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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 476 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 metaheuristic-based bandwidth optimization. Three predictors were analyzed: population size ($X_1$), literacy rate ($X_2$), and mean years of schooling ($X_3$). 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: $X_1$ showed no significant local effect, whereas educational factors ($X_2$ and $X_3$) 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. These findings demonstrate that education-related variables are the primary drivers of HDI variation in East Java, while demographic size contributes minimally. 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.
A Study on Multi-Class Topic Prediction for E-commerce Review Data Using Ensemble Learning Alifviansyah, Kevin
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 exponential growth of e-commerce platforms has generated massive volumes of unstruc tured user reviews, necessitating advanced automated analysis methodologies to extract actionable insights for strategic decision-making. This study addresses multi-class text classi f ication challenges by integrating BERTopic-based topic modeling with ensemble learning algorithms to analyze Indonesian e-commerce reviews. A dataset comprising 24,000 customer reviews from Google Play Store underwent systematic preprocessing and topic extraction using BERTopic, yielding eight distinct thematic clusters reflecting application performance, product quality, pricing, delivery logistics, and service reliability. The dataset exhibited severe class imbalance with an imbalance ratio of 65:1, where the dominant class represented 76.02% of instances while minority classes constituted less than 2.12%. Hybrid resampling techniques combining undersampling and oversampling successfully reduced the imbalance ratio to 1.4:1. TF-IDF vectorization transformed preprocessed text into numerical features, followed by supervised classification using CatBoost and Extra Trees classifiers optimized through randomized hyperparameter search with stratified k fold cross-validation. CatBoost demonstrated superior performance, achieving balanced accuracy of 0.829, recall of 0.829, and AUC of 0.965, attributed to its ordered boosting mechanism and capacity for handling categorical and imbalanced data. Independent validation of 2025 data confirmed robust gen eralization with prediction confidence exceeding 0.90, revealing significant temporal evolution in which product-related topics emerged dominant at 70.35%, pricing concerns increased from 6.58% to 16.57%, while application issues decreased from 76.02% to 2.51%. This research establishes a methodologically rigorous framework integrating unsupervised topic discovery with supervised ensemble classification, demonstrating computational efficiency while providing scalable solutions for automated review categorization.
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 Ring 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, PG(R), is a graph whose set of vertices consists of elements of R, and two distinct vertices are adjacent if their product in the ring is zero. In this paper, we study the prime graph of the Cartesian product of rings Zp1 Zp2, where p1 and p2 are distinct prime numbers. We determine several properties of PG(Zp1 Zp2), including its order, size, number of triangles, and Wiener index. Furthermore, we construct the line graph of PG(Zp1 Zp2) and compute the order, size, and Wiener index of L(PG(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 aims to review existing research on environmentally friendly shortest path problems and to identify the current state of the art in green shortest path optimization. A Systematic Literature Review is conducted using the PRISMA guideline and supported by bibliometric analysis to examine research trends and optimization methods discussed in the literature. The review indicates that most studies focus on metaheuristic and artificial intelligence–based approaches, while deterministic methods with explicit objective prioritization receive less attention. Based on the synthesis of previous studies, this paper discusses emerging research directions and outlines a conceptual framework for priority-based multi-objective shortest path optimization. The results of this review provide a clear overview of current methods and can support future research on eco-friendly shortest path models.
ResNet-50 and ResNeXt-50 for Multiclass Classification of Chronic Wound Images under Gaussian Blur Andhika, Reynaldi; 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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