigrup yang setiap ideal fuzzynya merupakan ideal prima fuzzy. Selanjutnya, pada tesis ini akan diteliti karakteristik dari ideal prima fuzzy. Kemudian akan diteliti juga karakteristik dari semigrup prima fuzzy penuh dan karakteristik untuk semigrup yang setiap ideal kanan fuzzynya merupakan ideal kanan prima fuzzy.

A fuzzy membership function is a function that maps the nonempty set $X$ to a closed interval [0,1]. Furthermore, if the function domain is replaced with a semigroup, then the function is called fuzzy subset. A fuzzy subset mapping S to 1 is denoted by C_S. A fuzzy subset f is called fuzzy ideal if it satisfies both C_S o subset f and f o C_S subset f. Moreover, f is called a fuzzy prime ideal if for any fuzzy ideal g and h, with g o h subset f implies g subset f or h subset f. Furthermore, a fully fuzzy prime semigroup is a fuzzy semigroup which its ideals are fuzzy prime ideal. Furthermore, in this paper be investigated about some characteristics of prime fuzzy ideals. In this paper will also be investigated the characteristics of fully fuzzy prime semigroups and semigroups which any of its fuzzy right ideal is prime.

Kata Kunci : semigrup, fuzzy, ideal fuzzy, ideal prima fuzzy, ideal kanan prima fuzzy, semigrup prima fuzzy penuh.