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Yopi Andry Lesnussa, S.Si., M.Si
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Redaksi BAREKENG: Jurnal ilmu matematika dan terapan, Ex. UT Building, 2nd Floor, Mathematic Department, Faculty of Mathematics and Natural Sciences, University of Pattimura Jln. Ir. M. Putuhena, Kampus Unpatti, Poka - Ambon 97233, Provinsi Maluku, Indonesia Website: https://ojs3.unpatti.ac.id/index.php/barekeng/ Contact us : +62 85243358669 (Yopi) e-mail: barekeng.math@yahoo.com
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INDONESIA
BAREKENG: Jurnal Ilmu Matematika dan Terapan
Published by Universitas Pattimura
ISSN : 19787227     EISSN : 26153017     DOI : https://search.crossref.org/?q=barekeng
BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure Mathematics (analysis, algebra & number theory), - Applied Mathematics (Fuzzy, Artificial Neural Network, Mathematics Modeling & Simulation, Control & Optimization, Ethno-mathematics, etc.), - Statistics, - Actuarial Science, - Logic, - Geometry & Topology, - Numerical Analysis, - Mathematic Computation and - Mathematics Education. The meaning word of "BAREKENG" is one of the words from Moluccas language which means "Counting" or "Calculating". Counting is one of the main and fundamental activities in the field of Mathematics. Therefore we tried to promote the word "Barekeng" as the name of our scientific journal also to promote the culture of the Maluku Area. BAREKENG: Jurnal ilmu Matematika dan Terapan is published four (4) times a year in March, June, September and December, since 2020 and each issue consists of 15 articles. The first published since 2007 in printed version (p-ISSN: 1978-7227) and then in 2018 BAREKENG journal has published in online version (e-ISSN: 2615-3017) on website: (https://ojs3.unpatti.ac.id/index.php/barekeng/). This journal system is currently using OJS3.1.1.4 from PKP. BAREKENG: Jurnal ilmu Matematika dan Terapan has been nationally accredited at Level 3 (SINTA 3) since December 2018, based on the Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia, with Decree No. : 34 / E / KPT / 2018. In 2019, BAREKENG: Jurnal ilmu Matematika dan Terapan has been re-accredited by Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia and accredited in level 3 (SINTA 3), with Decree No.: 29 / E / KPT / 2019. BAREKENG: Jurnal ilmu Matematika dan Terapan was published by: Mathematics Department Faculty of Mathematics and Natural Sciences University of Pattimura Website: http://matematika.fmipa.unpatti.ac.id
Articles 1,369 Documents
CONTROL LIMITS OF THE G CHART BASED ON FAST DOUBLE BOOTSTRAP WITH GENERALIZED KULLBACK-LEIBLER DIVERGENCE PARAMETER ESTIMATION Muhammad Yahya Matdoan; Muhammad Mashuri; Muhammad Ahsan
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1807-1820

Abstract

The g chart is a type of attribute control chart that is effective for monitoring processes with low defect rates. If the process parameters on the g chart are unknown, parameter estimation is performed. The most effective parameter estimation method for data contaminated with outliers is GKL divergence. This parameter estimation was developed to avoid the limitations of previous robust methods, namely the truncation method and the truncation method. However, in practice, the g chart developed from the GKL divergence parameter estimator has weaknesses, especially if there are no nonconforming items in the phase I sample, which causes a lack of sensitivity at the control limits. To overcome this problem, a bootstrap-based and double bootstrap-based control limit approach was developed. However, this approach requires high accuracy, a long time, and high computational costs. Therefore, the purpose of this study is to develop a g chart with fast double bootstrap-based control limits. The data used in this study were simulation data with contaminated and non-contaminated outliers and empirical data sourced from PT. X. regarding container weight measurements. This study found that the control limits of the g chart based on fast double bootstrap were more sensitive than the conventional and bootstrap approaches. The results indicate that the container weighing process is still under control.
APPLICATION OF TRUNCATED SPLINE AND FOURIER SERIES IN MODELING THE OPEN UNEMPLOYMENT RATE IN KALIMANTAN ISLAND Aridha Pebriani Kusmiran; Nur Salam; Agus Muslim
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1821-1836

Abstract

Unemployment is a complex problem because it is one of the benchmarks for measuring the success of a region's economic development. According to the National Medium-Term Development Plan 2020-2024 and the Government Work Plan Summary 2023, Kalimantan Island is expected to have a maximum Open Unemployment Rate of 3.4%. However, provinces in Kalimantan Island still have an Open Unemployment Rate above 3.4%. Therefore, an analysis is needed to model the Open Unemployment Rate. The analytical method used is nonparametric regression, as the correlation pattern between Open Unemployment Rate and each predictor variable forms a random pattern. The estimators to be used are the truncated spline and fourier series. This study aims to compare the truncated spline and Fourier series methods in modeling the Open Unemployment Rate and determine the variables that affect Open Unemployment Rate on Kalimantan Island in 2023. Both the truncated spline and fourier series estimators have good flexibility. Based on the modelling results, it was concluded that the truncated spline method is better. The truncated spline model yields a lower GCV value (1,67545), a higher R² (0.57399), and a smaller MAE (0.821277) than the Fourier series model. Based on the analysis results, all predictor variables used, namely the Human Development Index, District Minimum Wage, population, and economic growth, significantly effect the Open Unemployment Rate with a coefficient of determination of 57.4%.
SPATIAL MODELING OF CHILD MALNUTRITION IN INDONESIA USING GEOGRAPHICALLY WEIGHTED MULTIVARIATE REGRESSION (GWMR) Teguh Susanto; Toha Saifudin; Nur Chamidah
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1837-1854

Abstract

In Indonesia aspires to become a developed nation by 2045, with one of its key pillars being the improvement of human resource quality through the achievement of Sustainable Development Goal (SDG) 2: ending hunger and ensuring access to adequate nutrition. However, the prevalence of stunting, wasting, and underweight among children under five remains a critical challenge that hampers these efforts. This study aims to simultaneously analyze the determinants influencing these three forms of malnutrition among Indonesian children by incorporating spatial aspects through the Geographically Weighted Multivariate Regression (GWMR) approach. The analysis employs nine predictor variables representing socioeconomic, demographic, and environmental factors across all provinces in Indonesia. The findings reveal that Complete Basic Immunization, Knowledge of Stunting Prevention, and Lower-Middle Economic Status consistently have significant effects on stunting and underweight. Meanwhile, Complete Basic Immunization and Complementary Feeding Practices play major roles in influencing wasting across provinces.Spatial analysis highlights varying patterns of determinants across regions. Western Indonesia (Java, Sumatra, and western Kalimantan) is more influenced by community behavior (mothers without a MCH Book,Children receiving complete basic immunizations receiving and children recheived complementary feeding), access to adequate sanitation, and lower-middle economic status. In contrast, Eastern Indonesia (Maluku and Papua) is more affected by structural conditions such as preterm births, low immunization coverage, knowledge of stunting prevention, and economic limitations. Central Indonesia demonstrates a more complex and varied combination of influencing factors. Furthermore, the GWMR model exhibits substantially better performance compared to the global (multivariate linear regression) model, as indicated by a significantly lower AIC value (Global AIC = 287.537; GWMR AIC = 44.956). These findings underscore the importance of spatially adaptive and decentralized nutrition policies to ensure more targeted and context-specific interventions.
CONSTRUCTING AN OPTIMAL PORTFOLIO USING CLUSTERING LARGE APPLICATION AND VALUE AT RISK ANALYSIS FOR IDX80 STOCKS Sania Pujianti; Hendra Perdana; Neva Satyahadewi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1855-1868

Abstract

Investment is a way to manage wealth and achieve financial goals in the future. Stocks are an attractive investment instrument due to their high potential returns, although they also carry significant risks. These risks can be minimized through portfolio diversification. Diversification is carried out by selecting representative stocks from the clustering results. This study aims to construct an optimal portfolio using the Clustering Large Application (CLARA) method and conduct portfolio risk analysis using Value at Risk (VaR). The data used includes IDX80 stock closing prices from November 1, 2024, to January 31, 2025, the financial ratios of IDX80 stocks on December 2024, and the Bank Indonesia (BI-Rate) interest rate from November 2024 to January 2025. The CLARA method produces four stock clusters with a silhouette coefficient of 0.18226. This value indicates a low level of separation between clusters, as there might be overlapping features among the clusters. Representative stocks from each cluster are selected based on the highest Sharpe ratio: SCMA, JPFA, GOTO, and BRIS. The portfolio weights based on MVEP are 15.002% (SCMA), 29.786% (JPFA), 1.858% (GOTO), and 53.354% (BRIS). The VaR calculation shows a potential maximum loss of Rp137,139 in one day, with a 99% confidence level, from an initial investment of Rp10,000,000.
COMPARISON OF MIXED EFFECT REGRESSION TREE (MERT) AND LINEAR MIXED MODEL (LMM) FOR CLUSTERED DATA ON CASE STUDY HOUSEHOLD POVERTY IN WEST JAVA PROVINCE Nur Fitriyani Sahamony; Asysta Amalia Pasaribu; Bagus Sartono; Khairil Anwar Notodiputro
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1869-1892

Abstract

This study compares the performance of the Linear Mixed Model (LMM) and the Mixed Effect Regression Tree (MERT) in analyzing the determinants of household consumption expenditure in West Java Province. The LMM integrates fixed and random effects to account for both individual and regional variations, while MERT extends this approach by incorporating a regression tree framework to capture nonlinear relationships and complex interactions among socio-economic variables. Using data from the 2023 National Socioeconomic Survey (SUSENAS), household consumption expenditure is modeled as an indicator of poverty. The results show that key determinants across both models include the gender and age of the household head, highest educational attainment, household size, land and car ownership, and welfare card ownership. Education and asset ownership consistently emerge as major factors influencing household welfare. The MERT model demonstrates superior predictive performance, with lower RMSE and MAE values compared to the LMM, while offering greater interpretability by identifying specific household profiles. Female-headed households with higher education and no car ownership tend to have higher expenditure in the high-income group, whereas female-headed households with welfare cards remain vulnerable in the low-expenditure group. From a policy perspective, these findings highlight the importance of improving educational access, enhancing asset ownership, and strengthening targeted social protection for vulnerable groups. Overall, while both models contribute valuable insights, the MERT model provides a more flexible and powerful framework for identifying and interpreting the determinants of household welfare in West Java.
A COMPARATIVE STUDY OF IBNR CLAIM RESERVE ESTIMATION USING BENKTANDER, WALTER NEUHAUS, AND OPTIMAL CREDIBILITY LOSS RATIO APPROACHES Dwi Mahrani; Edward Al Faruq Purba
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1893-1910

Abstract

Reinsurance plays a crucial role in risk transfer for insurance companies, particularly in managing large and volatile losses. One of the key challenges in reinsurance is the accurate estimation of Incurred But Not Reported (IBNR) claim reserves, especially for nonproportional assumed property business, which is characterized by high claim volatility and delayed reporting patterns. This study provides an empirical comparison of credibility-based reserving methods—namely the Benktander and Walter Neuhaus approaches—using reported claims and earned premium data from United States reinsurance companies for the period 2010–2019. Unlike most existing studies that focus on proportional or direct insurance portfolios, this research evaluates the performance of these methods in a nonproportional reinsurance context and benchmarks them against the Optimal Credibility Loss Ratio method, which minimizes Mean Squared Error (MSE). Claim reserves are estimated using run-off triangle techniques, loss development factors, and credibility weighting schemes, and the accuracy of each method is assessed through MSE ratios. The results show that the Benktander method produces reserve estimates that are consistently closer to the optimal benchmark, with an average MSE ratio of 1.0265, compared to 1.4184 for the Walter Neuhaus method. These findings indicate that the Benktander approach offers a more stable and statistically efficient reserve estimation for immature and volatile nonproportional reinsurance data. The study contributes to actuarial reserving literature by providing empirical evidence on the relative effectiveness of credibility-based methods and offering practical insights for actuaries in selecting appropriate IBNR reserving techniques under high uncertainty.
ROBUST QUASI-NEWTON EQUATIONS IN QUASI-NEWTON METHOD FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS Basim A. Hassan; Manal I. Mohammed
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1911-1922

Abstract

Quasi-Newton methods are among the most widely used and effective general-purpose algorithms for unconstrained optimization. These methods traditionally rely on the quasi-Newton equation, which serves as the foundation for updating approximations of the Hessian matrix at each iteration. The goal is to construct accurate second-order curvature information to accelerate convergence toward the optimum. In this paper, we derive a novel quasi-Newton equation based on an enhanced quadratic model. A key feature of this new formulation is that it incorporates both gradient information and objective function values, enabling higher-order accuracy in approximating the second-order curvature of the objective function. This new equation stands out for its ability to provide a more precise representation of the function's curvature, which in turn improves the overall efficiency and performance of the optimization method. Theoretical analysis shows that the proposed method is globally convergent under certain reasonable assumptions. To validate the effectiveness of the approach, we conducted a series of numerical experiments using standard benchmark problems. The results demonstrate that the modified Broyden, Fletcher, Goldfarb, and Shanno (BFGS) method, which integrates the new quasi-Newton equation, outperforms existing BFGS-type methods in terms of numerical efficiency and solution accuracy.
MODEL HYBRID MARS ARIMA FOR TRIBAL-BASED MALARIA PREDICTION IN TANAH BUMBU DISTRICT, SOUTH KALIMANTAN Abdul Khair; Bambang Widjanarko Otok; Noraida Noraida; Angga Dwi Mulyanto; Cindy Cahyaning Astuti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1923-1936

Abstract

Tanah Bumbu Regency has the highest rate of malaria in South Kalimantan Province. Due to the non-linear fluctuations in malaria cases by ethnicity, a hybrid model combining Autoregressive Integrated Moving Average (MARS ARIMA) and Multivariate Adaptive Regression Splines was proposed for time series forecasting. The purpose of this study is to use the MARS ARIMA hybrid model to predict malaria cases by ethnicity in Tanah Bumbu Regency. The findings demonstrate that the best inputs for MARS modeling are significant lags found using ACF and PACF. The hybrid MARS ARIMA model performs better than standalone ARIMA or MARS models, according to predictions. Key findings show that the number of patients over 35 during the preceding two periods influences increases in malaria cases for the Banjar ethnic group. Cases exceeding 13 in two prior periods and 19 in one prior period are associated with increases for the Javanese group. Cases of more than two or fewer than two in the preceding two periods and more than eleven in one preceding period have an impact on increases among the Bugis. Prior cases below 26 have an impact on Banjar case declines, whereas prior cases below 13 and above 3 have a significant impact on Javanese case declines. This study demonstrates how well the MARS ARIMA hybrid model predicts malaria cases according to ethnicity.
MODELING THE 3S13P BATTERY SYSTEM WITH SOC ESTIMATION MODELS AND MACHINE LEARNING PREDICTION FOR BMS APPLICATIONS Rina Latuconsina; Luwis Herman Laisina
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1937-1948

Abstract

This study aims to enhance estimation accuracy and energy management by incorporating thermal aspects into Battery Management Systems (BMS). Through experimental evaluation and mathematical modeling, key parameters such as charging time, internal resistance, State of Charge (SOC), Depth of Discharge (DOD), and effective capacity are analyzed. The SOC profile follows a logistic curve, with system energy efficiency ranging from 93% to 97%, depending on internal resistance variations. An Adaptive Kalman Filter (AKF) is applied for real-time SOC estimation, achieving an accuracy of ±1.5%, while a Long Short-Term Memory (LSTM) neural network performs time-series SOC prediction with an RMSE of 0.95%. Furthermore, three-dimensional thermal modeling reveals a significant increase in resistance beyond 45 °C, emphasizing the effect of temperature on battery dynamics. These findings highlight the importance of integrating real-time estimation and AI-based prediction algorithms into adaptive BMS architectures, contributing to advancements in intelligent energy management for electric mobility and stationary storage systems. However, this study was conducted under controlled temperature and fixed charging conditions, which may limit generalization to dynamic real-world operations; future work will address these factors.
AN EXPLAINABLE FUZZY CLUSTERING FRAMEWORK FOR MODELING LEARNING TRAJECTORIES IN OUTCOME-BASED EDUCATION Rustam Rustam; Koredianto Usman
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
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Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1949-1966

Abstract

Although various studies have applied clustering and categorization techniques in educational assessment, most rely on deterministic thresholds or heuristic-based partitions that fail to uncover latent conceptual structures. Existing fuzzy clustering applications in education also seldom incorporate rigorous validity-index-driven model selection or explainability-focused interpretation, leaving a gap in modeling the gradual and overlapping nature of learning progression. Outcome-Based Education (OBE) emphasizes measurable learning outcomes as the cornerstone of curriculum design and assessment. However, traditional methods for classifying student performance—typically based on fixed score thresholds—fail to reflect the inherent complexity of conceptual learning. This study proposes an Explainable Fuzzy Clustering Framework to model student learning trajectories in an OBE environment. Using final scores derived from multiple Course Learning Outcomes (CLOs), the Fuzzy C-Means (FCM) algorithm is applied to cluster students into conceptual performance levels with soft membership assignments. The optimal number of clusters is determined using the Tang–Sun–Sun (TSS) and Xie–Beni (XB) validity indices. The resulting fuzzy clusters are then compared with three conventional manual classification schemes—fixed thresholding, quantile partitioning, and mean–standard deviation banding—using cross-tabulation, heatmaps, and quantitative agreement metrics such as Adjusted Rand Index (ARI) and Normalized Mutual Information (NMI). Visualization techniques including stacked membership plots and cluster-size bar charts are employed to enhance interpretability. Results show that fuzzy clustering moderately aligns with manual schemes while revealing latent transitions and overlapping boundaries that rigid methods overlook. Quantitatively, the fuzzy clusters formed a natural distribution of 17.9% Low, 36.9% Moderate, and 45.2% High performers, with agreement scores of ARI = 0.405–0.462 and NMI = 0.550–0.629. These findings confirm the robustness and interpretability of the proposed model. The framework provides a principled, explainable, and adaptive approach to formative assessment, contributing to the advancement of interpretable learning analytics in higher education.

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