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BAREKENG: Jurnal Ilmu Matematika dan Terapan
Published by Universitas Pattimura
ISSN : 19787227     EISSN : 26153017     DOI : https://search.crossref.org/?q=barekeng
Core Subject : Economy, Science, Education, Engineering,
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation
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
Arjuna Subject : Matematika - Matematika Terapan
Articles 1,309 Documents
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EVALUATING THE EFFECTIVENESS OF KERNEL EXTREME LEARNING MACHINES OVER CONVENTIONAL ELM FOR AIR QUALITY INDEX PREDICTION Kallista, Meta; Wibawa, Ignatius Prasetya Dwi; Obie, Sultan Chisson
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1373-1388

Abstract

Air pollution presents a substantial threat to human health, especially in urban areas like Jakarta, Indonesia, which ranked eleventh worldwide for poor air quality and urban pollution in mid-2025. This study is conducted with the objective of forecasting air quality over a designated future period by employing two advanced machine learning techniques: the Extreme Learning Machine (ELM) and its kernel-based variant, the Kernel Extreme Learning Machine (K-ELM). These methodologies are applied to predict the concentrations of five features of pollutants—PM10 (Particulate Matter), SO2 (Sulfur Dioxide), CO (Carbon Monoxide), O3 (Ozone), and NO2 (Nitrogen Dioxide)—which are critical indicators of environmental air quality and have significant implications for human health and environmental sustainability. Both methods are evaluated for their efficiency in time series regression, with a focus on training speed and generalization performance. The results demonstrate that the K-ELM model, especially when utilizing a Laplacian kernel, outperforms the standard ELM in predicting air quality based on the air quality index (AQI) dataset. Performance metrics indicate that K-ELM achieves superior accuracy, with an RMSE of 0.041, MSE of 0.002, MAE of 0.019, and an R-squared value of 0.898, confirming its effectiveness for air quality prediction in Jakarta. Furthermore, the Nemenyi post-hoc analysis across all metrics showed that K-ELM with the Laplacian kernel consistently achieved the highest rank and exhibited statistically significant improvements in multiple pairwise comparisons.
A COMPARATIVE EVALUATION OF SARIMA AND FUZZY TIME SERIES CHEN MODELS FOR RAINFALL FORECASTING IN MAKASSAR Claudia, Gavrilla; Dewi, Atika Ratna; Riyana Putri, Aina Latifa
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1389-1404

Abstract

High rainfall intensity in Makassar often leads to flooding. Therefore, forecasting the amount of rainfall is necessary as a reference for taking appropriate mitigation measures. This study was conducted to select the best model between the SARIMA and Fuzzy Time Series (FTS) Chen based on a comparison of their forecasting accuracy, as well as to forecast the amount of rainfall in Makassar for 2024 using the best model. For this study, monthly rainfall data covering the period from January 2014 to December 2024 were collected from the official website of the Central Statistics Agency (BPS) Makassar. Based on the analysis results, SARIMA(7,2,3)(1,1,1)12 was selected as the best model, with an MAE value of 2.654 and an RMSE value of 3.846. The contribution of this study lies in providing an empirical comparison between SARIMA and FTS Chen for rainfall forecasting in tropical regions. However, the limitation of this study is that the forecasting relies solely on historical rainfall data, without incorporating other meteorological variables that may influence rainfall patterns.
OPTIMIZATION OF ARIMA RESIDUALS USING LSTM IN STOCK PRICE PREDICTION OF PT MEDCO ENERGI INTERNASIONAL TBK Ababil, Achmad Fachril Yusuf; Hamid, Abdulloh; Khaulasari, Hani; Novitasari, Dian Candra Rini; Utami, Wika Dianita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1405-1420

Abstract

The capital market plays an important role in the economy by providing a means for companies to obtain capital and as a place to invest. Stocks are one of the popular investment instruments because their potential profits are attractive to investors. The stocks used in this study are PT Medco Energi Internasional Tbk (MEDC) shares. The purpose of this study is to obtain the optimal ARIMA-LSTM residual optimization model, how much the accuracy, and to predict Medco stock prices for the next 8-month period. The data used starts from January 4, 2021, to October 31, 2024, was obtained from the yahoofinance.com website. The ARIMA model, which is known to be effective in handling linear data, will be combined with LSTM. The use of residuals in the LSTM model can help LSTM capture patterns in the entire stock data so as to increase prediction accuracy. The research results obtained are the optimal ARIMA-LSTM optimization model, namely, ARIMA ([5,9],1,[5,9,11]) and LSTM with the best hyperparameter, namely, hidden layer 64, batch size 16, and learning rate 0.01. The accuracy of the ARIMA-LSTM optimization model is classified as very accurate, with a MAPE value of 0.3%. Medco Energi’s stock price for the next 8-month period is predicted to increase from IDR1312 to IDR1430 or an increase of 9%.
AN INVESTOR’S OPTIMAL PLAN IN A DC SCHEME WITH REFUND OF CONTRIBUTIONS FOR MORTGAGE HOUSING SCHEME Akpanibah, Edikan Edem; Samaila, Sylvanus Kupongoh; Esabai, Ase Matthias
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1421-1436

Abstract

In this paper, we investigate an investor’s portfolios in a defined contributory (DC) Pension Scheme with return of contributions for a mortgage housing scheme and managerial fees for time-inconsistent utility. A portfolio with a fixed deposit (risk-free asset) and two stocks (risky assets) is taken into consideration, where the stock market prices of the risky assets follow the geometric Brownian motion (GBM) and the instantaneous volatilities form a positive definite matrix. To determine the number of scheme members (SM) interested in the mortgage housing, the Abraham De Moivre function is used. Furthermore, the dynamic programming and game techniques were used to obtain our optimization problem by maximizing the expected utility (mean-variance utility) subject to the SM’s wealth. Using the variable change technique, the optimal value function (OVF), investor’s optimal plan (IOP), and the efficient frontier were obtained under mean variance utility function. . Furthermore, some numerical results of some sensitive parameters such as risk-free interest rate (RIR), risk averse coefficient (RAC), entry age (EA) of SM, managerial charges (MC), optimal fund size (OFS), instantaneous volatilities (IV) and appreciation rates (AR) of the risky assets were presented to explain their impact on the IOP. It was observed that the IOP, which is the fraction of SM’s accumulations invested in the risky assets, is a decreasing function of RIR, RAC, IV, EA, OFS, and MC but an increasing function of the AR.
ENHANCING CERVICAL CANCER IMAGES QUALITY: HYBRID SMO-PMD FILTER FOR NOISE REDUCTION Khozaimi, Ach; Darti, Isnani; Anam, Syaiful; Kusumawinahyu, Wuryansari Muharini
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1437-1452

Abstract

This study presents an image denoising method for cervical cancer images using the Perona–Malik Diffusion (PMD) filter optimized with the Spider Monkey Optimization (SMO) algorithm. The BRISQUE is proposed as the new objective function. The method was simulated on three datasets: SIPaKMeD, Herlev, and Mendeley Liquid-Based Cytology (LBC). Enhanced image quality was evaluated using MSE, SSIM, PSNR, and Entropy. On the SIPaKMeD dataset, the SMO-PMD filter achieved an average MSE of 0.0454, SSIM of 0.9984, PSNR of 62.27 dB, and Entropy of 5.425. The Mendeley dataset recorded an MSE of 0.3991, SSIM of 0.9994, PSNR of 53.08 dB, and Entropy of 5.489. The Herlev dataset achieved an MSE of 8.1191, SSIM of 0.9688, PSNR of 55.77 dB, and Entropy of 5.203. The SMO algorithm was compared with Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). SMO showed better results across all metrics. The proposed method produces images with lower noise, higher structural similarity, and improved visual quality. The stable entropy values across the datasets indicate that essential diagnostic information was preserved. These findings provide a new perspective for enhancing cervical cancer images using a hybrid SMO-PMD filter. A limitation of this study is that experiments were limited to three datasets, and SMO’s reliance on extreme κ values might reduce stability in other contexts
A GENETIC ALGORITHM–PARTICLE SWARM OPTIMIZATION OPTIMIZED DOFCM APPROACH TO ENHANCE CLUSTERING AND OUTLIER DETECTION Afriyani, Sintia; Fajriyah, Rohmatul
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1453-1472

Abstract

In the era of Industry 4.0, Big Data from the IoT demands advanced analysis techniques. Outlier detection is vital as anomalies may indicate sensor failures, fraud, or abnormal medical records. Fuzzy clustering methods such as DOFCM are often applied, yet their performance depends on accurate cluster center placement, which remains challenging. While several Fuzzy C-Means extensions address outlier sensitivity, most rely on single optimization strategies. The integration of PSO and GA into DOFCM has been rarely explored, making this study novel in evaluating how different evolutionary algorithms enhance clustering robustness and anomaly detection. This research introduces DOFCM-PSO and DOFCM-GA, tested on five benchmark datasets with outliers: Iris, Wine, Sonar, Diabetes, and Ionosphere. The Silhouette Coefficient (SC) was used as the evaluation metric. Results show that GA consistently outperforms PSO, with SC values improving by approximately 0.02–0.03 (equivalent to an increase of 8–12%) across datasets. For instance, the Iris dataset improved from 0.6029 (PSO) to 0.6291 (GA), while the Wine dataset increased from 0.2759 to 0.2958. In addition, evaluation of computational time and outlier detection further supports these findings. Although GA required slightly longer runtime than PSO, it substantially reduced the number of outliers while still achieving higher SC values. A similar pattern was observed in the Diabetes dataset, where GA decreased outliers from 20 to 7 with a modest SC improvement. These results indicate that PSO is more efficient in runtime, but GA provides more robust clustering by minimizing anomalies and producing better separation quality. Despite promising results, this study is limited by the relatively small dataset sizes and sensitivity to parameter settings, which may influence outcomes. Future work should apply the method to larger datasets and include additional clustering indices. Overall, DOFCM-GA can be considered a robust approach for fuzzy clustering in the presence of anomalies.
IMPLEMENTATION OF KALMAN FILTER, RECURRENT NEURAL NETWORK, AND DECISION TREE METHOD TO FORECAST HIV CASES IN EAST JAVA Nurwijayanti, Nurwijayanti; Yudianto, Firman; Radono, Panca; Sinulungga, Rizky Amalia; Romli Arief, Mochammad; Utami, Rahayu Budi; Arof, Hamzah
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1473-1484

Abstract

HIV (Human Immunodeficiency Virus) is a virus that infects cells in the body and weakens the human immune system, making it more susceptible to various diseases. Meanwhile, the symptoms of the disease arising from HIV itself are referred to as AIDS (Acquired Immune Deficiency Syndrome). Approximately 50% of people with AIDS in Indonesia are adolescents. Until now, HIV/AIDS has ranked second in East Java province. HIV/AIDS is classified as a dangerous disease because of the risk of death. Unfortunately, there is no treatment method or vaccine that could prevent this disease. This monitoring program to prevent the development of dangerous health cases such as HIV/AIDS is very helpful for local governments. Along with the development of information technology, the emergence rate of new HIV/AIDS cases can now be forecasted using machine learning as a monitoring tool to support. This machine learning-based monitoring program works with past data for statistical analysis. In this study, the methods used are Kalman Filter, Recurrent Neural Network, and Decision Tree. The Kalman Filter is a type of filter method that is used to predict the state of a dynamic, stochastic, linear, discrete system. A Recurrent Neural Network (RNN) is a development of a Neural Network. RNN deals with input sequence/time-series data by individual sector at each step and preserves the information it has captured at previous time steps in a hidden state. A Decision Tree is one of the classic tree-based prediction methods. The best error value (RMSE) achieved by each method is 0.0885 for the Kalman Filter, then for the Recurrent Neural Network method achieved 0.198, and the Decision Tree method successfully achieved 0.0287.
SPATIAL EXTRAPOLATION OF MALARIA CASES IN CENTRAL PAPUA USING CO-KRIGING BASED ON RAINFALL AND OBSERVATIONAL DATA FROM PAPUA PROVINCE Saifudin, Toha; Chamidah, Nur; Zhafira, Azizah Atsariyyah; Budijono, Gabriella Agnes; Sihite, Rivaldi; Baihaqi, Mochamad; Januarta, R. Arya
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1485-1500

Abstract

Malaria is an infectious disease that remains a significant health burden in Indonesia, particularly in Papua Province. This province has the highest malaria incidence rate nationally, influenced by various environmental factors such as rainfall. This study aims to estimate the number of malaria cases in districts/cities of Central Papua Province that do not have direct observation data, by utilizing the Co-Kriging method based on rainfall as a secondary variable and malaria cases as a primary variable from Papua Province. The secondary data used in this study were obtained from the official website of the Badan Pusat Statistik (BPS) of Papua Province, which includes the number of malaria cases in districts/cities as well as rainfall data from meteorological stations in the same region, collected in 2023. Three types of semivariogram models-spherical, exponential, and gaussian-were used to select the best model through statistical evaluation using Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). The results showed that the Gaussian semivariogram model provided the most optimal prediction results with an MSE of 10.895 and an MAPE of 4.67%. The estimates show that malaria cases in Central Papua are relatively uniform, with the highest incidence in Puncak Jaya district (219/1000 population) and the lowest in Mimika district (211/1,000 population). This approach is expected to be an important tool in spatially based disease planning and control and support the achievement of Sustainable Development Goals (SDGs), especially goals 3 (Good Health and Well-Being) and 13 (Climate Action).
APPLICATION OF DISCRETE HIDDEN MARKOV MODELS IN ANALYZING BLOOD TYPE INHERITANCE PATTERNS Hayati, Nahrul; Sulistyono, Eko; Anggraeni, Andini Setyo
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1501-1512

Abstract

This research investigates the application of a Discrete Hidden Markov Model (DHMM) to analyze inheritance patterns of ABO blood types. Leveraging the DHMM’s ability to model systems with hidden states, the study aims to improve the understanding of blood type inheritance dynamics in populations. The model employs six hidden states representing ABO genotypes (IAIA, IAi, IBIB, IBi, IAIB, and ii) and four observable states corresponding to blood type phenotypes (A, B, AB, and O). The transition and emission matrices followed Mendelian inheritance principles using population allele frequencies, whereas the initial probabilities were computed under Hardy-Weinberg Equilibrium (HWE) assumptions, with parameters calibrated to Indonesian blood type distributions. As a case study, we calculated the likelihood of observing phenotype A across five consecutive generations. Using the forward-backward algorithm, the probability of this sequence was calculated as 19%. The Viterbi algorithm further identified the most probable sequence of hidden genotypes, revealing a transition from the heterozygous IAi to the homozygous IAIA genotype over the five generations. One iteration of the Baum-Welch algorithm improved model accuracy, increasing log-likelihood from -1.661 to 0. Our results demonstrate the DHMM’s efficacy in decoding complex inheritance dynamics and provide a foundation for future population genetics research.
RESIDUAL-BASED MEWMA CONTROL CHART FOR DRINKING WATER QUALITY MONITORING AT PDAM TIRTA Takdir, Agung Muhammad; Herdiani, Erna Tri; Sunusi, Nurtiti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1513-1526

Abstract

Ensuring the consistent quality of drinking water remains a major challenge in Indonesia, particularly due to natural variability and operational limitations in regional water companies (PDAMs). Statistical quality control methods such as the Multivariate Exponentially Weighted Moving Average (MEWMA) chart, are widely applied for monitoring; however, their assumption of independent and identically distributed observations reduces their effectiveness when applied to autocorrelated time-series data. This study proposes a Vector Autoregressive (VAR)-based MEWMA control chart for monitoring water quality parameters, turbidity, and residual chlorine at PDAM Tirta. Daily observations from 2023 (n = 365) were analyzed. The VAR(3) model was selected using the Akaike Information Criterion (AIC), and residuals were validated to be free from autocorrelation. These residuals were then incorporated into the MEWMA framework with a smoothing parameter λ = 0.03. A comparative analysis was conducted between the standard MEWMA and the VAR-based MEWMA through Monte Carlo simulations (5,000 replications) across three shift scenarios. Results showed that both methods achieved comparable ARL₀ values (≈3), confirming stability under in-control conditions. However, the VAR-based MEWMA consistently demonstrated lower ARL₁ values in detecting small shifts, especially in turbidity, with improvements of up to 22% compared to the standard MEWMA. These findings highlight the VAR-based MEWMA as a more sensitive and reliable monitoring tool, offering water utilities an early-warning system that enables timely corrective actions and ensures compliance with drinking water quality standards.

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