STRUKTUR SEMIGRUP DAN IDEAL KOMUTATIF DARI BCK-ALJABAR BERDASARKAN STRUKTUR HIMPUNAN KUBIK PERSILANGAN
SEMIGROUP AND IDEAL COMMUTATIVE STRUCTURES OF BCK-ALGEBRA BASED ON THE STRUCTURE OF CUBIC CROSSING SET
Himpunan fuzzy merupakan alat yang berguna untuk pengolahan informasi positif, tetapi memiliki keterbatasan dalam pengolahan informasi negatif. Struktur himpunan kubik persilangan dibangun dari himpunan fungsi bernilai interval dan himpunan fungsi bernilai negatif. Struktur semigrup dibangun dengan operasi biner pada struktur himpunan kubik persilangan. Konsep ideal kubik persilangan komutatif diperkenalkan dengan menerapkan struktur himpunan kubik persilangan pada ideal komutatif dalam BCK-Aljabar, dan beberapa sifat diselidiki. Hubungan antara ideal kubik persilangan dan ideal kubik persilangan komutatif dibahas. Sebuah contoh untuk menunjukkan bahwa ideal kubik persilangan tidak bersifat komutatif diberikan dan kemudian syarat-syarat agar ideal kubik persilangan dapat menjadi ideal kubik persilangan komutatif dieksplorasi. Karakterisasi ideal kubik persilangan komutatif dibahas dan hubungan antara ideal kubik persilangan komutatif dan himpunan level kubik persilangan dibicarakan.
Kata Kunci: Himpunan Fuzzy, Kubik persilangan, BCK-Aljabar
Fuzzzy sets are a useful tool for processing positive information, but have limitations in processing negative information. The structure of a crossed cubic set is built from a set of interval-valued functions and a set of negative-valued functions. The semigroup structure is built with binary operations on the crossed cubic set structure. The concept of commutative crossed cubic ideals is introduced by applying the structure of crossed cubic sets to commutative ideals in BCK-Algebra, and several properties are investigated. The relationship between the crossed cubic ideal and the commutative crossed cubic ideal is discussed. An example to show that a crossing cubic ideal is not commutative is given and then the conditions for a crossing cubic ideal to be a commutative crossing cubic ideal are explored. The characterization of the commutative crossing cubic ideal is discussed and the relationship between the commutative crossing cubic ideal and the set of crossing cubic levels is discussed.
Keywords: Fuzzy sets, crossover cubic, BCK-Algebra