Diophantine Journal of Mathematics and Its Applications

Kinerja Peramalan Autoregressive Integrated Moving Average dan Seasonal Autoregressive Integrated Moving Average dalam Memprediksi Kejadian Gempa Bumi Sumatra

2025-04-22T07:31:31+00:00

Pulau Sumatra merupakan salah satu wilayah di Indonesia dengan tingkat risiko gempa bumi yang tinggi akibat jalur subduksi dan keberadaan sesar aktif. Penelitian ini bertujuan untuk memodelkan dan meramalkan magnitudo tertinggi gempa bumi tahunan di Pulau Sumatra menggunakan metode Autoregressive Integrated Moving Average (ARIMA) dan Seasonal Autoregressive Integrated Moving Average (SARIMA). Data yang digunakan adalah magnitudo tahunan dari tahun 1900 hingga 2023. Sebelum pemodelan, dilakukan uji stasioneritas data melalui transformasi Box-Cox untuk varians dan uji Augmented Dickey-Fuller (ADF) untuk rataan. Setelah proses differencing, data dinyatakan stasioner terhadap rataan. Identifikasi model awal dilakukan dengan analisis plot ACF dan PACF, diikuti dengan seleksi model berdasarkan signifikansi parameter. Evaluasi model menggunakan kriteria AIC, BIC, MAE, RMSE, dan MAPE. Hasil analisis menunjukkan bahwa model SARIMA (1,1,1) (1,1,0)²⁴ memiliki performa terbaik berdasarkan nilai AIC, BIC, MAE, dan MAPE. Namun, dalam tahap peramalan data testing, model ARIMA (2,1,2) menunjukkan hasil prediksi yang lebih mendekati nilai aktual. Penelitian ini menunjukkan bahwa kombinasi penggunaan ARIMA dan SARIMA dapat membantu dalam memodelkan kejadian gempa bumi di Sumatra, dengan pemilihan model terbaik disesuaikan berdasarkan tujuan peramalan.

Analisis Perbandingan Metode Hirearchical, K-Means, dan K-Medoids Clustering dalam Pengelompokan Kasus Penyakit Menular di Bengkulu Tengah

2024-01-13T05:18:19+00:00

In Indonesia, infectious diseases are still a persistent problem. Experts have accumulated knowledge regarding the emergence of the disease. In the last ten years, Indonesia is still experiencing the problem of triple burden diseases. Where Indonesia is still hit by infectious diseases, non-communicable diseases (NCDs) and diseases that should have been resolved, apart from that, infectious diseases are also still a big problem that must be faced. Researchers are interested in conducting research on infectious diseases in Central Bengkulu Regency. When analyzing infectious diseases, grouping can be done. Cluster analysis is an approach to looking for similarities in data and placing similar data into groups. There are two grouping methods in cluster analysis, hierarchical methods and non-hierarchical methods. One of the cluster analyzes using hierarchical methods is the average linkage method, while non-hierarchical ones are K-Means and K-Medoids. The variables used in this research are TBC and DHF in 2022. The highest rates of TB and DHF occurred in Pondok Kelapa sub-district, namely 29 and 23 cases. Based on the results of the analysis, it consists of 2 clusters, with cluster 1 consisting of 9 sub-districts, while cluster 2 consists of 2 sub-districts. Based on the results of evaluating the best method using the Calinski-Harabasz Index, it was found that the K-medoids method was the best method with a value of 0.

Optimalisasi Jadwal Menggunakan Pewarnaan Vertex Graf

2025-04-22T07:29:28+00:00

The preparation of subject schedules at SMP Negeri 2 Karanganyar Demak is still done manually and there are still errors that occur, such as teachers teaching at the same time but in different classes so the schedule is not optimal. This problem can be solved using scheduling techniques through graph coloring using the dot coloring method by substituting subjects in each class as vertices and the relationship between each subject and the subjects of each other class if the teacher who teaches the same subject is expressed as an edge. The algorithm for graph coloring is to determine the chromatic number using a vertex coloring algorithm, that is, using the minimum color type possible without anyone using the same color on neighboring edges. In this article, scheduling is only carried out for class VII at SMP Negeri 2 Karanganyar Demak. Based on the research results, it was found that the minimum number of colors in subject scheduling at SMP Negeri 2 Karanganyar Demak is that the coloring of the class 7 lesson schedule has 78 vertices resulting in 14 colors. Scheduling using point coloring produces a schedule without any overlapping schedules.

Penerapan Logika Fuzzy Mamdani dalam Menentukan Prioritas Penerima Bantuan Langsung Tunai (BLT) di Desa Sukarami

2025-04-22T07:52:55+00:00

Penyaluran Bantuan Langsung Tunai (BLT) merupakan salah satu program pemerintah untuk membantu masyarakat dalam menghadapi dampak ekonomi. Namun, dalam pelaksanaannya sering kali terjadi ketidaktepatan sasaran yang menyebabkan BLT tidak tersalurkan ke orang yang benar-benar layak dan membutuhkan. Untuk mengatasi permasalahan ini, peneliti mengusulkan penggunaan logika fuzzy dengan metode Fuzzy Mamdani sebagai solusi dalam menentukan kelayakan penerima bantuan. Metode Fuzzy Mamdani digunakan untuk mengolah data dengan beberapa kriteria penerima BLT. Melalui proses Fuzzy Mamdani dengan bantuan software Python akan menghasilkan keputusan yang lebih tepat dalam menentukan sasaran penerima BLT. Hasil penelitian dengan metode Fuzzy Mamdani, diperoleh nilai , yang mana dapat disimpulkan calon penerima berada pada tingkat prioritas penerima yang rendah. Hal ini menunjukkan bahwa metode Fuzzy Mamdani terbukti mampu menyaring penerima BLT secara lebih objektif dan sistematis, serta berpotensi besar dalam menekan ketidaktepatan sasaran penerima BLT di Desa Sukarami.

Forecasting Indonesia's Non-Oil and Gas Exports Using the Exchange Rate as an Exogenous Variable with the ARIMAX Model

2025-06-25T09:53:54+00:00

This study aims to develop an ARIMAX model for forecasting Indonesia’s non-oil and gas export values for the period of March to June 2025. The variables used include Indonesia’s non-oil and gas exports (Z) and the exchange rate (X), obtained from the Ministry of Trade and Bank Indonesia. The export data is monthly time series data characterized by autocorrelation. The forecasting method employed is the Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX), which extends the ARIMA model by incorporating external predictor variables. The results show that the ARIMAX(0,1,1) model is the most suitable for forecasting, yielding a Mean Absolute Percentage Error (MAPE) of 5.01%. Using the Maximum Likelihood Estimation (MLE) method, the derived model is Ẑₜ = Zₜ₋₁ - 0.4153εₜ₋₁ - 0.00000608Xₜ. The forecast indicates that Indonesia’s non-oil and gas exports will reach USD 23,692.17 million in June, with the lowest projected value in April at USD 23,003.46 million.