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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 501 Documents
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Quadratic and Truncated Spline Structural Equation Modeling With Double Bootstrap in The Waste Management Economy Rizqia, Anggun Fadhila; Solimun, Solimun; Nurjannah, Nurjannah; Hidayat, Kamelia; Junianto, Fachira Haneinanda
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.37591

Abstract

This study aims to develop and apply a semiparametric Structural Equation Modeling (SEM) approach that integrates quadratic and truncated spline estimation, enhanced with a double bootstrap resampling method. Semiparametric SEM is used to overcome the limitations of conventional SEM, particularly when data complexity and social behavior do not fully satisfy the linearity assumptions. The model was applied to analyze the public mindset and participation in waste management based on the 3R (Reduce, Reuse, Recycle) principle, focusing on the role of waste banks in optimizing the economic value of waste. The truncated spline approach enables flexible modeling of non-linear relationships among latent variables, while the quadratic term captures global curvature effects. Furthermore, the double bootstrap approach yields smaller standard errors and higher relative efficiency in parameter estimation. The simulation and empirical results demonstrate that the semiparametric SEM with double bootstrap produces higher model stability and more accurate parameter estimation compared to the single bootstrap approach. This method provides a robust analytical framework for modeling complex social phenomena, such as community-based waste management.
Management in Design-Build Projects by Construction Management Consultants: SEM-PLS and IPMA Approaches Kautzar, Al; Amin, Mawardi; Suroso, Agus
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.37117

Abstract

This study investigates the factors influencing the potential audit findings in Design and Build (DB) construction projects in Indonesia, employing Structural Equation Modelling–Partial Least Squares (SEM-PLS) and Importance–Performance Map Analysis (IPMA). Data were collected from 100 respondents, including project owners, contractors, and construction management consultants. The SEM-PLS results reveal that Integrity & Compliance Culture (β = −0.169, p = 0.045) and Administrative & Financial Compliance (β = −0.193, p = 0.027) significantly reduce the probability of audit findings, while other technical factors such as planning, supervision, and team competence show no direct effect. IPMA highlights Integrity & Compliance Culture and Contract & Documentation Management as top improvement priorities. These findings demonstrate that governance and compliance dimensions are more critical than technical performance in shaping audit outcomes. Strengthening compliance culture, enhancing administrative transparency, and implementing robust contract management are therefore key strategies to minimize audit risks in DB projects. The study contributes to the applied statistics literature in construction management and offers practical insights for policymakers, contractors, and auditors aiming to achieve accountable and transparent infrastructure delivery in Indonesia.
Implementation of DBSCAN and K-MEANS++ Methods for Flood Vulnerability Cluster Mapping in East Java Province, 2024 Nugrahanto, Zalfa Zaliana; Sofro, A'yunin
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.37410

Abstract

Flood vulnerability in East Java varies across districts due to differences in hydrometeorological pressure and exposure levels. This study compares two clustering algorithms—DBSCAN and K-Means++—for identifying patterns in eleven flood-impact indicators. DBSCAN parameter selection was conducted using a k-distance graph, resulting in ε = 0.8 and MinPts = 3, which produced five clusters and three noise points. The Silhouette Index for DBSCAN was 0.3266, calculated including noise points to ensure fair evaluation against K-Means++, which obtained a Silhouette Index of 0.2453 for five clusters. The findings indicate that DBSCAN produced higher internal cohesion under the given dataset. However, the resulting clusters are not interpreted as validated flood risk zones or as physically causal patterns, due to the absence of external validation layers such as historical flood maps, hydrological data, or topographic information. The results therefore provide a methodological comparison between density-based and centroid-based clustering for flood-impact variables without making geographical or causal inferences.
Spatial Variation of HDI in East Java: A Tricube-Based Geographically Weighted Regression–Flower Pollination Algorithm Modeling Approach Gani, Friansyah; Pramoedyo, Henny; Efendi, Achmad
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.38007

Abstract

Understanding spatial disparities in human development is essential for designing equitable development policies. This study examines the spatial variation of the Human Development Index (HDI) in East Java Province using an integrated Geographically Weighted Regression–Flower Pollination Algorithm (GWR–FPA) optimized with a Tricube kernel. The integration of GWR and FPA enables simultaneous spatial weighting and bandwidth optimization using the corrected Akaike Information Criterion (AICc) as the objective function. For standard GWR, the bandwidth was selected using Cross-Validation (CV) to minimize prediction error, while for the GWR–FPA model, bandwidth optimization was performed using the Flower Pollination Algorithm (FPA) with the corrected Akaike Information Criterion (AICc) as the objective function. Three predictors were analyzed: population size (X1), literacy rate (X2), and mean years of schooling (X3). Statistical diagnostics indicated significant spatial autocorrelation and heteroskedasticity in the OLS residuals, justifying the use of a spatial modeling framework. The GWR estimates revealed strong spatial non-stationarity: X1 showed no significant local effect, whereas educational factors (X2 and X3) were significant in all 38 districts and cities. The FPA optimization enhanced bandwidth selection, resulting in improved model fit. Model comparison based on AIC and AICc showed that the GWR–FPA–Tricube model achieved the lowest values (AIC = 135.8821; AICc = 137.0045), outperforming both global OLS and standard GWR. The results highlight the dominant contribution of education-related components to the spatial decomposition of HDI variation across East Java. The optimized model provides a more accurate spatial representation of local development disparities, supporting targeted policy interventions and illustrating the effectiveness of integrating metaheuristic optimization within spatial regression.
Sensitivity Analysis of the SIRD Model for TB-Related Life Insurance Claims in Southeast Sulawesi Asni, Asriani Arsita; Fitriyani, Fitriyani; Puspita, Ira
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.36490

Abstract

Tuberculosis (TB) remains a major public health challenge in Indonesia and generates significant mortality-related risk for the life insurance sector. This study develops an integrated Susceptible–Infected–Recovered–Deceased (SIRD) model to analyze TB transmission dynamics in Southeast Sulawesi and to estimate related life insurance claims. The model is calibrated using regional TB data from 2021–2023 and validated against 2024 observations. Analytical results include equilibrium analysis and the basic reproduction number, while long-term dynamics are examined through scenario-based simulations. Epidemiological outcomes are translated into actuarial projections by converting cumulative TB-related deaths into annual incremental deaths and expected insurance claims under optimistic, baseline, and pessimistic scenarios. Parameter sensitivity is assessed using Latin Hypercube Sampling and Partial Rank Correlation Coefficients. The results show that the transmission rate is the most influential determinant of the present value of TB-related insurance claims, followed by the recovery rate, whereas TB-induced mortality has a smaller but significant effect. These findings highlight that reducing transmission and improving treatment effectiveness can simultaneously mitigate public health impacts and lower long-term insurance liabilities, demonstrating the relevance of integrating epidemiological modeling with actuarial risk assessment.
BERTopic-Based Multi-Class Topic Classification on Indonesian Shopee E-commerce Reviews Using Ensemble Learning Alifviansyah, Kevin; Saefuddin, Asep; Rahardiantoro, Septian
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.37941

Abstract

The rapid growth of e-commerce platforms has resulted in a large volume of unstructured user reviews, creating challenges for scalable analysis. This study proposes a multi-class topic classification framework for Indonesian Shopee application reviews by integrating BERTopic-based embedding-driven topic modeling with ensemble learning. A total of 23,956 reviews are analyzed, with BERTopic applied exclusively to 19,167 training reviews to derive eight dominant topic labels, which serve as pseudo-labels for supervised classification using CatBoost and Extra Trees. Model performance is evaluated on a held-out test set under baseline and hybrid resampling settings to address severe class imbalance. The results show that hybrid resampling substantially improves balanced accuracy, particularly for CatBoost, while ROC–AUC remains consistently high, indicating robust class discrimination. Analysis of an unlabeled 2025 dataset, used solely in a deployment-style setting, reveals semantically consistent topic distributions on unseen data. Overall, the findings demonstrate that embedding-based topic modeling combined with ensemble learning provides an effective and scalable solution for multi-class topic classification in highly imbalanced e-commerce review data, with clear separation between training, evaluation, and post-deployment analysis.
Triple-Mutation Bat Algorithm–Optimized Extreme Learning Machine for Fetal Health Classification Wisnumurti, Prabowo; Anam, Syaiful; Muslikh, Mohammad
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.37525

Abstract

Fetal health assessment is essential for preventing perinatal complications, yet manual interpretation of cardiotocography (CTG) signals is prone to variability and diagnostic delays. This study introduces TMBA–ELM, a hybrid intelligent model that optimizes Extreme Learning Machine (ELM) parameters using the Triple Mutation Bat Algorithm (TMBA). The novelty of this work lies in extending TMBA—originally designed for continuous optimization—into a mixed-variable optimization framework that simultaneously tunes the hidden-node size and the activation function. This is achieved through the integrated use of Cauchy, Gaussian, and time-based mutation strategies, representing the first adaptation of TMBA for ELM parameter optimization and its first application to CTG-based fetal health classification. The model was evaluated on an imbalanced CTG dataset comprising 2,126 samples and benchmarked against BA-ELM, EMD-FA-ELM, and PSO-EM-ELM. TMBA-ELM achieved 89.23% ± 0.44% accuracy, outperforming BA-ELM (ELM models with parameters tunned by ELM) with accuracy 87.37%±0.63%, PSO-EM-ELM (Error-minimizaed-ELM parameters tunned with particle swarm optimization) with accuracy 82.76% ± 1.83%, and EMD-FA-ELM (ELM parameters tunned with firefly algorithm and data decompositioned by empirical decomposition) with accuracy 87.76% ± 1.95%. However, TMBA-ELM required 164.23 ± 12.76 seconds of computation time, which is substantially higher than BA-ELM and PSO-EM-ELM with computing time 60.9 ± 10.24 seconds and 59.69 ± 5 seconds, respectively. Overall, TMBA-ELM provides improved accuracy compared with existing ELM-based models, while its increased computational cost represents a limitation for time-constrained applications.
Some Properties of Prime Graph of Cartesian Product of The Rings and It's Line Graph Krisnawati, Vira Hari; Musyarrofah, Ayunda Faizatul; Hidayat, Noor; Fatimah, Farah Maulidya
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.32154

Abstract

The prime graph of the ring R, P G(R), is a graph which set of vertices consists of elements of R and two different vertices are adjacent if their product in the ring is zero. We study the prime graph of cartesian product of the rings Zp1 × Zp2 for distinct prime numbers p1 and p2. We find that some properties of P G(Zp1 × Zp2 ) such as order, size, the number of triangles, and Wiener index. Further, we construct the line graph of P G(Zp1 × Zp2 ) and calculate the order, size, and Wiener index of L(P G(Zp1 × Zp2 )).
Systematic Literature Review of GPS-based Multi-Objective Environmentally Friendly Shortest Path with a Proposed Lexicographic Framework Salsabila, Thania Nur; Chaerani, Diah; Napitupulu, Herlina
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.40489

Abstract

Environmentally friendly path planning has become an important topic in transportation research as concerns about carbon emissions continue to grow. This study presents a Systematic Literature Review (SLR) and bibliometric analysis to identify the state of the art in green shortest path optimization. Using the PRISMA guideline, the study analyzes 20 articles selected from Scopus, ScienceDirect, and Dimensions databases published between 2021 and 2025. Results indicate that the field is dominated by metaheuristic and AI-based approaches, while deterministic methods with explicit objective prioritization remain underutilized. Bibliometric visualization identifies traffic congestion and carbon emission policies as major research clusters, yet few studies integrate these with real-time GPS data in developing countries. Based on these findings, this paper proposes a conceptual framework for a GPS-based Lexicographic Multi-Objective Optimization model. The proposed framework prioritizes carbon emission minimization as the primary objective, followed by travel time, offering a transparent decision-making tool for sustainable urban transportation.
ResNet-50 and ResNeXt-50 for Multiclass Classification of Chronic Wound Images under Gaussian Blur Andhika, Reynaldi Ikbar Surya; Surono, Sugiyarto; Thobirin, Aris
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.40323

Abstract

Chronic wound image classification is important for supporting the assessment of conditions such as diabetic foot ulcers (DFU) and pressure ulcers (PU). While convolutional neural network (CNN)--based approaches have shown promising results, most previous studies focus on binary classification and rarely evaluate robustness in multiclass chronic wound scenarios. This study investigates multiclass classification of chronic wound images, distinguishing DFU, PU, and Normal Skin, using ResNet-50 and ResNeXt-50 architectures. A total of 2,146 publicly available images were stratified at the image level into training (70%), validation (15%), and test (15%) sets. Both models were trained under an identical configuration using data augmentation and class-weighted loss. On clean test images, ResNet-50 and ResNeXt-50 achieved strong and comparable performance, with accuracies of 0.9877 and 0.9938 and macro-averaged F1-scores of 0.9866 and 0.9928, respectively. Robustness was evaluated by applying Gaussian blur at the inference stage to simulate image defocus. Under stronger blur ((σ = 2.0), ResNeXt-50 maintained higher performance (accuracy 0.9723, macro-F1 0.9679) than ResNet-50 (accuracy 0.9200, macro-F1 0.9123). These results highlight the contribution of this study in evaluating robustness to blur in multiclass chronic wound image classification, while emphasizing that robustness is limited to resistance against image blur or defocus.

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