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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.
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Articles 14 Documents
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Search results for , issue "Vol. 14 No. 4 (2025)" : 14 Documents clear
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.

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