Jurnal Matematika, Statistika dan Komputasi
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The Non-Isolated Domination Number of a Graph
Full text linkA subset S of the vertex set V (G) of a graph G is said to be a dominating set if every vertex not in S is adjacent to at least one vertex in S. In this research, we introduce a new domination parameter called the non-isolated domination number of a graph. A subset S of V of a nontrivial graph G is said to be a non-isolated dominating set if S is a dominating set and there are no zero-degree vertices in the subgraph induced by S. The minimum cardinality taken over all non-isolated dominating sets is called the non-isolated domination number and is denoted by γI. In this research, we obtained lower and upper bounds for the non-isolated domination number of a connected graph. We also determine the characterization of connected graphs that have the non-isolated domination numbers 2 and 3. Furthermore, we determine the non-isolated domination number of complete, n-partite complete, wheel, fan, star, cycle, and path graphs. We also determine the characterization of tree graphs that have the non-isolated domination number 2γ
Forecasting the Number of Domestic Flight Passengers at Minangkabau International Airport Using Sliding Window-Based Backpropagation
Full text linkThis study discusses the forecasting of domestic passenger numbers at Minangkabau International Airport using an Artificial Neural Network (ANN) with a Backpropagation algorithm based on the Sliding Window technique. The data used comes from BPS West Sumatra Province for the 2018-2023 period. The Sliding Window technique transforms time series data into cross-sectional data, which is then modeled using ANN with variations in the number of neurons and hidden layers. The results show that the best model uses 1 hidden layer, 5 hidden neurons, a learning rate of 0.01, and a window size of 5, with an MSE of 0.0027 and a MAPE of 0.0860%. This model has proven to be highly accurate and can be used as a decision-making tool for airport capacity management and operations
Connected Size Ramsey Numbers for The Pair Complete Graph of Order Two versus Union Complete Graph of Order Three
Full text linkLet F,G, and H be finite, simple, and undirected graphs. The connected size Ramsey number r ̂_c (G,H) of graph G and H is the least integer k such that there is a connected graph F with k edges and if the edge set of F is arbitrarily colored by red or blue, then there always exists either a red copy of G or a blue copy of H. This paper shows that the connected size Ramsey number r ̂_c (2K_2,〖nK〗_3 )=4n+3, for n≥4
Comparison of Forecasting Model Using Chen and Lee High Order Fuzzy Time Series (Farmer’s Terms of Trade of Crops Subsector in Nusa Tenggara Timur Province Case)
Full text linkThe farmer’s terms of trade of food crops subsector (NTPP) in Nusa Tenggara Timur Province has always been below 100 in 2019-2023. Food crops are a substantial agricultural subsector in which its contribution to the PDRB is significant and concerns the food adequacy of the region. NTPP is a proxy indicator to see farmers’ welfare and its value is expected to grow periodically. Therefore, predictive modeling is required to know future NTPP values and to know the purchasing power of food crop farmers. The aim of this research is to compare the accuracy of Chen and Lee model with the high order fuzzy time series for NTPP forecasting in Nusa Tenggara Timur Province. This research uses monthly data from NTPP Nusa Tenggara Timur from January 2016 to October 2024. The research results show that additions up to the 3rd order increase forecast accuracy and the Lee model is more accurate than the Chen model seen from the smaller RMSE and MAPE values. The MAPE values of the 3rd order fuzzy time series Chen and Lee model are 0.5453% and 0.5088% respectively. Based on the MAPE value, the 3rd order Lee model is the most accurate in forecasting NTPP in Nusa Tenggara Timur Province.
Komparasi Metode Extreme Learning Machine (ELM) dan Multi-Support Vector Machine (Multi-SVM) pada Identifikasi Tanaman Herbal
Full text linkIn Indonesia, there are more than 2.039 species of herbal medicinal plants, which sometimes have similarities and make it difficult to identify the type of herbal plant. The purpose of this study is to facilitate the identification of herbal plant species by comparing the performance of the Extreme Learning Machine (ELM) and Multi-Support Vector Machine (Multi-SVM) methods. The ELM method was created to overcome the weaknesses of feedforward artificial neural networks, especially in terms of learning speed, while the Multi-SVM method is an advanced development of the SVM method. The stages of this research begin with image input which is through previous data acquisition, data preprocessing, and then the identification with ELM and Multi-SVM methods. Based on the simulations that have been carried out, the average accuracy on training data for the ELM method is 93%, while the Multi-SVM method is 44%. Also, the average accuracy on testing data for the ELM method is 85%, while the Multi-SVM method is 40%.Secara turun-temurun masyarakat Indonesia memanfaatkan tanaman herbal untuk dijadikan bahan pembuatan obat tradisonal, bahkan dengan kemajuan teknologi, sudah dimanfaatkan pada bidang industri farmasi yang berkhasiat bagi kesehatan. Ada sekitar lebih 2.039 spesies merupakan jenis dari tumbuhan obat herbal di Indonesia yang terkadang memiliki kemiripan, sehingga menyulitkan dalam mengidentifikasi jenis tanaman herbal dan beralih menggunakan obat-obat kimia yang lebih praktis. tujuan dari penelitian ini untuk memudahkan dalam mengidentifikasi jenis tanaman herbal menggunakan metode-metode machine learning dan citra digital dengan membandingkan kinerja metode Extreme Learning Machine (ELM) dan Multi-Support Vector Machine (Multi-SVM), sehingga dapat diperoleh metode yang paling efektif dan efisien untuk identifikasi tanaman herbal. Metode ELM dibuat untuk mengatasi kelemahan-kelemahan dari jaringan syaraf tiruan feedforward terutama dalam hal learning speed, sedangan metode Multi-SVM merupakan algoritma pembelajaran mesin terawasi yang membantu dalam masalah klasifikasi dan metode ini juga merupakan pengembangan lanjutan dari metode SVM. Berdasarkan simulasi yang telah dilakukan, identifikasi pada metode ELM diperoleh akurasi untuk 5 jenis data tanaman herbal, training dan testing masing-masing akurasinya 100%. 10 jenis data tanaman herbal, data training diperoleh akurasi 99% dan data testing sebesar 96.667%. 20 jenis data tanaman herbal data training diperoleh akurasi 91% dan data testing sebesar 75%. 30 jenis tanaman herbal data training diperoleh akurasi 80.33% dan data testing sebesar 68%. Adapun untuk metode Multi-SVM pada identifikasi 5 jenis data tanaman herbal diperoleh akurasi data training. 52% dan testing 66.667%. 10 jenis tanaman herbal untuk data training diperoleh akuarasi sebesar 39% dan testing 30%. 20 jenis tanaman herbal untuk data training diperoleh akuarasi sebesar 23.5% dan testing 23.33%. dan 30 jenis tanaman herbal untuk data training diperoleh akuarasi sebesar 16.67% dan testing 14.44
Spectral Characteristics of The Antiadjacency Matrix of Kite Graph
Full text linkLet G=(V,E) be a connected graph, where V is the set of vertices and E is the set of edges of G. The kite graph, denoted by Kiten,m, is a graph obtained by appending a complete graph Kn to a pendant vertex of path Pm. This research investigates the spectrum of antiadjacency matrix of kite graph. The antiadjacency matrix of a graph G of order n is a square matrix with order n where the entries of the matrix represent the nonadjacency of the vertices.
Deteksi Komunitas, Analisis Topik, dan Sentimen Isu Palestina-Israel
Full text linkThe combination of community detection, topic modeling, and sentiment analysis provides deep insights into conversation data on the social media platform X (formerly Twitter) regarding the Palestine-Israel issue. The data, collected in Indonesian using several keywords, resulted in 108,969 tweets. The analysis process began with community detection using the Leiden algorithm, which identified five communities. The three dominant communities identified are Community 1 comprising 37.13% of users, Community 2 with 26.95%, and Community 3 with 19.76%. Topic modeling using LDA revealed that these communities focused on various aspects of the conflict. Sentiment analysis using the IndoBERT model uncovered that the majority of users expressed negative attitudes such as disappointment and anger. This study provides insights into public opinions and social dynamics surrounding the conflict.Kombinasi deteksi komunitas, pemodelan topik, dan analisis sentimen memberikan wawasan mendalam terhadap data percakapan di media sosial X (sebelumnya Twitter) terkait isu Palestina-Israel. Data yang dikumpulkan dalam bahasa Indonesia menggunakan beberapa kata kunci menghasilkan 108.969 tweet. Proses analisis dimulai dengan deteksi komunitas menggunakan algoritma Leiden, yang mengidentifikasi lima komunitas, dengan tiga komunitas dominan beranggotakan 37,13%, 26,95%, dan 19,76% dari total pengguna. Pemodelan topik menggunakan LDA menunjukkan komunitas-komunitas ini fokus pada berbagai aspek konflik. Analisis sentimen menggunakan model IndoBERT mengungkapkan mayoritas pengguna memiliki sikap negatif seperti kekecewaan dan kemarahan. Penelitian ini memberikan wawasan tentang pandangan publik dan dinamika sosial terkait konflik tersebut
Penerapan ARIMA dan Residual Bootstrap untuk Peramalan Mortalitas Dinamis Model PLAT pada Penduduk Laki-Laki di Indonesia
Full text linkThe development of mortality tables in Indonesia so far has been based on static mortality tables, which only consider the probability of death by age, even though they are applied across different years. A dynamic analysis of mortality tables, which takes into account the observation year and the birth year of individuals, becomes important for mitigating risks, particularly in life insurance and pension fund applications. Numerous methods and models for determining stochastic mortality to form dynamic mortality tables exist, but in this study, the PLAT stochastic mortality model was used to establish dynamic mortality tables because it is suitable for all age ranges, captures cohort effects, aligns with historical data, has a non-trivial (yet not overly complex) correlation structure, does not have robustness issues, and can account for parameter risk, while maintaining a relatively simple model structure. From these mortality tables, future survival probabilities for the next several years were forecasted using the ARIMA method, and the forecast range was estimated using residual bootstrap. The forecasting results show values that do not differ significantly from Indonesia’s 2023 mortality table. Additionally, the width of the confidence intervals derived using residual bootstrap was larger than the intervals without using the residual bootstrap method, particularly for younger ages. This is significant for mortality research in pension planning, as they provide interval simulations that reflect various factors during the estimation process.Pembentukan tabel mortalita yang ada di Indonesia selama ini adalah tabel mortalitas statik yang hanya melihat peluang meninggal berdasarkan usia saja meskipun pada tahun yang berbeda. Analisis tabel mortalita secara dinamik yang memperhatikan tahun pengamatan dan juga kapan individu lahir menjadi penting untuk memitigasi risiko terutama dalam penerapannya di bidang asuransi jiwa dan dana pensiun. Banyak metode dan model terkait penentuan moratlita secara stokastik untuk pembentukan tabel mortalitas dinamik, namun pada penelitian ini digunakan model mortalita stokastik model PLAT untuk menentukan tabel mortlaitas dinamik karena memiliki model yang sesuai untuk semua rentang usia, menangkap efek cohort, sesuai dengan data historis, memiliki non-trivial (tetapi tidak begitu kompleks) struktur korelasi, tidak memiliki masalah dengan robust dan dapat memperhitungkan risiko parameter, sedangkan strukturnya modelnya tetap relatif sederhana. Kemudian dari tabel mortalitas tersebut dibuat suatu peramalan nilai peluang hidup untuk beberapa tahun ke depan menggunakan metode ARIMA dan dicari rentang peramalannya menggunakan residual bootstrap. Hasil peramalan menunjukkan nilai yang tidak jauh ebrbeda dengan tabel mortalita Indonesia tahun 2023 selain itu lebar interval kepercayaan hasil peramalan menggunakan residual bootstrap lebih besar dari interval tanpa menggunakan metode residual bootstrap terutama untuk usia yang lebih muda. Hal ini sangat berpengaruh apabila dilakukan penelitian terhadap pengaruh tingkat kematian dalam perencanaan pensiun karena diperoleh simulasi interval yang dipengaruhi oleh berbagai macam faktor selama melakukan estimasi
Optimizing Credit Scoring Performance Using Ensemble Feature Selection with Random Forest
Full text linkCredit scoring has a very important role in the financial industry to assess the eligibility of loan applicants and mitigate credit risk. However, the main challenge in credit scoring modeling is the large number of features that need to be considered. Feature selection becomes an inevitable step to improve model performance. This research proposes the use of hybrid ensemble boosting techniques through XGBoost, LightGBM, and CatBoost methods, as well as aggregation techniques for feature selection, the results of which are then used to build predictive models using Random Forest. Experimental results show that the aggregation technique using feature slices selected by the three methods provides the best model with the least number of features, which is only about 11% of the total features. The use of fewer features not only increases the computational speed and efficiency of the model but also improves the generalization ability, which allows the model to perform better on new data. In addition, this model shows the smallest difference between train accuracy and mean cross-validation score, indicating high model stability and reliability
Comparison Of FCM And FKNN Methods For Clustering Provinces In Indonesia Based On People\u27s Welfare Indicators
Full text linkImproving people\u27s welfare is one of the main indicators of a country\u27s successful development. Public welfare covers various aspects, such as population, social, economic, and labor, which continue to evolve along with the growth and changes in human life needs. In Indonesia, various challenges such as rapid population growth, uneven population distribution, unemployment, poverty, and low Human Development Index (HDI) require strategic solutions to ensure equitable welfare. This study compares the Fuzzy C-Means (FCM) and Fuzzy K-Nearest Neighbor (FKNN) methods to cluster provinces in Indonesia based on public welfare indicators using variables of population density, population growth rate, percentage of poverty rate, Human Development Index (HDI), and Open Unemployment Rate (TPT). The clustering results are expected to support the government in formulating development policies that are more targeted and effective. The results showed that the best method was the Fuzzy C-Means method as many as 2 clusters with the highest Silhouette coefficient value of which states that the cluster structure formed in this clustering is very good. Cluster 1 is categorized as prosperous and cluster 2 is categorized as less prosperous