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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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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. The semiparametric SEM is employed to overcome the limitations of conventional SEM, particularly when data complexity and social behavior do not fully satisfy linearity assumptions. The model was applied to analyze 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 improves estimation precision by reducing bias and refining confidence intervals. 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 Sofro, A'yunin; Nugrahanto, Zalfa Zaliana
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 disasters remain one of the most frequent natural hazards in Indonesia, particularly in East Java Province, where variations in rainfall, population density, and land use contribute to differing levels of flood vulnerability. Although numerous studies have explored flood susceptibility using geospatial and statistical models, comparative analyses of clustering algorithms specifically designed for complex regional topographies remain limited. This study aims to implement and compare two clustering algorithms Density Based Spatial Clustering of Applications with Noise (DBSCAN) and K-Means++ to map flood vulnerability patterns across the region. The urgency of this study lies in the province’s increasing flood frequency and its impact on infrastructure and livelihoods, which demand an adaptive and data driven spatial analysis approach. DBSCAN was selected for its ability to detect irregular, non-linear cluster shapes, while K-Means++ offers efficiency and stability through improved centroid initialization. The dataset includes hydrometeorological and socio-environmental indicators such as rainfall, elevation, slope, land cover, and population density. Clustering performance was assessed using the Silhouette Index (SI) and Davies Bouldin Index (DBI). Results showed that DBSCAN achieved a higher SI (0.3266) compared to K-Means++ (0.2453), indicating better cohesion and separation. Spatially, DBSCAN generated four distinct clusters corresponding to actual flood prone areas, particularly in Jember, Lumajang, Pasuruan, and Sidoarjo. These findings suggest that density-based clustering provides a more reliable representation of heterogeneous spatial flood patterns, supporting local governments in targeted mitigation planning and regional disaster risk management.
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 crucial for preventing perinatal risks; however, the manual interpretation of cardiotocography (CTG) signals remains susceptible to variability and diagnostic delays. To address this challenge, this study aims to develop an accurate and computationally efficient model for automated fetal health classification. This study proposes a hybrid intelligent model named TMBA–ELM (Extreme Learning Machine parameters optimized with Triple Mutation Bat Algorithm) for accurate and efficient classification of fetal health conditions. The purpose of this research is to improve the diagnostic reliability of CTG data analysis while maintaining low computational complexity. The proposed TMBA–ELM integrates the adaptive exploration–exploitation mechanism of the Tuned Modified Bat Algorithm (BA) with the fast learning capability of the Extreme Learning Machine (ELM) to optimize both the hidden neuron size and the activation function. Three adaptive mutation strategies: Cauchy, Gaussian, and position modification—are applied to enhance convergence and population diversity. The model was evaluated using an imbalanced CTG dataset containing 2,126 samples classified as Normal, Suspect, or Pathological, and benchmarked against BA-ELM (ELM parameters tunned with BA), EMD-FA-ELM (ELM parameters tunned with firefly algorithm and the data decompositioned by empirical mode decomposition), and PSO-EM-ELM (error minimized ELM parameters tunned with particle swarm optimization) using five performance metrics: accuracy, precision, recall, F1-score, and computation time. Experimental results show that TMBA–ELM achieve high performance with 91.4% accuracy, 82.8% precision, 77.77% recall, and 79.93% F1-score, while maintaining the high computation time (164.23 second) with moderate stability (deviation = 12.76 second). The model also demonstrates improved recall for minority classes, confirming robustness in handling data imbalance. Although have bad computational efficiency, TMBA-ELM offers highest recall and F1-score, making it suitable for real-time fetal monitoring. The originality of this study lies in integrating triple adaptive mutation strategies within the Bat Algorithm to optimize ELM parameters.
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 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 ring Z_(p_1 )×Z_(p_2 ) for distinct prime numbers p_1 and p_2. We find that some properties of PG(Z_(p_1 )×Z_(p_2 ) ) such as order, size, the number of triangles, and Wiener. Further, we construct the line graph of PG(Z_(p_1 )×Z_(p_2 ) ) and calculate the order, size, and Wiener index of L(PG(Z_(p_1 )×Z_(p_2 ) )).

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