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Jurnal Matematika UNAND
Published by Universitas Andalas
ISSN : 2303291X     EISSN : 27219410     DOI : -
Core Subject : Science, Education,
Computer Science & IT Mathematics
Fokus dan Lingkup dari Jurnal Matematika FMIPA Unand meliputi topik-topik dalam Matematika sebagai berikut : Analisis dan Geometri Aljabar Matematika Terapan Matematika Kombinatorika Statistika dan Teori Peluang.
Arjuna Subject : -
Articles 858 Documents
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ON HEREDITARY NOETHERIAN AND PRIME MODULES OVER LEAVITT PATH ALGEBRA: SINK AND INFINITE EMITTER Risnawita, Risnawita; GEMA HISTA MEDIKA; ANANDA, TRIYARDI GUSTI
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.390-399.2025

Abstract

This study explores the structural and homological characteristics of left modules over Leavitt path algebras, focusing on those generated by specific vertex types in a directed graph, particularly sinks and infinite emitters. The paper examines the module \( L_K(E)u \), where \( u \in E^0 \) represents either a sink or an infinite emitter, and determines whether this module exhibits the properties of being hereditary, Noetherian, and prime. Our findings indicate that \( L_K(E)u \) is indeed hereditary, implying that all its submodules are projective. Additionally, the module satisfies the ascending chain condition, making it Noetherian. However, it fails to qualify as an a-prime module, since there exist nontrivial left ideals \( I \subsetneq L_K(E) \) for which \( IM \subsetneq M \), thus does not meet the criteria for primality. These results emphasize how the presence of sinks and infinite emitters significantly affects the module-theoretic behavior of Leavitt path algebras.
Performance of Prediction Interval Estimators based on Random Forest Models with Correlated Predictors Ilma, Meisyatul; Sartono, Bagus; Wijayanto, Hari
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.320-332.2025

Abstract

Uncertainty in prediction results is a crucial aspect that needs to be taken into account in regression modeling, especially when there is a high correlation between explanatory variables. This study aims to evaluate the performance of three prediction interval formation approaches, namely Out-of-Bag Prediction Interval (OOB-PI), Quan tile Regression Forest (QRF), and Split Conformal Prediction (SC), in Random Forest modeling. The evaluation was conducted through a simulation study with a variety of data structures, including the level of correlation between variables, the shape of the mean function, and the type of error distribution. Further validation was conducted using data from the National Socio-Economic Survey (SUSENAS) of West Java Province in 2023. The results show that increasing the correlation between explanatory variables can improve the efficiency and accuracy of prediction interval estimation. Overall, OOB-PI showed the most balanced performance compared to the other two methods, with a prediction coverage rate close to 90% and a narrower interval width than QRF and SC. This finding indicates that OOB-PI is an adaptive and efficient approach for various data structures, including socioeconomic data with highly correlated predictors.
New Entropy Pythagorean Fuzzy Set And Its Application In Multicriteria Decision Making Munandar, Arif
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.439-450.2025

Abstract

In this study, a new entropy measure for Pythagorean fuzzy sets is proposed. The validity of the entropy is rigorously verified through the satisfaction of keyaxiomatic properties such as minimality, maximality, symmetry, and resolution. Oncevalidated, the newly developed entropy is applied to a multi-criteria decision-making(MCDM) problem using the TOPSIS method. The integration of this entropy with TOPSIS provides a robust and systematic approach to determining optimal alternatives indecision-making scenarios involving uncertainty and imprecision. The proposed methodenhances the ability to model and analyze complex problems, thereby contributing a noveland effective tool to the field of fuzzy decision-making
SOFT GRAPHS OF THE BARBELL STAR GRAPH Helmi, Monika Rianti; Sy, Syafrizal; Nazra, Admi; Muhafzan; Hanifa, Nurul; Alfiany, Noverina
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.366-375.2025

Abstract

\textit{Let $G^*=(V(G^*),E(G^*))$ is a simple graph and $A$ be a non-empty set of parameter. Let $R\subseteq A\times V(G^*)$ be a arbitrary relation from $A$ to $V(G^*)$. A mapping $F:A\to P(V(G^*))$ can be defined as $F(x)=\left\{y\in V\mid xRy \right\}$ and a mapping $K:A\to P(E(G^*))$ can be defined as $K(x)=\left\{uv\in E\mid \left\{u,v\right\}\subseteq F(x)\right\}$. A pair $(F,A)$ and $(K,A)$ are soft sets over $V(G^*)$ and $E(G^*)$ respectively, then $(F(a),K(a))$ is a subgraph of $G^*$. The 4-tuple $G=(G^*,F,K,A)$ is called a soft graph of $G$. In this paper, we enumerate soft graph of amalgamation of path and star.}
AN EXPLAINABLE HYBRID AI FRAMEWORK USING FUZZY ROUGH SET RULES FOR MENTAL HEALTH PREDICTION Rustam, Rustam
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.341-354.2025

Abstract

The increasing use of artificial intelligence (AI) in mental health prediction highlights the need for models that are not only accurate but also mathematically interpretable and theoretically grounded. This paper presents a mathematical modeling framework for explainable AI that integrates the K-Nearest Neighbors (KNN) algorithm with rule induction based on fuzzy rough set theory. The proposed hybrid framework is formulated to combine statistical classification with symbolic reasoning, providing transparent post hoc explanations through a set of fuzzy linguistic rules. A large-scale mental health dataset is utilized, comprising behavioral, psychological, and lifestyle attributes, with "coping struggles" as the target classification variable. The mathematical formulation of the fuzzy rough set-based rule induction is explicitly defined using fuzzy similarity relations, lower and upper approximations, and soft rule matching with tunable thresholds. Performance evaluation demonstrates that the hybrid model achieves 94.5% accuracy, 87.7% precision, 100% recall, and 93.4% F1-score, while also producing high-coverage fuzzy rules that align closely with the base KNN predictions. Comparative analysis with a traditional fuzzy inference system (FIS) reveals the superior scalability and fidelity of the proposed method, particularly in high-dimensional feature spaces. This work contributes a modular and mathematically rigorous approach to explainable AI, offering potential applications in clinical screening, early intervention, and intelligent decision support for mental health.
AUTOMORPHISM GROUPS IN LOTUS GRAPH AND UNIFORM BOW GRAPH Khotimah, Husnul; Dewi, Novi Rustiana
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.311-319.2025

Abstract

This research aims to explore the connection between abstract algebraand graph theory through the study of lotus graph and uniform bow graph. The focus ison determining all automorphisms of both graphs and analyzing the algebraic structurethey form. It is shown that the set of automorphisms, under composition, satisfies thegroup axioms, thus illustrating a natural link between group theory and graph theory.Keywords: Automorphism group, lotus graph, uniform bow graph.
Mathematical Analysis of Sexual Violence Dynamics with Recidivist Perpetrators Zakiyyah, Abqorry; Bahri, Susila; Putri, Arrival Rince
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.411-423.2025

Abstract

Sexual violence remains a serious social issue with far-reaching consequences for both victims and society at large. To capture the dynamics of its spread, this study develops a compartmental mathematical model that divides the population into four subgroups: susceptible individuals ($S$), perpetrators ($V$), punished offenders ($P$), and rehabilitated individuals ($R$). The model incorporates a recidivist parameter, representing the tendency of punished individuals to relapse into offending, that is return from the $P$ to the $V$ class. The analysis includes the determination of equilibrium points, computation of the basic reproduction number using the Next Generation Matrix approach, and assessment of local stability through eigenvalue evaluation of the Jacobian matrix. The results indicate that both equilibrium points are asymptotically stable under certain condition. In addition, the presence of recidivist perpetrators increases the basic reproduction number, thereby amplifying the likelihood of sustained sexual violence within the population. In particular, the relapse rate is shown to play a critical role in destabilizing the violence-free equilibrium, underscoring the importance of addressing recidivism in prevention and intervention strategies. These findings provide new insights into the mathematical modeling of sexual violence and highlight the necessity of targeted policies to mitigate its persistence.
IMPLEMENTASI ALGORITMA SUPER ENKRIPSI VIGENERE CIPHER DAN ROUTE CIPHER PADA PENYANDIAN PESAN TEKS BAHRI, SUSILA; Jihan, Fitrahul; RUDIANTO, BUDI
Jurnal Matematika UNAND Vol. 12 No. 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.168-175.2023

Abstract

Kemajuan teknologi diiringi dengan meningkatnya ancaman terhadap keamanan serta kerahasiaan informasi pada pesan. Salah satu cara untuk mengamankan pesan dapat menggunakan teknik super enkripsi. Super enkripsi merupakan suatu konsep yang menggunakan kombinasi dari cipher substitusi dan cipher transposisi untuk meningkatkan keamanan pesan. Cipher substitusi adalah metode untuk merubah setiap karakter pesan melalui operasi matematika. Cipher transposisi adalah metode untuk merubah susunan setiap karakter pesan. Pada penelitian ini, Vigenere cipher sebagai cipher substitusi dan route cipher sebagai cipher transposisi. Penelitian ini bertujuan untuk mengimplementasikan algoritma super enkripsi Vigenere cipher dan route cipher pada penyandian pesan teks. Penyandian pesan dimulai dengan enkripsi menggunakan persamaan Vigenere cipher kemudian dienkripsi kembali menggunakan route cipher dengan merubah susunan karakter pesan sesuai rute kunci. Pengembalian pesan atau dekripsi dimulai dengan route cipher lalu didekripsi kembali menggunakan Vigenere cipher. Proses penyandian dan pengembalian pesan akan diimplementasikan menggunakan bahasa program PHP.
PERBANDINGAN METODE FUZZY TIME SERIES MARKOV CHAIN DAN FUZZY TIME SERIES CHENG DALAM MERAMALKAN NILAI TUKAR RUPIAH TERHADAP DOLAR AMERIKA SERIKAT (AS) HIDAYATULLAH, M.PIO; YOZZA, HAZMIRA; RAHMI HG, IZZATI
Jurnal Matematika UNAND Vol. 12 No. 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.121-134.2023

Abstract

Nilai tukar mata uang atau yang sering disebut dengan kurs merupakanharga satu unit mata uang asing dalam mata uang domestik atau dapatjuga dikatakan harga mata uang domestik terhadap mata uang asing.Nilai tukar rupiah terhadap dolar Amerika Serikat memainkan peranan sentraldalam perdagangan internasional, karena nilai tukar rupiah terhadap dolarAmerika Serikat memungkinkan seseorang untuk membandingkan harga-hargasegenap barang dan jasa yang dihasilkan berbagai negara. Pertumbuhan nilaitukar mata uang yang stabil menunjukkan bahwa negara tersebut memilikikondisi perekonomian yang stabil. Oleh sebab itu perlu dilakukan peramalannilai tukar rupiah terhadap dolar Amerika Serikat untuk beberapa waktu yangakan datang sebagai dasar pengambilan keputusan bagi pemerintah. Beberapametode peramalan yang dapat dilakukan untuk meramalkan data time seriesnilai tukar rupiah terhadap dolar Amerika Serikat adalah metode fuzzy timeseries markov chain dan fuzzy time series Cheng. Kedua metode ini akan ditentukanhasil peramalannya kemudian dibandingkan tingkat akurasinya menggunakanMSE, MAE, dan MAPE sehingga diperoleh metode peramalan yangpaling tepat untuk meramalkan nilai tukar rupiah terhadap dolar AmerikaSerikat. Pada penelitian ini diperoleh metode terbaik untuk meramalkan nilaitukar rupiah terhadap dolar Amerika Serikat adalah metode fuzzy time seriesmarkov chain.
BILANGAN RAMSEY MULTIPARTIT HIMPUNAN (R-M-H) M_j(C_n, C_s) UNTUK CYCLE Majid, Abdul -; SY, SYAFRIZAL; NAZRA, ADMI
Jurnal Matematika UNAND Vol. 12 No. 4 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.4.309-317.2023

Abstract

Diberikan dua graf G dan H sembarang. Bilangan Ramsey multipartit himpunan (R-M-H) M_j(G, H) dengan bilangan asli j ≥ 2, adalah bilangan bulat positif terkecil t sedemikian sehingga jika semua sisi dari graf multipartit seimbang lengkap K_{t×j} diberi sebarang 2−pewarnaan merah-biru, maka graf K_{t×j} senantiasa memuat G berwarna merah sebagai subgraf atau H berwarna biru sebagai subgraf. Graf C_n adalah suatu graf cycle dengan n ≥ 3 titik. Pada artikel ini, Penulis akan menentukan bilangan R-M-H M_j(C_n, C_s) untuk sebarang bilangan asli n ≥ 3 ganjil dan s ≥ 3. Hasil dari penelitian ini adalah ditemukannya bilangan R-M-H Mj (C_n, C_s) untuk cycle.

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