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COMPARISON OF CLUSTERING EARTHQUAKE PRONE AREA IN SUMATRA ISLAND USING K-MEANS AND SELF-ORGANIZING MAPS Ardiyani, Faradilla; Sulandari, Winita; Susanti, Yuliana
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0017-0030

Abstract

An earthquake is a sudden vibration on the earth's surface caused by the shifting of tectonic plates. One region in Indonesia that is particularly prone to earthquakes is Sumatra Island, due to its geographical location at the convergence of two tectonic plates, namely the Indo-Australian plate, which is actively subducting beneath the Eurasian plate. While earthquakes cannot be prevented or avoided, effective disaster mitigation strategies can help minimize the impact. The purpose of this research is to classify earthquake-prone areas on Sumatra Island based on depth and magnitude, allowing for further analysis to determine the characteristics of the clustering results. The study employs two clustering methods to analyze earthquake data from 1973 to 2024: the K-means and Self-Organizing Maps (SOM) algorithm. K-means algorithm is preferred for its simplicity and efficiency in handling large datasets, and suitability for numerical earthquake data analysis. Conversely, the SOM algorithm offers more stable clustering results and preserves the topological structure of the data, making it advantageous for exploring spatial patterns. The research findings indicate that the K-means algorithm provides better grouping, achieving a Silhouette Coefficient of 0.53, compared to 0.47 for the SOM algorithm. The K-means clustering resulted in two clusters: Cluster 1 contains 1,213 members and is characterized by shallow depths (3.9 km-41 km) and larger magnitudes (5 - 8.92 ), indicating a higher risk level. In contrast, Cluster 2 includes 412 members and represents areas with greater depths (40.8 km-70 km) and smaller magnitudes (5 - 6.85 ), corresponding to a lower risk level. This research aims to support the government in its earthquake disaster mitigation efforts, especially on Sumatra Island.
FORECASTING STATIONARY CLIMATE DATA USING AUTOREGRESSIVE MODELS AND HIGH-ORDER FUZZY Kayyisa, Alfien Diva; Sulandari, Winita; Slamet, Isnandar
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0313-0324

Abstract

Forecasting is essential for improving aviation safety, with air humidity being a critical factor influenced by air temperature. This study analyzes daily humidity data from I Gusti Ngurah Rai Airport, one of Indonesia’s busiest air stations, using two time series modeling approaches: Autoregressive (AR) and high-order fuzzy modeling. The objective is to evaluate and compare their forecasting accuracy. Historical daily data from the Meteorology, Climatology, and Geophysics Agency of Indonesia were used to build the forecasting models. The optimal linear AR model served as the foundation for constructing the AR high-order fuzzy model, which incorporates linguistic rules to capture nonlinear patterns. Both models were implemented and evaluated using the Mean Squared Error (MSE) metric. Results show that the AR(2) model outperforms the AR high-order fuzzy model, achieving a lower MSE of 13.23. This suggests that the AR(2) model provides more accurate humidity forecasts over the observed period. These findings offer practical insights for policymakers and decision-makers in forecasting daily humidity levels and supporting aviation operations. While the study confirms the effectiveness of traditional AR modeling, it also highlights limitations of the fuzzy approach, particularly its sensitivity to parameter tuning and data sparsity. The integration of high-order fuzzy modeling represents a novel contribution to this domain, though further refinement is needed to enhance its forecasting performance.
Exploring Spatial Nonstationarity in the Number of Motor Vehicles in East Java Using Robust Geographically Weighted Regression with an MM-Estimator Isnaini, Bayutama; Isnandar Slamet; Sulandari, Winita; Khoirunissa, Husna Afanyn
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 20 No. 2 (2025)
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v20i2.90866

Abstract

The number of motor vehicles in each region is quite diverse, not least in East Java Province. The variety of number of motor vehicles can be affected by local factors that are important to study so that vehicle growth can be adequately anticipated. On the other hand, economic growth incentives are influenced by people's purchasing power. In addition, motor vehicles are one of the essential things in the sustainability of economic activities. This study aims to evaluate a robust, geographically weighted regression model with an MM-estimator (RGWR MM-estimator), which is considered suitable for analyzing the number of motor vehicles in East Java. The results showed that the RGWR MM-estimator model generates an estimate of the number of motor vehicles based on the HDI explanatory variables, road length, sex ratio, poverty gap index, and the number of colleges that is accurate compared to other models formed. In addition, there are significant differences in the influence of the five explanatory variables in each region. Districts/cities located near the capital of East Java Province tend to have many explanatory variables that have a significant effect compared to regencies/cities far from the provincial capital.