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INDONESIA
Jurnal Fourier
Published by Universitas Islam Negeri Sunan Kalijaga Yogyakarta
ISSN : -     EISSN : -     DOI : -
Core Subject : Economy, Science, Education,
Computer Science & IT Economics, Econometrics & Finance Education Mathematics
FOURIER adalah Jurnal Ilmiah bidang yang memadukan dan mengembangkan ilmu Matematika dan pembelajarannya yang diintegrasikan dan interkoneksikan dengan nilai-nilai keislaman terbit sejak tahun 2012 dengan frekuensi terbit 2 kali dalam setahun yang dengan bahasa utama (Bahasa Indonesia dan Bahasa Inggris) yang proses reviewernya sesuai dengan disiplin ilmunya (Analisis, Aljabar, Matematika Terapan, Statistika, dan Pendidikan Matematika).
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Articles 1 Documents
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Search results for , issue "Vol. 11 No. 1 (2022)" : 1 Documents clear
Ideal Fuzzy Semiring Atas Level Subset Saman Abdurrahman
Jurnal Fourier Vol. 11 No. 1 (2022)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2022.111.1-6

Abstract

Semiring merupakan salah satu perluasan dari ring, dengan cara menghilangan salah satu aksioma pada operasi pertama yaitu aksioma invers. Pada semiring terdapat konsep subsemiring dan ideal dengan kondisi bahwa setiap ideal semiring adalah selalu subsemiring. Tetapi kondisi kebalikannya belum tentu berlaku. Selain konsep subsemiring dan ideal semiring, pada struktur semiring diperkenalkan konsep homomorfisma semiring. Kondisi ini, analog dengan homomorfisma di ring, sehingga sifat-sifat yang ada pada semiring dapat dinduksi dari sifat - sifat di ring, seperti konsep image dan preimage di bawah homomorfisma semiring analog dengan konsep image dan preimage di bawah homomorfisma ring. Konsep ideal pada semiring jika dipadukan dengan konsep fuzzy, akan menghasilkan konsep baru, yaitu konsep ideal fuzzy semiring. Pada makalah ini, akan diperkenalkan konsep ideal fuzzy semiring, image dan preimage ideal fuzzy dari suatu homomorfisma semiring. Lebih lanjut, akan diselidiki sifat-sifat ideal fuzzy semiring, image dan preimage ideal fuzzy dibawah homomorfisma semiring melalui suatu level subset. [Semiring is one of the extensions of the ring by disappearing one of the axioms in the first operation, namely the inverse axiom. In semiring, there is the concept of subsemiring and ideal with the condition that every ideal semiring is always subsemiring. However, the opposite condition does not necessarily apply. In addition to the concept of subsemiring and the ideal of a semiring, in the semiring structure was introduced the concept of semiring homomorphism. This condition is analogous to the homomorphism in the ring so that the properties present in the semiring can be induced from the properties in the ring, such as the concept of image and preimage under the homomorphism of semiring analogous to the concept of image and preimage under the homomorphism of the ring. If combined with the fuzzy concept, the ideal concept in semiring will produce a new concept, namely the ideal concept of fuzzy semiring. This paper will introduce the concept of an ideal fuzzy semiring, image, and preimage ideal fuzzy from a semiring homomorphism. Furthermore, the properties of the fuzzy ideal semiring, image, and preimage of the fuzzy ideal will be investigated under the semiring homomorphism through a subset level.]

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