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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 868 Documents
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K-Means Cluster with Calinski Harabasz Index Evaluation to Map Forest Degradation and Deforestation Areas Rahimah, Ummi; Martha, Shantika; Imro'ah, Nurfitri
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.237-248.2026

Abstract

Although Indonesia is home to a rich biodiversity, the country is threatenedby forest degradation and deforestation, particularly in West Kalimantan. As asignificant contributor to the agricultural sector’s gross domestic product (PDRB), the Sanggau Regency is vital for preserving the environment and promoting sustainable development. This research uses the K-Means Cluster to categorize regions in Sanggau that can potentially experience forest degradation. Then, the Calinski Harabasz Index will be used to determine which clusters are the most effective. Two thousand twentythree, the research findings revealed five ideal clusters, each with a Calinski Harabasz Index value of 3.87. The first cluster consists of one sub-district, the second cluster consists of three sub-districts, the third cluster consists of two sub-districts, the fourth cluster consists of five sub-districts, and the fifth cluster consists of four sub-districts, which are all included in the distribution of clusters. A map illustrating the degree of urgency associated with forest degradation is produced as a result of this study. The map serves as a strategic reference for the government of Sanggau in its efforts to reduce theforest’s degradation and develop areas per the peculiarities of each sub-districts.
An Exploration of the Optimal Solution for the Tuberculosis Transmission Model considers the Post-recovery Treatment using Optimal Control Theory Tresna, Sanubari Tansah; Choirul Basir; Usep Rahmat; Enggar Prasetyawan
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.224-236.2026

Abstract

Tuberculosis, also known as TB, is among the most communicable diseases. It is strenuous to detect TB infection early, so the number of cases increases over time. Consequently, the cost of treating the TB-infectious sufferer is getting higher. However, since the recovered people from TB can become infected again, the post-treatment intervention needs to be conducted. Many mathematical models have been developed to study TB transmission among people. However, the study of cost-effectiveness analysis is not well-studied. Therefore, we are proposing a reformulated model of TB transmission into an optimal control model by considering the post-treatment intervention to reduce the cases of re-infected TB. The numerical simulations are performed to figure out the projection of its population dynamics under TB transmission. Next, we calculate the Average Cost-Effectiveness Ratio (ACER) and Incremental Cost-Effectiveness Ratio (ICER) to explore the most cost-effective strategy.
THE SPACE OF CONTINUOUS FUNCTIONS WITH $2$-NORMS Ekariani, Shelvi; IDRIS, MOCHAMMAD; ICHWANA PUTRA, DODY
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.213-223.2026

Abstract

The purpose of this paper is to study the space of continuous functions, $C[a,b]$ as a $2$-normed space. In particular, we show that the space is complete with respect to some linearly independent set.
Analysis of the Brownian Motion on the Matrix Lie Group SO(2) for Determining a Short-Term Interest Rate Model: A Simulation Approach Arief Budiman, Muhammad; Kurniadi, Edi; Sukono
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.132-149.2026

Abstract

In this paper, we observe the special orthogonal matrix Lie group containing of all 2x2 real matrices, denoted by SO(2), which can be geometrically visualized as the one-dimensional torus S1 which is nothing but the unit circle. A Brownian motion on SO(2) can be constructed and represented by a stochastic differential equation defined over a dynamic state space. The research aims to derive a short-term interest rate model on SO(2) through Brownian motion analysis which is a geometric approach. We employ a qualitative methodology, including a literature review of Brownian motion, stochastic differential equations, and dynamical state-space techniques on SO(2). Firstly, we prove the isomorphism SO(2) is isomorphic to S1, secondly, we determine Brownian motion on SO(2) and its equivalent, and thirdly, we formulate the corresponding stochastic differential equation, and the last, determine the short-term interest rate equation on SO(2). In this study, it is confirmed Lim and Privault’s work that the interest rate equation on SO(2) is given by rt = beta + 2 gamma cos(Wt) with beta, gamma is constant and Wt is standard Brownian motion. To clarify the obtained results, this study also gave a quantitative approach that is Python simulation of interest rate calculation using the matrix Lie group interest rate and other equations. The interest rate equation uses the matrix Lie group SO(n) with n greater than or equal to three still open to further research that can be applied to long-term interest rates.
SOME PROPERTIES OF CLEAR RINGS Yassin Dwi Cahyo; PERMATASARI, C. NOVITA; SUBASTIAN, NANDA; FARIZI, SALMAN; PUSPITA, NIKKEN PRIMA; SURYOTO, SURYOTO
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.196-212.2026

Abstract

Let (R, +, ·) be a ring with unity. An element in R is called a cleanelement if it is the sum of a unit element and an idempotent element. A ring R is calleda clean ring if all elements in R are clean elements. The notion of a clean element wasgeneralized to a clear element by replacing the idempotent element with a unit-regularelement. An element in R is called a clear element if it is the sum of a unit elementand a unit-regular element. A ring R is called a clear ring if all elements in R are clearelements. In this paper, we study the new properties of clear elements in a ring andclear properties in certain special rings, such as opposite rings, quotient rings, cornerrings, Morita rings, and group rings.
Optimal Bonus-Malus Premium with the Claim Frequency Distribution is Negative Binomial and the Claim Severity Distribution is Truncated Weibull Maulidi, Ikhsan; MAULIDIA, IZZAH; Radhiah, Radhiah; Apriliani, Vina
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.179-195.2026

Abstract

The optimal bonus-malus system is a system for determining the amount of premium in the next period based on the frequency and severity of claims filed by policyholders in the previous period. In this article, we study the insurance premium formula using the optimal bonus-malus system with the claim frequency has a negative binomial distribution and the claim severity has a truncated Weibull distribution. The method to derive the bonus-malus formula uses a Bayes solution with a quadratic loss function. The formula obtained has been also applied to the data of motor vehicle insurance to calculate the risk premium that must be paid by the policyholder. From the calculation results, the insurance premiums that use the optimal bonus-malus system with a truncated Weibull distribution are more profitable for both the company and the insurer than the Weibull distribution.
ALGEBRAIC LAWS AND PROPERTIES OF PICTURE FUZZY SETS Oktaviani, Dinni Rahma; Habiburrohman, Muhammad; Norasia, Yolanda; Candra, Ainun Esti
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.150-162.2026

Abstract

This paper investigates the fundamental algebraic laws and properties that hold in the framework of Picture Fuzzy Sets (PFS). Picture fuzzy sets extend classical fuzzy and intuitionistic fuzzy sets by incorporating an additional degree of neutrality, providing a more refined representation of uncertainty. We examine the validity of standard algebraic laws such as commutativity, associativity, distributivity, and idempotency under picture fuzzy operations, and identify the conditions under which these laws are preserved. The study contributes to a deeper understanding of the algebraic behavior of PFS and forms a theoretical basis for their further applications in fuzzy decision-making and information processing.
Locally Weighted KNN-Based Fuzzy Regression for Property Valuation under Market Uncertainty Yozza, Hazmira; Efendi, Riswan; Samat, Nor Azah; Rahmi, Izzati; Saputra, Ridho
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.163-178.2026

Abstract

Accurate evaluation of house valuation is crucial. Misestimation of house prices creates serious consequences for a variety of stakeholders. House prices can be modeled as a function of their constituent attributes. House prices are fuzzy due to negotiation and unpredictable market conditions. This study aims to develop rules to predict triangular fuzzy numbers of price for a given new house by implementing locally weighted KNN-based fuzzy regression, and to compare its performance with possibilistic fuzzy regression. The dataset used is the house valuation dataset. Data is examined using the modified Cheng and Lee k-nearest neighbor fuzzy regression and Tanaka’s possibilistic fuzzy regression. It is found that the modified Cheng and Lee k-nearest neighbor fuzzy regression outperforms possibilistic fuzzy regression in predicting the triangular fuzzy number of the house prices. The best performance is achieved when data is trained using the modified Cheng and Lee k-nearest neighbor fuzzy regression using: = 29 nearest neighbors, Minkowski distance with exponent parameter = 1.6 and an unequal weighting scheme with r = 1.

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