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CAUCHY: Jurnal Matematika Murni dan Aplikasi
Published by Universitas Islam Negeri Maulana Malik Ibrahim Malang
ISSN : 20860382     EISSN : 24773344     DOI : 10.18860
Core Subject : Education,
Mathematics
Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh Mitra Bestari (reviewer) untuk dinilai substansi kelayakan naskah. Redaksi berhak mengedit naskah sejauh tidak mengubah substansi inti, hal ini dimaksudkan untuk keseragaman format dan gaya penulisan.
Arjuna Subject : -
Articles 438 Documents
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Comparative Study of Hybrid ARIMA-LSTM and ARIMAX-LSTM for Bitcoin Forecasting with Data Partitioning Sembiring, Fikrie Hartanta; Permata, Regita Putri; Ni'mah, Rifdatun
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.35118

Abstract

The extreme volatility of Bitcoin prices poses significant challenges for accurate forecasting using conventional models. While ARIMA excels at capturing linear trends, it struggles with non-linear dynamics; conversely, LSTM networks can model non-linearity but often overfit noisy data. To address these limitations, this study investigates six forecasting configurations: standalone ARIMAX, standalone LSTM, and four hybrid ARIMA/ARIMAX-LSTM models employing both single-split and two-stage split strategies. A comprehensive out-of-sample evaluation on daily Bitcoin closing prices reveals that the two-stage split hybrid ARIMA-LSTM achieves a remarkable MAPE of 2.60%, outperforming all other configurations. The results demonstrate that residual structure and strategic data partitioning critically influence hybrid model performance by enhancing residual learnability. These findings offer practical guidance for researchers and practitioners designing robust forecasting pipelines for highly volatile financial markets.
Systematic Literature Review: Optimal Stopping and Investment Optimization for Bankruptcy Risk Management in Sharia Insurance Okta Yohandoko, Setyo Luthfi; Chaerani, Diah; Sukono, F
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.35523

Abstract

The increasing demand for Sharia-compliant financial services in Muslim-majority countries such as Indonesia has driven the rapid development of Sharia insurance (Takaful). Despite its growth, the Sharia insurance sector faces significant challenges in managing investment portfolios and mitigating bankruptcy risks. Addressing these challenges requires a comprehensive understanding of the existing mathematical and financial models configured according to Islamic principles. Several studies have introduced stochastic approaches to model surplus processes, investment returns, and risk probabilities in insurance operations. Among these, the Cramér–Lundberg model has been widely used to estimate surplus dynamics and bankruptcy risks, while the Vasicek model provides a stochastic framework for modeling investment returns. Quadratic programming has also been applied to optimize asset allocation under specific constraints. However, these methodologies have typically been explored in isolation, which limits their ability to provide an integrated and effective framework for simultaneous bankruptcy risk mitigation and Sharia-compliant investment optimization. This methodological gap constrains the advancement of comprehensive, practically applicable, and theoretically sound solutions that are specifically designed to address the distinctive operational characteristics of Shariainsurance. The objective of this systematic review of the literature is to synthesize and critically analyze the methods used in previous research and to explore how they can be systematically integrated to form a comprehensive risk and investment management framework for Sharia insurance. The review identifies the strengths, limitations, and potential for combining optimal stopping theory, stochastic surplus modeling, and investment optimization to support robust financial decision making. This review contributes by offering a structured research agenda for the development of integrated models that simultaneously address the complexities of bankruptcy risk and Sharia-compliant investment strategies. Furthermore, this study provides valuable information for academics and practitioners seeking to improve the financial sustainability of the Islamic Insurance industry.
Ensemble Bagging in Binary Logistic Regression for Transportation Mode Selection Nabila, Nuzulul Laili; Abusini, Sobri; Sa'adah, Umu
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.32241

Abstract

This study examines train versus bus transportation mode choice on the Malang–Blitar route using binary logistic regression combined with ensemble bagging. Data from 100 respondents were analyzed using 80% for training and 20% for testing with k-fold cross-validation. Variables included travel cost differences, time, safety, comfort, and ease of access. Bagging was selected over other ensemble methods due to its effectiveness in reducing variance and overfitting with small datasets. Results showed the standard logistic regression achieved 85% accuracy on test data, while ensemble bagging with 200 replications improved accuracy to 90.83% (confidence interval: 90.379%–91.187%). McNemar’s test confirmed a statistically significant improvement (p 0.01). Under equivalent conditions, 20.6% of respondents preferred trains while 79.4% chose buses. Ease of access emerged as the primary decision factor, outweighing cost and time considerations. The optimal replication number was 200; exceeding 300 replications decreased model performance. This research contributes an optimized ensemble methodology for transportation mode prediction in developing countries, demonstrating that accessibility infrastructure significantly influences passenger preferences over traditional economic factors.
Health Insurance Claim Classification using Support Vector Machine with Velocity Pausing Particle Swarm Optimization Jayanti, Luh Putu Dharma; Anam, Syaiful; Ardiyansa, Safrizal Ardana; Maharani, Natasha Clarissa
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.31914

Abstract

classification is a serious problem. Identifying claim classification is difficult. Machine Learning (ML) can predict potential claim decisions. Support Vector Machine (SVM) is a ML model that can generalize well to test data. SVM achieves an -score of 73.39% and 89.88% with a linear kernel, 73.34% and 73.34% with Radial Basis Function (RBF) kernel. Particle Swarm Optimization (PSO) improves the performance, because it can find the best parameters for SVM. However, the SVM parameters found by PSO are not guaranteed to be the global optimum. Velocity Pausing PSO (VPPSO) can address this problem. SVM-VPPSO performs better compared with SVM and SVM-PSO. SVM-VPPSO with linear kernel achieves -score of 90.17%, 90.16%, and 90.06% with 10, 20, and 30 particles respectively. The linear kernel also performs better than RBF kernel with a difference of 0.39% on the testing data. The best configuration is SVM-Linear-VPPSO with 10 particles. This configuration also achieves computation time of 46.938 seconds, which faster than SVM-Linear-VPPSO with 20 particles. The variance in computational time with 10 particles is 1.832 seconds, which better than with 20 particles with variance of 37.909 seconds.
Numerical Solution of the Time-Fractional Black-Scholes Equation and Its Application to European Option Pricing Dihna, Elza Rahma; Rusyaman, Endang; Sukono, Sukono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.35248

Abstract

The classical Black-Scholes model is widely used in option pricing but relies on idealized assumptions such as constant volatility and memoryless market dynamics, which limit its accuracy in capturing real-world financial behavior. To overcome these limitations, the time-fractional Black-Scholes model incorporates a fractional-order derivative—specifically the Caputo derivative—which introduces memory effects and accommodates time-varying volatility. This study focuses on numerically solving the time-fractional Black-Scholes equation using the finite difference method (FDM) and applying the results to the pricing of European call options. The model is discretized using an implicit finite difference scheme to ensure stability and accuracy over the time domain. Numerical simulations are conducted for various values of the fractional order α, illustrating that the option price is sensitive to the fractional parameter. Lower values of α tend to increase option prices, highlighting the influence of memory effects on pricing behavior. The results confirm that the finite difference method is an effective numerical tool for solving fractional partial differential equations and demonstrate that the fractional Black-Scholes model offers improved flexibility and realism in option  valuation, particularly in markets characterized by irregular volatility and non-Markovian features.
MILP Model Solution Steps: Implementation of Big M Simplex and Branch and Bound in the Coffee Supply Chain Islamiyah, Ananda Hans; Sa'adah, Umu; Karim, Corina
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.35380

Abstract

This research aims to develop a Mixed-Integer Linear Programming (MILP) model to optimize the distribution of coffee from producing sub-districts to storage warehouses, and subsequently to destination markets in Malang Regency during the 2020–2024 period. This model minimizes total logistics costs, which include distribution, shipping, and warehouse operating costs. The Big M Simplex method is used to handle logical constraints in the model, while the Branch and Bound algorithm is used to determine the operational state of the warehouse as a binary variable. The optimization results show that the warehouse is actively operated every year, with a distribution flow capable of meeting all market demands. The optimal purpose function value obtained is IDR 43,265,867,761,500,-. for five years. This shows that the combination of MILP, Big M, and Branch and Bound is effective as a decision-making framework in the optimization of the agribusiness sector's supply chain. This model considers temporal, spatial, and operational cost aspects, so it can be applied practically to data-driven distribution planning. This research contributes to the development of a relevant structured optimization approach for multi-period supply chain systems and discrete decisions
Locating Metric Coloring on The Cherry Blossom, Sun Flower and Closed Dutch Windmill Graphs Kristiana, Arika Indah; Khusnul, Agustina Hotimatus; Dafik, Dafik
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33636

Abstract

Locating metric coloring is a variation of metric coloring in graphs that integrates vertex coloring with the uniqueness of metric representations. In this coloring, each vertex in a connected graph  is assigned a color such that the distance vectors to each color class are distinct for every pair of different vertices. Let  be a coloring function (not necessarily proper). The coloring ccc is called a locating metric coloring if, for any two distinct vertices , their distance vectors , so it is obtained represents the partition of vertices by color classes. Thus, for every vertex, the distance vector  are different. Vertices may share the same color, whether adjacent or not, as long as their metric representations are unique. The smallest number of colors required for such a coloring is called the locating metric chromatic number, denoted  T This study focuses on analyzing locating metric coloring for three specific graphs: the Cherry Blossom graph , the Sun Flower graph , and the Closed Dutch Windmill graph . These graphs were chosen due to the absence of prior research on their locating metric coloring properties. The research method combines pattern recognition and a deductive-axiomatic approach. The proof process begins by determining lower bounds, followed by the construction of upper bounds through coloring function analysis. The resulting locating metric chromatic numbers for each graph are then established.
Reliable and Efficient Sentiment Analysis on IMDb with Logistic Regression Ulya, Diah Mariatul; Juhari, Juhari; Yuliana, Rossima Eva; Jamhuri, Mohammad
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33809

Abstract

Understanding public opinion at scale is essential for modern media analytics. We present a reproducible, leakage-safe evaluation of logistic regression (LR) for binary sentiment classification on the IMDb Large Movie Review dataset and compare it with five widely used baselines: multinomial Naive Bayes, linear support vector machine (SVM), decision tree, k-nearest neighbors, and random forest. Using a standardized text pipeline (HTML stripping, stopword removal, WordNet lemmatization) with TF–IDF unigrams–bigrams and nested, stratified cross-validation, we assess threshold-dependent and threshold-independent performance, probability calibration, and computational efficiency. LR attains the best overall balance of quality and speed, achieving 88.98% accuracy and 89.13% F1, with strong ranking performance (OOF ROC–AUC ≈ 0.9568; PR–AUC ≈ 0.9554) and well-behaved calibration (Brier ≈ 0.0858). Training completes in seconds per fold and CPU inference reaches about 2.46×10^6 samples per second. While a calibrated linear SVM yields slightly higher precision, LR delivers higher F1 at markedly lower compute. These results establish LR as a robust, transparent baseline that remains competitive with more complex neural and ensemble approaches, offering a favorable performance–efficiency trade-off for practical deployment and reproducible research on IMDb sentiment classification.
An Explainable Deep Learning Approach for Brain Tumor Detection Using MobileNet and Grad-CAM Visualization Gaib, Amalan Fadil; Ardiyansa, Safrizal Ardana; Wijaya, Anggito Karta; Julianto, Eric; Mahayudha, I Gusti Ngurah Bagus Ferry; Royan, Ando Zamhariro
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.35901

Abstract

Brain tumor detection remains a significant challenge due to the complex variations in tumor appearance. Although deep learning models have demonstrated high accuracy, their limited interpretability hinders clinical adoption. To address this issue, this study integrates Gradient-weighted Class Activation Mapping (Grad-CAM) into Convolutional Neural Networks (CNNs) to enhance the visual interpretability of predictions. Grad-CAM extends Class Activation Mapping (CAM) and is applicable to a wide range of deep learning architectures. The primary contribution of this work is the demonstration that combining Grad-CAM with MobileNet architectures yields an interpretable and efficient framework for diagnosis of brain tumor, effectively balancing accuracy, computational efficiency, and clinical transparency. Using a Brain Tumor MRI dataset, MobileNetV4 achieved an accuracy of 98.29% with the shortest training time (1738.82 seconds) and an ROC accuracy of 99.96%. MobileNetV3 achieved 99.62% accuracy with an ROC accuracy of 99.92%. Grad-CAM effectively highlighted tumor regions while showing uniform attention in non-tumor cases, thereby reducing false positives. These results demonstrate that lightweight models can achieve a strong balance between predictive performance, training efficiency, and interpretability. The proposed framework thus supports the development of explainable and efficient diagnostic tools for clinical practice.
Optimizing Profit-to-Cost Ratios in Bakery Production Using the Hasan–Acharjee Fractional Programming Method Adisty, Fahliza; Lubis, Riri Syafitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.35738

Abstract

Production optimization under resource constraints can be effectively modeled using Linear Fractional Programming (LFP), where the objective function is defined as a profit-to-cost ratio. This study applies the Hasan–Acharjee method to optimize production planning in a household-scale bakery enterprise in Indonesia, considering four product types and three resource constraints (materials, labor, and equipment). The model was reformulated as a single linear program and solved using LINGO 21.0. Validation against the classical Charnes–Cooper transformation confirmed identical optimal solutions, demonstrating the robustness of the Hasan–Acharjee approach. Sensitivity and trade-off analyses further revealed how variations in costs and production capacity influence profitability. The results highlight both the theoretical relevance of the Hasan–Acharjee method in fractional programming and its practical applicability to small and medium-sized enterprises seeking efficient resource utilization under limited conditions.

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