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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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Maluku
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
LEVERAGING XGBOOST, LIGHTGBM, AND CATBOOST FOR ENHANCED CUSTOMER SEGMENTATION IN THE AUTOMOTIVE INDUSTRY Novri Suhermi; Rahida Rihhadatul Aisy; Aulia Afifatur Rohmah; Anis Alif Nurhayati; Agnes Nathania Pramesty; Aura Lovi Ardanika; Fauziyah Nurul Isnaini
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/barekengvol20iss3pp2281-2298

Abstract

This study evaluates the performance of three gradient boosting algorithms, XGBoost, LightGBM, and CatBoost, for customer segmentation in the automotive industry. Utilizing a dataset of 8,068 training and 2,627 testing observations with 11 demographic and behavioral variables, the research aims to classify customers into four segments. The methodology includes preprocessing (handling missing values, encoding), hyperparameter tuning via Randomized Search Cross-Validation, and evaluation using ROC AUC. Results indicate that XGBoost outperforms other models, achieving an AUC of 0.5837 on testing data with significant variables, while LightGBM and CatBoost scored 0.5834 and 0.5759, respectively. Key findings highlight the importance of feature selection, with Age, Profession, and Spending Score being the most influential predictors. The study concludes that XGBoost is the most robust for segmentation tasks, though all models exhibit challenges in distinguishing overlapping classes. These insights can guide data-driven marketing strategies in automotive and related sectors.
DYNAMIC TIME WARPING-BASED FUZZY C-MEANS WITH MULTIDIMENSIONAL SCALING FOR TIME SERIES CLUSTERING Sri Hidayati; Regita Putri Permata; Fidi Wincoko Putro
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/barekengvol20iss3pp2299-2310

Abstract

Weather refers to atmospheric conditions such as temperature, humidity, air pressure, wind speed, and rainfall, all of which influence human activities. Rainfall is particularly important due to its impact on agriculture and water resource management. This study classifies regions on Java Island based on rainfall patterns using the Fuzzy C-Means algorithm. Rainfall variations are influenced by geographical, topographical, and climatic factors, requiring methods that can capture spatial and temporal changes. Fuzzy C-Means was selected for its ability to manage data uncertainty and overlapping clusters. To measure rainfall pattern similarity between regions, the Dynamic Time Warping (DTW) method was applied. Since DTW is a non-Euclidean metric and incompatible with Fuzzy C-Means, the Multidimensional Scaling (MDS) method was used to convert DTW distance matrices into Euclidean feature vectors. The study used secondary daily rainfall data from NASA (2021–2024). Clustering performance was evaluated using the Silhouette Coefficient, yielding a value of 0.413184, indicating good compactness and separation. Results identified three clusters: low rainfall (Cluster 0), moderate rainfall (Cluster 1), and high rainfall (Cluster 2). ANOVA results confirmed significant differences in average rainfall between clusters, with Tukey HSD tests showing Cluster 2 significantly differs from Clusters 0 and 1, while Clusters 0 and 1 are not significantly different. These findings demonstrate that combining DTW, MDS, and Fuzzy C-Means effectively identifies temporal rainfall patterns and produces statistically meaningful clustering. The spatial distribution of each cluster is visualized using GeoJSON and a database for clearer interpretation.
PERFORMANCE ANALYSIS OF MODIFIED-ODBOT AND SMOTE FOR TREE-BASED CLASSIFICATION OF IMBALANCED HUMAN DEVELOPMENT INDEX DATA Yunna Mentari Indah; Anwar Fitrianto; Indahwati Indahwati
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/barekengvol20iss3pp2311-2326

Abstract

Classification of Human Development Index (HDI) data presents significant challenges due to severe class imbalance, where low-development regions are substantially underrepresented. This imbalance reduces classification performance because machine learning models tend to be biased toward the majority classes, making it challenging to accurately identify minority classes. This study proposes a modified ODBOT that replaces Euclidean distance with Mahalanobis distance within the oversampling mechanism (Mahalanobis-based ODBOT) and compares its performance with Euclidean-based ODBOT with and without Principal Component Analysis (PCA), as well as the conventional SMOTE technique. Four tree-based classifications were used, namely Random Forest, Double Random Forest, XGBoost, and LightGBM. The Human Development Index (HDI) data set from the Central Statistics Agency, consisting of 514 observations and four features, with an imbalance ratio (IR) of 19.0, was divided into training and testing sets (ratio 80:20) with 30 repetitions and evaluated using F1-Measure (F1-M), Geometric Mean (G-M), Area Under the Curve (AUC), and computation time. The results show that Mahalanobis-based ODBOT achieved the highest performance on the AUC evaluation metric across all classification models and the highest on the G-M evaluation metric in three of the four classification models, but required significantly longer computation time (2545.66 seconds). In contrast, the Euclidean-based ODBOT with PCA improved F1-M while reducing computation time (7.21 seconds) compared to the original ODBOT (68.23 seconds), while SMOTE consistently improved G-M and AUC across all experiments. These findings suggest that oversampling techniques should be selected based on practical application needs. Specifically, the Mahalanobis-based ODBOT can be recommended when improving prediction performance is a priority, while the Euclidean-based ODBOT with PCA or SMOTE is preferable for real-world implementations that require faster execution and lower computational cost.
A COMPOUND CYCLIC POISSON STOCHASTIC MODEL FOR PREMIUM DETERMINATION IN WEATHER INDEXED AGRICULTURAL INSURANCE: CASE STUDY IN SOUTH SULAWESI, INDONESIA Ika Reskiana Adriani; Miftahulkhairah Miftahulkhairah; Gemala Hardinasinta; Hafidzah Hafidzah
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/barekengvol20iss3pp2327-2338

Abstract

The agricultural sector in developing countries is highly susceptible to significant losses due to weather variability and seasonal risks. Existing premium calculation methods often rely on homogeneous risk assumptions, which fail to account for claim patterns that are highly dependent on agricultural seasonality. This limitation often leads to mispriced premiums, deterring farmer participation in crucial insurance schemes. To address this, our study proposes and analyzes a compound cyclic Poisson model designed to estimate agricultural insurance premiums under weather-dependent shocks. The model explicitly integrates seasonal variations in claim frequency and severity, aligning premium calculation with actual agricultural risk profiles. Our approach uses a quantitative, stochastic modeling method based on a compound cyclic Poisson process, which effectively captures cyclical claim patterns that correspond with planting and harvesting seasons. As a case study, the research was conducted in South Sulawesi province, an ideal representation of an agrarian region with high weather risk intensity. The weather index used in this study combines rainfall and temperature indicators to better represent climate-induced risks. Through simulations, we found that the insurance premium, derived from our model, ranges from IDR 36,796 during low weather index conditions to IDR 328,713 during high weather index conditions, approximately 20-80% below the fixed AUTP market premium of IDR 180,000. This flexible pricing range allows farmers to choose the most suitable policy for their risk level and empowers insurance companies to set fair and financially sustainable premiums, ultimately encouraging broader participation in agricultural insurance. The originality of this study lies in the integration of a compound cyclic Poisson process to model seasonal claim dynamics in agricultural insurance. This approach contributes to the literature by providing a stochastic framework that bridges theoretical modelling and practical premium calibration under real world weather variability.
GARDNER PROBLEM REVISITED: FURTHER PROPERTIES OF INDAH RADICAL Puguh Wahyu Prasetyo; Muhammad Ardiyansyah
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/barekengvol20iss3pp2339-2348

Abstract

Radical theory arises naturally from the study of non-commutative rings and plays a central role in the structural analysis of ring classes. Among the radical classes that have received considerable attention are the prime radical β and the IndaH radical , whose relationship is closely related to the Gardner conjecture. While several structural properties of β are well established, the corresponding properties of have remained less clear. In this paper, we investigate the IndaH radical using deductive arguments and structural analysis within the framework of radical theory. In particular, we examine whether satisfies corner-hereditariness, corner-strictness, very corner-hereditariness, and the hereditary phantom corner (HPC) property. We show that possesses all four properties, thereby placing it in closer structural alignment with the prime radical β. The results are obtained under standard assumptions on associative rings and radical classes.
IMPROVING NEURON STATE DIVERSIFICATION IN LOGIC SATISFIABILITY VIA SMISH ACTIVATION AND AN ENHANCED UPDATING RULE Nurshazneem Roslan; Saratha Sathasivam
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/barekengvol20iss3pp2349-2362

Abstract

A deeper understanding of the learning and retrieval phase of the Discrete Hopfield Neural Network (DHNN) is essential for advancing its application in intelligent systems. This study investigates the performance of a non-systematic logical rule, namely Conditional Random 2 Satisfiability logic (CRAN2SAT) in DHNN (DHNN-CRAN2SAT) in retrieving diverse and optimal final neuron states. The findings show that the Election Algorithm consistently retrieves the maximum global minimum solution value of 1 across all tested neuron sizes, outperforms Exhaustive Search. In addition, the implementation of a new updating rule during the retrieval phase significantly enhances the diversity of final neuron states. This improvement is reflected by lower Sokal–Sneath similarity indices with an average value of 0.3809 and increased neuron state variation with an average value of 8809. These results highlight the significance of both the learning algorithm and updating strategy in the retrieval phase of DHNN. By enabling a broader range of final neuron states, this approach offers meaningful improvements for logic mining models, particularly in addressing real-world classification challenges.
FORECASTING WIND DIRECTION IN ALOR SETAR USING MACHINE LEARNING TIME SERIES MODELS WITH TRIGONOMETRIC TRANSFORMATION Nur Arina Bazilah Kamisan; Pow Jing Huei; Muhammad Hisyam Lee
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/barekengvol20iss3pp2363-2374

Abstract

Forecasting wind direction is inherently challenging due to its circular nature, where conventional numerical models often encounter discontinuities at the 0°/360° boundary. This study compares two modelling strategies for daily wind direction prediction in Alor Setar, Malaysia, using data from 2013–2017. A transformation-based approach and a direct numerical approach are compared for forecasting wind direction to assess their differences. In the transformation-based method, wind direction values are converted into sine and cosine components to preserve circularity, with predictions later reconstructed using inverse trigonometric functions. The direct approach predicts wind direction values without transformation. Three models, Prophet, Random Forest, and Holt-Winters, are applied under both strategies. Model performance is evaluated using time series plots, wind rose diagrams, and angular error metrics, including Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). Results indicate that the Random Forest model is the best model for forecasting the wind direction in Alor Setar, and the transformation-based approach produces more accurate and stable predictions, effectively capturing directional continuity, while the direct approach yields higher angular errors and fails to replicate the observed wind direction distribution. To our knowledge, this is one of the first studies in Malaysia to systematically apply transformation-based approaches for wind direction forecasting. The findings highlight the practical importance of improved wind direction prediction for renewable energy optimization, aviation safety, and environmental monitoring.
LOGIC MINING FOR TELECOMMUNICATION CHURN CLASSIFICATION: PERMUTATION WEIGHTED RANDOM 2 SATISFIABILITY REVERSE ANALYSIS APPROACH Nur Ezlin Zamri; Nurul Ain Najwa Mohamad Jamil; Nurul Atiqah Romli; Mohd Shareduwan Mohd Kasihmuddin
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/barekengvol20iss3pp2375-2388

Abstract

The telecommunications industry is experiencing rapid transformation, resulting in tense competition and increased customer volatility. Telecom churn, which refers to the discontinuation of services by customers, poses a serious challenge due to its direct impact on revenue and long-term profitability. Addressing this issue requires effective methods for understanding and predicting customer behavior. Hence, a logic mining approach is introduced in this study, namely the Permutation Weighted Random 2 Satisfiability Reverse Analysis Method, to classify customer churn in the telecommunications sector. The proposed method is based on a logical rule known as Weighted Random 2 Satisfiability, which is implemented in the Discrete Hopfield Neural Network. The logical rule facilitates the dynamic allocation of negative literals, contributing to improved logical representation. Furthermore, the Election algorithm is incorporated during the training phase to enhance the accuracy of logical structure interpretation. The proposed method is capable of extracting optimal data patterns and generating induced logic that accurately describes customer churn behaviour. This induced logic not only predicts whether a customer will churn but also provides interpretable insights into the underlying causes. Experimental results demonstrate a strong average accuracy of 85.6%, indicating the effectiveness and scalability of the proposed approach for knowledge discovery. Although the proposed approach achieves strong accuracy, the lower F1-Score and Matthews Correlation Coefficient reveal limitations in churn customer classification, highlighting the need for further improvement in handling class imbalance. This study contributes to the field of data mining by offering a logic-based framework for churn classification and emphasizing its practical relevance in supporting strategic customer retention efforts in a competitive telecommunications sector.
LOGIC MINING CLASSIFICATION FOR PHONE PRICES DATASET USING DISCRETE HOPFIELD NEURAL NETWORK AND WEIGHTED RANDOM 2 SATISFIABILITY Nurul Najwa Ahmad Azam; Nur Ezlin Zamri; Mohd Shareduwan Mohd Kasihmuddin; Nurul Atiqah Romli; Mohd. Asyraf Mansor
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/barekengvol20iss3pp2389-2400

Abstract

Smartphones have become essential in today’s technology-driven world, with various models offering unique features like camera quality, screen resolution, and storage. Understanding how these features influence smartphone prices can help consumers make informed purchasing decisions. This study introduces a logic mining technique to classify smartphone features that contribute to pricing using Weighted Random k Satisfiability with Modified Reverse Analysis. The model implements a Discrete Hopfield Neural Network, a Modified Niched Genetic Algorithm for training, and the Jaccard Feature Selection Method. The Phone Prices Dataset from Kaggle was used for experimentation, revealing the model’s ability to extract optimal patterns in the form of induced logic. The results show that the proposed model outperforms existing methods, achieving an accuracy of 0.8083, precision of 0.8925, specificity of 0.9760, Matthew’s correlation coefficient of 0.5334, and an F1-score of 0.5887, demonstrating its effectiveness in analyzing and classifying smartphone pricing factors.
OSCILLATION PROPERTIES OF SOLUTIONS TO CONFORMABLE FRACTIONAL DELAY DIFFERENTIAL SYSTEMS M. Deepa; M. Sathish Kumar; K. Karuppiah; S. Abhirami
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/barekengvol20iss3pp2401-2412

Abstract

This article examines the oscillation of solutions to a particular class of conformable fractional nonlinear delay differential systems of order α and 0<α≤1. By employing the equivalence transformation and the associated Riccati substitution technique, we are able to produce some new necessary conditions for the oscillation of all of the solutions of the differential system. Several results reported are extended, unified, and improved over established results. Two examples are provided to show the importance of the main results.

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