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Journal of Fundamental Mathematics and Applications (JFMA)
Published by Universitas Diponegoro
ISSN : 26216019     EISSN : 26216035     DOI : https://doi.org/10.14710
Core Subject : Science,
Decision Sciences, Operations Research & Management
Journal of Fundamental Mathematics and Applications (JFMA) is an Indonesian journal published by the Department of Mathematics, Diponegoro University, Semarang, Indonesia. JFMA has been published regularly in 2 scheduled times (June and November) every year. JFMA is established to highlight the latest update of mathematical researches in both theoretical and applied works. The scope in JFMA is pure mathematics and applied mathematics. All accepted papers will be published both in print and online versions. The online version can be accessed via the DOI link of each article. The print version can be ordered to the journal administrator. JFMA welcomes both theoretical and applied research work to be published in the journal. The topics include but are not limited to: (1) Mathematical analysis and geometry (2) Algebra and combinatorics (3) Discrete Mathematics (4) Mathematical physics (5) Statistics (6) Numerical method and computation (7) Operation research and optimization (8) Mathematical modeling (9) Mathematical Logic in Computer Science, Informatics, etc.
Arjuna Subject : Matematika - Matematika Terapan
Articles 135 Documents
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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.
PENGARUH FAKTOR KLAIM COVID-19 DALAM PENENTUAN MODEL KERUGIAN AGREGAT PADA ASURANSI KESEHATAN MANFAAT RAWAT JALAN BERDASARKAN SIMULASI Indah Kristin Utami; Leopoldus Ricky Sasongko; Tundjung Mahatma
Journal of Fundamental Mathematics and Applications (JFMA) Vol 5, No 1 (2022)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v5i1.14306

Abstract

Abstract. Risk might happen at any time; it demands human to have protection, which can be achieved through insurance. In health insurance, there are two types of benefits, namely inpatient and outpatient. Outpatient health insurance benefit is considered for health treatment without hospitalization. In Covid-10 pandemic time, the insurance company should include decrement of Covid-19 in its cost and can use aggregate loss distribution model. The cost spend by the company can be used to calculate the premium. The data used were in the parameter form and were based on the secondary data from various sources. Those parameters were used to calculate the premium based on simulation. There were two focuses in this research, namely the health insurance of outpatient benefit with the additional of Covid-19 patients with random cost and fixed cost. Those two aspects did not show significant differences on the premium between the simulation with including Covid-19 risk or excluding Covid-19 risk, and the loss aggregate distribution model was normally distributed.Abstrak. Risiko yang dapat terjadi sewaktu-waktu menuntut manusia untuk mempunyai sebuah perlindungan, yang mana perlindungan tersebut dapat diperoleh melalui asuransi. Dalam asuransi terdapat asuransi kesehatan yang tergolong setidaknya menjadi dua manfaat yaitu manfaat rawat inap dan manfaat rawat jalan. Asuransi kesehatan manfaat rawat jalan merupakan manfaat asuransi yang menanggung biaya terhadap suatu rangkaian perawatan kesehatan yang tidak memerlukan opname. Dalam menghitung besar biaya yang harus dikeluarkan oleh perusahaan asuransi, digunakan penambahan decrement Covid-19 dan model distribusi kerugian aggregat. Biaya yang dikeluarkan perusahaan dapat digunakan untuk menghitung premi. Data yang digunakan merupakan data dalam bentuk parameter yang ditetapkan, yang mana parameter diperoleh berdasarkan data sekunder dari berbagai sumber. Parameter-parameter tersebut digunakan untuk melakukan penghitungan premi berdasarkan simulasi. Terdapat dua kasus yang menjadi fokus penelitian, yaitu asurasni kesehatan manfaat rawat jalan dengan penambahan penyebab covid dengan biaya acak dan tetap. Dari ke-2 kasus tidak menunjukkan perbedaan premi yang besar menunjukkan perbedaan kerugian agregat antara model simulasi dengan Covid-19 dan tanpa Covid-19, serta diperoleh model distribusi kerugian aggregat yaitu distribusi normal.
GENERALIZED NON-BRAID GRAPHS OF RINGS Cahyati, Era Setya; Maharani, Rambu Maya Imung; Nurhayati, Sri; Susanti, Yeni
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.v5i2.14152

Abstract

In this paper, we introduce the definition of generalized non-braid graph of a given ring. Let $R$ be a ring and let $k$ be a natural number. By generalized braider of $R$ we mean the set $B^k(R):=\{x \in R~|~\forall y \in R,~ (xyx)^k = (yxy)^k\}$. The generalized non-braid graph of $R$, denoted by $G_k(\Upsilon_R)$, is a simple undirected graph with vertex set $R\backslash B^k(R)$ and two distinct vertices $x$ and $y$ are adjacent if and only if $(xyx)^k \neq (yxy)^k$. In particular, we investigate some properties of generalized non-braid graph $G_k(\Upsilon_{\mathbb{Z}_n})$ of the ring $\mathbb{Z}_n$.
Ruang Barisan Selisih Diperumum Tipe Cesaro pada Ruang Bernorma-n Ahmad, Mizan; Aspriyani, Riski
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.v5i2.15747

Abstract

Pada tulisan ini dibahas mengenai beberapa kelas ruang barisan selisih diperumum Cesaro pada ruang bernorma-n. Diselidiki kelengkapan masing-masing kelas dan hubungan antar kelas. Pada akhir tulisan ini, dikonstruksikan dual Kothe-Toeplitz dari beberapa ruang barisan selisih diperumum Cesaro pada ruang bernorma-n.
ESTIMASI PARAMETER MODEL ARCH MENGGUNAKAN METODE BAYES Dewi, Mila Setia; Sutarman, Sutarman
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.v5i2.15029

Abstract

 Penelitian ini bertujuan menaksir parameter model ARCH menggunakan Metode Bayes kemudian akan dibandingkan dengan metode Maksimum Likelihood. Pada metode Bayes distribusi prior digabungkan dengan fungsi Likelihood untuk memperoleh distribusi posterior, yang akan menjadi dasar dalam inferensi. Pemilihan prior yang berbeda akan menghasilkan inferensi yang berbeda pula. Distribusi prior yang digunakan dalam penelitian ini adalah prior berdistribusi eksponensial. Setelah distribusi posterior diperoleh, dilakukan simulasi Markov Chain Monte Carlo dengan menggunakan Algoritma Metropolist-Hasting. Dari hasil simulasi MCMC tersebut diperoleh estimator model ARCH menggunakan metode Bayes dan kemudian dibandingkan dengan estimator model ARCH menggunakan metode Maksimum Likelihood. Berdasarkan penelitian ini diketahui bahwa dengan menggunakan data yang sama nilai mean residual dan standard error menggunakan metode Bayes lebih kecil dibandingkan metode Maksimum Likelihood.  Hasil mean residual dan standard error menggunakan metode Bayes adalah 0,4372 dan 0,0272. Sedangkan Mean residual dan standard error menggunakan metode Maksimum Likelihood adalah 0,9166 dan 0,0456. Dari hasil tersebut dapat dilihat bahwa estimasi parameter menggunakan metode Bayes baik digunakan pada model ini.
DIAMETER DAN GIRTH GRAF NILPOTEN RING MATRIKS Fibriyanti, Regita Agustin Wahyu; Wijayanti, Indah Emilia
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.v5i2.15576

Abstract

Diberikan suatu graf sederhana $G$. Diameter graf $G$ merupakan jarak terbesar sebarang dua titik $u,v$ di $G$. \textit{Girth} graf $G$ adalah panjang sikel terpendek di graf $G$. Misalkan $R$ suatu ring dengan elemen satuan. $N(R)$ merupakan himpunan nilpoten di $R$. ${Z_N}(R)$ merupakan himpunan semua $x$ di $R$ dengan $xy$ nilpoten pada $R$, untuk $y$ di $R^*$. Graf nilpoten, ${\Gamma _N}(R)$, merupakan graf dengan himpunan titiknya adalah ${Z_N}{(R)^ * }$, dan dua titik yang berbeda $x,y$ bertetangga jika dan hanya jika $xy$ nilpoten di $R$. Pada tulisan ini diberikan beberapa karakterisasi terkait diameter dan \textit{girth} graf nilpoten pada ring matriks atas lapangan $F$. Diberikan lapangan $F$, diameter graf $\left( {{\Gamma _N}\left( {{M_n}\left( F \right)} \right)} \right)$ adalah $2$, untuk $n \geq 3$ dan diameter graf $\left( {{\Gamma _N}\left( {{M_2}\left( F \right)} \right)} \right)$ adalah $3$. Serta jika $F$ suatu lapangan dan $n \geq 2$, maka girth graf $\left( {{\Gamma _N}\left( {{M_n}\left( F \right)} \right)} \right)$ adalah $3$.
ANALISIS PERBANDINGAN METODE ARIMA DAN DOUBLE EXPONENTIAL SMOOTHING DARI BROWN PADA PERAMALAN INFLASI DI INDONESIA Saragih, Shella Melati; Sembiring, Pasukat
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.v5i2.15312

Abstract

Penelitian ini bertujuan untuk mendapatkan metode peramalan terbaik dalam memprediksi inflasi di Indonesia dengan membandingkan metode ARIMA dan Double Exponential Smoothing dari Brown. Data yang digunakan adalah data inflasi di Indonesia selama 8 tahun, mulai dari Januari 2014 sampai Desember 2021. Data yang akan diolah adalah data pada periode Januari 2014 sampai September 2021, sedangkan data lainnya akan digunakan untuk melihat deviasi pada peramalan. Analisis dilakukan terhadap pola data inflasi, horizon waktu peramalan, tingkat akurasi, serta penggunaan dari masing-masing metode. Berdasarkan penelitian ini, diketahui bahwa data inflasi yang digunakan mengandung pola trend menurun. Selain itu, periode hasil prediksi dari kedua metode tersebut paling efektif dalam melakukan peramalan jangka pendek (kurang dari 3 bulan). Hasil prediksi inflasi menggunakan metode ARIMA memperoleh MAPE sebesar 15,163%. Sedangkan hasil prediksi inflasi menggunakan metode Double Exponential Smoothing dari Brown memperoleh MAPE sebesar 5,068132%. Kesimpulan yang diperoleh yaitu metode Double Exponential Smoothing dari Brown lebih baik digunakan untuk peramalan jangka pendek inflasi di Indonesia dibandingkan dengan metode ARIMA karena menghasilkan nilai Mean Absolute Percentage Error (MAPE) yang lebih kecil serta memiliki waktu komputasi yang lebih cepat dibandingkan ARIMA. 
FRACTIONAL MATHEMATICAL MODEL OF HIV AND CD4+ T-CELLS INTERACTIONS WITH HAART TREATMENT Nisardi, Muhammad Rifki; Kasbawati, Kasbawati; Putra, Restu Ananda
Journal of Fundamental Mathematics and Applications (JFMA) Vol 6, No 1 (2023)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i1.17174

Abstract

This study provides the mathematical model of the interaction between the HIV and CD4+ T cells. This research develops other research by formulating a model with the fractional Caputo derivative approach with fractional order α. Based on the model, we obtain the equilibrium point and analyze the stability criterion of the equilibrium point. Furthermore, we perform the Next Generation Matrix method to calculate the basic reproduction number. Then, we apply the Grunwald-Letnikov Explicit method to show the numerical result of the model.
A PYTHON CODE FOR GENERATING ALL PROPER SUBGROUPS OF DIHEDRAL GROUP Syarifudin, Abdul Gazir; Wijaya, Verrel Rievaldo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 6, No 1 (2023)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i1.15939

Abstract

The dihedral group of order 2n denoted by D_2n is the symmetry group of a regular -polygon consisting of rotation and reflection elements and the composition of both elements. Like any other group, the dihedral group also have a subgroup whose numbers differs depending on the value of n. This research is conducted by studying past literature and explore a new development to a theory. In this paper, all the form of proper subgroups of D_2n will be given and all of these proper subgroups of D_2n will be generated and counted with the help of Python program.
CLUSTERING LARGE APPLICATION USING METAHEURISTICS (CLAM) FOR GROUPING DISTRICTS BASED ON PRIMARY SCHOOL DATA ON THE ISLAND OF SUMATRA As-shofa, Naura Ghina; Lestari, Vemmie Nastiti
Journal of Fundamental Mathematics and Applications (JFMA) Vol 6, No 1 (2023)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i1.16468

Abstract

K-medoids is one of the partitioning methods with the medoid as its center cluster, where medoid is the most centrally located object in a cluster, which is robust to outliers. The k-medoids algorithm used in this study is Clustering Large Application Using Metaheuristics (CLAM), where CLAM is a development of the Clustering Large Application based on Randomized Search (CLARANS) algorithm in improving the quality of cluster analysis by using hybrid metaheuristics between Tabu Search (TS) and Variable Neighborhood Search (VNS). In the case study, the best cluster analysis method for classifying sub-districts on the island of Sumatra based on elementary school availability and elementary school process standards is the CLAM method with k=6, num local = 2, max neighbor = 154, tls = 50 and set radius = 100-10:5. It can be seen that based on the overall average silhouette width value, the CLAM method is better than the CLARANS method.

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