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All Journal JURNAL ILMIAH MATEMATIKA DAN TERAPAN Leibniz: Jurnal Matematika Buletin Sistem Informasi dan Teknologi Islam
Fathan, Morina A.
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Computer Science & IT Mathematics

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Grouping of Regencies/Cities in Indonesia Based on National Health Insurance (JKN) Participants with the Ensemble ROCK Approach Azwarini, Rahmania; Fathan, Morina A.; Widiantoro, Tri
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 21 No. 2 (2024)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22487/2540766X.2024.v21.i2.17512

Abstract

Health is a fundamental human need, and the National Health Insurance (JKN) program was established in Indonesia to provide equitable access to healthcare services for all citizens. Despite its implementation, disparities remain across regencies/cities, necessitating a comprehensive mapping of JKN participant profiles. This study aims to group 34 regencies/cities in Indonesia based on the characteristics of JKN participants, utilizing numerical and categorical data clustering. The Ensemble Robust Clustering using links (ROCK) method was employed, combining hierarchical clustering for numerical data and the ROCK method for categorical data. The study analyzed data comprising eight numerical variables (age, household size, household total expend, expend healthcare, tobacco expend, ATP, WTP, and expend insurance) and six categorical variables (living area, sex, education, reasons for joining JKN, ATP, WTP). Numerical clustering through single linkage yielded four clusters, while categorical clustering with the ROCK method at a threshold value of 0.2 produced three groups. The final ROCK ensemble analysis integrated these results, forming three quality-based clusters: low, medium, and high. Key findings revealed distinct socio-economic and demographic patterns among the clusters. For instance, the low-quality group exhibited lower household expenditures and healthcare spending, while the high-quality group had higher averages across these variables. Insights from this study can guide policy-makers in prioritizing healthcare resources and addressing regional disparities in JKN implementation.
Temperature Data Prediction in South Sulawesi Province Using Seasonal-Generalized Space Time Autoregressive (S-GSTAR) Model Rizal, Muhammad Edy; Fathan, Morina A.; Safitriani, Nur Rezky; Yahya, Muhammad Zarkawi; Asfar
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 21 No. 2 (2024)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22487/2540766X.2024.v21.i2.17516

Abstract

Indonesia's distinct tropical climate is influenced by its geographic location near the equator and its complex topography, resulting in pronounced seasonal temperature patterns. This study examines the application of the Seasonal Generalized Space-Time Autoregressive (SGSTAR) model to forecast the average air temperature in four regions of South Sulawesi Province: North Luwu, Tana Toraja, Maros, and Makassar. The dataset comprises monthly average temperatures from January 2019 to October 2024, sourced from BMKG's online database. The analysis includes stationarity testing using the Augmented Dickey-Fuller (ADF) test, seasonal pattern identification with autocorrelation function (ACF), and formal seasonal tests such as QS, QS-R, and KW-R. Spatial weight matrices were constructed based on Euclidean distances between regions. The best model was selected based on Mean Square Error (MSE), Root Mean Square Error (RMSE), Akaike Information Criterion (AIC), and adjusted R² criteria. The findings reveal that the seasonal GSTAR model with AR orders (p=3), (ps=4), and (s=12) is the optimal model. Evaluation indicates that the model achieves high accuracy, with forecast errors (MSE and RMSE) below 1°C. This model effectively captures seasonal and spatio-temporal patterns in climate data. The study is expected to serve as a foundation for further development of seasonal GSTAR models for other climate datasets, supporting improved environmental planning and resource management.
Perbandingan Ukuran Jarak pada Analisis Kluster Hirarki Yahya, Muh. Zarkawi; Sitti Nurhaliza; Morina A Fathan; Muhammad Edy Rizal; Andi Harismahyanti A
Leibniz: Jurnal Matematika Vol. 5 No. 02 (2025): Leibniz: Jurnal Matematika
Publisher : Program Studi Matematika - Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas San Pedro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59632/leibniz.v5i02.538

Abstract

Analisis klaster merupakan salah satu metode statistik untuk mengelompokkan objek berdasarkan kemiripan. Pada data kategorik, pemilihan ukuran jarak menjadi aspek penting karena memengaruhi struktur dan interpretasi klaster yang terbentuk. Penelitian ini bertujuan untuk membandingkan performa enam ukuran jarak Gower, Goodall1, Goodall2, Goodall3, Goodall4, dan Anderberg dalam analisis klaster hierarki menggunakan data kategorik dari Indonesian Family Life Survey (IFLS-5). Metode yang digunakan adalah hierarchical agglomerative clustering, dengan tahap awal pembersihan data dan konversi ke tipe faktor agar sesuai dengan karakteristik pengukuran jarak kategorik. Evaluasi hasil klaster dilakukan dengan dua indeks validasi internal, yaitu Silhouette dan Dunn, serta metrik eksternal Adjusted Rand Index (ARI) untuk menilai stabilitas klaster melalui proses bootstrapping. Ketiga metrik tersebut digunakan secara komplementer: Silhouette mengevaluasi konsistensi lokal anggota klaster (dengan nilai ? 0.5 umumnya dianggap baik), Dunn mengukur pemisahan antar-klaster secara global (semakin tinggi semakin baik), sementara ARI menunjukkan konsistensi struktur klaster terhadap variasi data (nilai mendekati 1 menunjukkan stabilitas tinggi). Hasil menunjukkan bahwa setiap ukuran jarak menghasilkan struktur klaster yang berbeda. Di antara semua ukuran yang diuji, Goodall4 memberikan hasil terbaik karena membentuk klaster yang mudah diinterpretasikan, memiliki nilai indeks Silhouette dan Dunn yang relatif tinggi, serta skor ARI mendekati sempurna. Hal ini mengindikasikan bahwa Goodall4 merupakan alternatif yang layak direkomendasikan dalam kasus serupa.
Aplikasi Sistem Monitoring Produksi dengan Diagram Kontrol Fuzzy Multivariat Berbasis Alpha-cut dan Transformasi Median Safitriani, Nur Rezky; Widyaningrum, Erlyne Nadhilah; Putri, Rizka Amalia; Khoirunnisa, Husna Afanyn; Fathan, Morina A.
Buletin Sistem Informasi dan Teknologi Islam (BUSITI) Vol 6, No 3 (2025)
Publisher : Universitas Muslim Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33096/busiti.v6i3.2874

Abstract

Pengendalian kualitas produksi yang adaptif menjadi kebutuhan mendesak dalam menghadapi data multivariat dengan ketidakpastian, disertai tuntutan untuk meningkatkan kualitas produk. Hal ini dapat diatasi menggunakan teori himpunan fuzzy melalui alat Statistical Process Control berupa diagram kontrol. Penelitian ini mengembangkan aplikasi sistem monitoring produksi menggunakan diagram kontrol multivariat fuzzy T2 Hotelling berbasis alpha-cut dan transformasi median. Aplikasinya dilakukan pada industri material bangunan di UD Tiga Beton sebagai penghasil batako press. Monitoring dilakukan pada dua karakteristik kualitas yang saling berkorelasi, yaitu kondisi fisik dan bidang permukaan, yang direpresentasikan dalam bentuk linguistik. Data pengamatan dikonversi ke dalam bilangan fuzzy menggunakan Triangular Fuzzy Number dan proses defuzzifikasi melalui transformasi median serta tambahan alpha-cut sebesar 0,6 agar dapat monitoring pergeseran mean yang kecil. Hasil penerapannya menunjukkan bahwa empat pengamatan terdeteksi berada di luar batas sehingga mengindikasikan proses produksi berada dalam keadaan out of control. Dengan demikian, aplikasi sistem ini terbukti mampu mendeteksi penyimpangan proses secara lebih akurat dan praktis. Diagram kontrol fuzzy multivariat berbasis alpha-cut dan transformasi median menjadi alternatif yang adaptif dalam pengendalian kualitas pada berbagai produksi.
Co-Authors Asfar Azwarini, Rahmania Erlyne Nadhilah Widyaningrum Harismahyanti A., Andi Khoirunnisa, Husna Afanyn Muhammad Edy Rizal Putri, Rizka Amalia Safitriani, Nur Rezky Sitti Nurhaliza Widiantoro, Tri Yahya, Muh. Zarkawi Yahya, Muhammad Zarkawi