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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Majalah Ilmiah Matematika dan Statistika (MIMS) Journal of Fundamental Mathematics and Applications (JFMA)
Agusfrianto, Fakhry Asad
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Decision Sciences, Operations Research & Management Mathematics

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ROUGH RINGS, ROUGH SUBRINGS, AND ROUGH IDEALS Agusfrianto, Fakhry Asad; Fitriani, Fitriani; Mahatma, Yudi
Journal of Fundamental Mathematics and Applications (JFMA) Vol 5, No 2 (2022)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v5i2.15194

Abstract

The basic concept in algebra that is set theory can be expanded into rough sets. Basic operations on the set such as intersections, unions, differences, and complements can still apply to rough sets. In addition, one of the applications of rough sets is the use of rough matrices in decision making. Furthermore, mathematical or informatics researchers who work on rough sets connect the concept of rough sets with algebraic structures (groups, rings, and modules) so that a concept called rough algebraic structures is obtained. Since the research related to rough sets is mostly carried out at the same time, different concepts have emerged related to rough sets and rough algebraic structures. In this paper, other definitions of rough ring and rough subring will be given along with related examples and theorems. Furthermore, it will also be defined the left ideal and the right ideal of the rough ring along with examples. Finally, we will discuss the theorem regarding rough ideals.
Modifikasi algoritma Hill cipher dengan matriks kunci berupa matriks ketetanggaan Agusfrianto, Fakhry Asad; Ambarwati, Lukita; Mahatma, Yudi
Majalah Ilmiah Matematika dan Statistika Vol. 23 No. 2 (2023): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v23i2.36346

Abstract

Cryptography is one of the parts in mathematics, especially applied mathematics. Cryptography is the science that studies how to secure information that we don't want others to know about the information we have. Based on the development of the times, cryptography is divided into two consisting of classical cryptography and modern cryptography. In this paper, the focus of discussion is on classical cryptography. Furthermore, there are many kinds of classical cryptographic algorithms, such as the Caesar cipher algorithm, the Playfair cipher algorithm, the Vigenere cipher algorithm, and the Hill Cipher algorithm. The focus of discussion in this paper is on the Hill cipher algorithm. The modifications made to the Hill cipher algorithm lie in its key matrix. In this paper, it will be shown how to encrypt and decrypt the message we want to send using the Hill cipher algorithm with the matrix being a adjacency matrix. In which case, the adjacency matrix itself is obtained from the representation of the graph. It is hoped that this algorithm can avoid crypt attacks, especially on ciphertext only-attack.Keywords: Hill cipher algorithm, cryptography, adjacency matrix, plaintext, ciphertextMSC2020: 94A60
Hyperstructures in Chemical Hyperstructures of Redox Reactions with Three and Four Oxidation States Agusfrianto, Fakhry Asad; Andromeda, Sonea; Hariri, Mariam
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i1.17011

Abstract

Hyperstructures find numerous applications across various disciplines. One notable application is in chemistry, particularly in the context of chemical reactions. In 2014, Davvaz introduced the concept of bi-hyperstructures, but their application specifically in chemical reactions, has yet to be thoroughly explored in previous studies. Thus, the primary aim of this paper is to examine and analyze the different types of bi-hyperstructures present within chemical hyperstructures. The scope of this study focuses on two types of chemical hyperstructures: redox reactions and reactions in electrochemical cells. Within these chemical hyperstructures, we investigate the possibility of bi-hyperstructures among bi-semihypergroups, bi-hypergroups, bi-H_v-semigroups, and bi-H_v-groups. Next, some properties of bi-hyperstructures related to hyperstructures are also investigate.
Co-Authors Andromeda, Sonea Fitriani Fitriani Hariri, Mariam Lukita Ambarwati Mahatma, Yudi