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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 533 Documents
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An Integrated Circular Intuitionistic Fuzzy MCDM Framework with Radius Operators for Same-Day Delivery Service Selection Dwi Nurkarimah; Noor Hidayat; Abdul Rouf Alghofari
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.42211

Abstract

The rapid expansion of e-commerce has increased the demand for rapid, reliable, and efficient logistics services, particularly same-day delivery (SDD). Selecting SDD service providers is a multi-criteria decision-making (MCDM) problem because it involves multiple evaluation criteria and expert judgments under uncertainty. This study develops a decision-making framework based on circular intuitionistic fuzzy sets (CIFS) for SDD service selection and evaluates the effect of different CIFS radius operators on ranking outcomes. The proposed methodology is implemented in a case study of SDD service selection in Malang, involving 30 experts, four criteria, and three alternatives. Expert evaluations are aggregated and analyzed using three radius operators: maximum Euclidean distance, radius algebraic product, and radius algebraic sum. A sensitivity analysis is also conducted over the full range of the parameter lambda. The results show that the radius algebraic product operator provides the most stable ranking, consistently producing (AL3 AL2 AL1). These findings indicate that the choice of CIFS radius operator significantly affects decision stability and supports more reliable recommendations.
Negative Binomial Modeling of District-Level Diarrhea Incidence in West Java Province Nurul Nabilah; A'yunin Sofro
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42057

Abstract

This study investigated district-level diarrhea incidence in West Java Province during 2022–2024 and identified an appropriate count-data regression model for longitudinal epidemiological data. The response variable was the annual number of diarrhea cases, while explanatory variables included sanitation access, inpatient health centers, community health workers, nutritional indicators, drinking water facilities, and households implementing clean and healthy living behavior (PHBS). A population offset term was incorporated to account for differences in population exposure across districts/cities. Poisson Regression was initially fitted as a baseline model; however, severe overdispersion was detected. Therefore, Negative Binomial Regression and Generalized Linear Mixed Models (GLMM) were estimated and compared using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log-likelihood values, and simulation-based residual diagnostics. The results showed that Negative Binomial Regression provided the best overall fit, yielding substantially lower AIC and BIC values than competing models. Residual diagnostics indicated no evidence of remaining overdispersion, zero inflation, or serious outliers. Sanitation access was significantly associated with lower diarrhea incidence rates, with a one-standard-deviation increase corresponding to an estimated 15.7% reduction in incidence. These findings highlight the importance of accounting for overdispersion and suggest that Negative Binomial Regression is an appropriate framework for modeling regional diarrhea incidence data.
Diabetes Classification Using SMOTE-Based Intuitionistic Fuzzy K-NN with Weighted HIAD Tio Valent Novi Yanti Sianturi; Raden Sulaiman
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.41935

Abstract

Diabetes risk classification is challenged by class imbalance and diagnostic uncertainty. This study investigates an Intuitionistic Fuzzy Set framework integrated with a proposed Hausdorff-Inspired Attribute Distance within the K-Nearest Neighbor algorithm. The framework models patient profiles using membership, non-membership, and hesitation components to capture clinical ambiguity. We evaluated this approach on the Pima Indians Diabetes dataset using Stratified 5-Fold Cross-Validation, incorporating class balancing and clinically informed feature weighting. Results showed that while a conventional Euclidean-based model achieved the highest accuracy (73.96%) and data balancing maximized sensitivity (77.61%), the intuitionistic fuzzy configurations achieved the highest specificity (89.80%), indicating a conservative uncertainty-aware classification behavior. The proposed distance measure yielded classification performance highly comparable to that of the conventional Hamming distance, providing an alternative maximum-deviation-based similarity formulation within the intuitionistic fuzzy framework. Furthermore, combining class balancing with feature weighting contributed to a more balanced sensitivity–specificity profile. Overall, the findings demonstrate how uncertainty representation, feature weighting, class balancing, and neighborhood configuration influence classification outcomes, highlighting the potential of intuitionistic fuzzy approaches for uncertainty-aware medical decision-support systems.
Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum Ivan Hadinata; Muhamad Abdillah Ahen
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42495

Abstract

In this paper, we present the existence and uniqueness property of the Ledin-Brousseau sum involving a polynomial and a homogeneous linear recurrence sequence. This sum is of the form k=1n P(k)shk+r, where n is a positive integer, P(x) is a polynomial in C[x], h and r are integers, and (sk)kZ is a homogeneous linear recurrence sequence of degree m 2 satisfying certain constraints.
Construction of a Family of Minimal Helicoid Surfaces Passing Through an Isoparametric Helix Curve Ridwan Prawira Yunaldi; Haripamyu Haripamyu; Efendi Efendi
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.41759

Abstract

This research concerns the construction of a family of minimal surfaces passing through a helical curve. The construction follows the research by Yoon, which employs an approach using the curvature and torsion functions of a given curve. The construction yields a family of generalized helicoids as the minimal surfaces passing through the helical curve.
Robust PCA Using MCD and MM Estimators in MARS A Simulation Study Uswatun Hasanah; Solimun Solimun; Atiek Iriany
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.41547

Abstract

Multivariate Adaptive Regression Splines (MARS) models nonlinear relationships through adaptive basis functions but remain sensitive to outliers in the predictor variables. Existing robust extensions of MARS primarily address response outliers, while the few studies integrating Robust Principal Component Analysis (RPCA) with MARS use RPCA only for dimension reduction without comparing robust estimators. This study evaluates RPCA as a robust predictor transformation and systematically compares two robust covariance estimatorsthe Minimum Covariance Determinant (MCD) and the MM-estimatorwithin the RPCA-MARS framework. A full factorial simulation with 100 replications per condition covered 45 conditions: five sample sizes (n = 50, 100, 200, 500, 1000), three outlier proportions (5%, 10%, 25%), and three MARS interaction levels (1, 2, 3) with eight predictor variables. Outliers were extreme values in a specified proportion of predictor observations. Performance was measured by Root Mean Square Error (RMSE). For analysis, the 45 conditions were collapsed into 15 scenarios by selecting the interaction level with the minimum RMSE for each sample size and outlier proportion. The MM estimator outperformed the MCD estimator in 8 of 15 scenarios, achieving lower RMSE under moderate-to-high outlier contamination (10%25%) with moderate sample sizes (n = 100500). MCD performed better in the remaining 7 scenarios: under low contamination (5%) at n 200 and n 1000, and across all contamination levels at n = 1000. MCD showed higher variability at small samples with moderate-to-high contamination, while MM produced tighter confidence intervals and lower standard deviations. Within the RPCA-MARS framework, MM is recommended for moderately sized, highly contaminated data, while MCD is preferable under low contamination or in large-scale settings.
Dynamical Analysis of Modified Leslie-Gower Beddington-DeAngelis Model with Prey Refuge and Intraspecific Competition Salsabil Faridah Saputri Kusbianti; Riska Wahyu Romadhonia; Dian Savitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.41945

Abstract

This study examines the dynamical behavior of a predator–prey model depicting the interaction between Perca fluviatilis (predator) and its natural prey, Rutilus rutilus. The model is formulated within a modified Leslie-Gower framework and employs the Beddington–DeAngelis functional response to capture mutual interference among predators during foraging. It further incorporates key ecological elements: prey refuge and nonlinear intraspecific competition arising from prey density dependence. Equilibrium points and their local stability are investigated using the Jacobian matrix and the Routh–Hurwitz criteria. The analysis identifies four equilibria: the trivial equilibrium, the predator-extinction equilibrium, the prey–extinction equilibrium, and the coexistence equilibrium. Numerical simulations corroborate these analytical results. The simulations reveal that under appropriate parameters, the stability of the system is significantly driven by both the availability of prey refuges and the degree of intraspecific competition, which ultimately determine the survival conditions for both populations.
A Multiscale Extension of Geographically Weighted Spline Nonparametric Regression: Model Formulation and Theoretical Properties Indi Rizqy Fahrani; Henny Pramoedyo; Atiek Iriany
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42954

Abstract

This study proposes a Multiscale Geographically Weighted Spline Nonparametric Regression (MS-GWSNR) model to simultaneously accommodate spatial heterogeneity, multiscale spatial variation, and nonlinear relationships within a unified regression framework. The proposed model extends Geographically Weighted Spline Nonparametric Regression (GWSNR) by incorporating component-specific bandwidths adapted from the Multiscale Geographically Weighted Regression (MGWR) approach. Parameter estimation is developed using a Weighted Least Squares (WLS) framework combined with a backfitting algorithm to address the absence of a closed-form estimator under multiple spatial weighting matrices. The theoretical properties of the estimator are derived through a smoothing matrix representation, including unbiasedness, variance, and Mean Squared Error (MSE). A numerical illustration using simulated spatial data with controlled multiscale heterogeneity shows that the proposed estimator converges stably within 12 iterations, with a final smoothing operator convergence value of 2.48 × 10−5. The estimation also yields satisfactory reconstruction accuracy with MAE of 0.0680 and RMSE of 0.0880. These results indicate that the proposed MS-GWSNR model can flexibly reconstruct nonlinear spatial relationships across different spatial scales while maintaining stable estimation performance.
Coefficient Bounds for a Subclass of Bi-Univalent Functions Alifira Meliana Rachman; Marjono Marjono; Sa’adatul Fitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.43761

Abstract

In this paper, we obtain explicit upper bounds for the initial seven coefficients and their inverses for a subclass of bi-univalent functions defined via subordination. Using coefficient estimates associated with the Carathodory class and coefficient comparison techniques, expressions for the bounds of a2, a3, , a7 are derived. Moreover, it is proved that the first seven inverse coefficients admit the same upper bounds as the corresponding coefficients of the original function. These findings generalize several existing results concerning lower-order coefficients and provide a framework for further investigations of higher-order coefficient and Hankel determinant problems in the theory of bi-univalent functions.
Multivariate Time Series Forecasting of KP-RI Financial Performance Using VARIMA and VARIMAX with a Dummy Variable Tri Candra Nur Muhaimin; Nurjannah Nurjannah; Rahma Fitriani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42429

Abstract

Cooperative financial performance is influenced by both internal financial dynamics and external policy interventions. However, the contribution of policy-intervention information to multivariate forecasting models in cooperative finance remains insufficiently explored. This study compares Vector Autoregressive Integrated Moving Average (VARIMA) and Vector Autoregressive Integrated Moving Average with Exogenous Variables (VARIMAX-Dummy) models for analyzing and forecasting monthly Interest Income (PHB) and Net Surplus (SHU) in a savings and loan cooperative during 2015–2024. The analysis employed stationarity testing, cointegration testing, model identification, Granger causality analysis, Impulse Response Function, Forecast Error Variance Decomposition, and out-of-sample forecasting evaluation. A pulse dummy variable representing mandatory savings policy adjustments was incorporated into the VARIMAX model. The results indicate bidirectional predictive relationships and stable dynamic responses in both models. Model identification indicated that VARIMA(1,1,0) provided the optimal endogenous dynamic structure, which was subsequently retained in the VARIMAX-Dummy resulting VARIMAX (1,1,0)-Dummy specification. Forecasting evaluation showed that the VARIMAX-Dummy model achieved lower RMSE values for SHU (0.2129) and PHB (0.2088) than the corresponding VARIMA model (0.7434 and 0.6060). These findings demonstrate that incorporating policy-intervention information improves forecasting accuracy and enhances the representation of cooperative financial dynamics. The study highlights the value of exogenous policy variables in multivariate forecasting models for cooperative financial management.

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