Eigen Mathematics Journal
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Comparison of the Trend Moment and Naive Methods in Forecasting Gross Regional Domestic Product in Blitar Regency
Get PDFGross Regional Domestic Product (GRDP) expenditure describes the final result of the production process within a region's territorial boundaries. Knowing GRDP expenses can describe the level of welfare economics, develop policy formulation, taxation, and export-import study. In estimating the GRDP of expenses in the following year, it is necessary to have a method of calculating systematically, one of which is forecasting. Some research showed that trend moment method and naive method produce higher accuracy than other methods. This method can be used in long-term forecasting and does not require the amount of data to be odd or even. The method is compared to get one of the best methods and has the highest accuracy value using MAPE calculation. The smaller MAPE, the better the forecasting accuracy. Comparing the two methods shows that the Naive method is the best method based on the MAPE criteria with an accuracy of 0.976 %. The result of data forecasting shows a decrease in GRDP Blitar Regency year 2021 and 2022
Peramalan Harga Beras dengan Metode Double Exponential Smoothing dan Fuzzy Time Series (Study Kasus : Harga Beras di Kota Mataram)
No full textRice has become the main staple food for almost the entire population of Indonesia. However, in Indonesia, the price of food commodities (rice) often fluctuates in price. Due to the rapid fluctuation of rice prices and the uncertainty in the future, it is necessary to forecast rice prices. This study aims to predict the price of rice in the city of Mataram using the Holt double exponential smoothing method and the Cheng fuzzy time series. The model's performance is based on Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) indicators. Forecasting model based on Holt's double exponential smoothing method, the MSE value is 705967.4994 and the MAPE value is 7.91%. On the other hand, based on Cheng's fuzzy time series method, the performance of the forecasting model based on the MSE indicator is 627400.307 and based on the MAPE value of 7.39%. Based on these results, Cheng's fuzzy time series method is more accurate than Holt's double exponential smoothing method.Rice has become the main staple food for almost the entire population of Indonesia. However, in Indonesia, the price of food commodities (rice) often fluctuates in price. Due to the rapid fluctuation of rice prices and the uncertainty in the future, it is necessary to forecast rice prices. This study aims to predict the price of rice in the city of Mataram using the Holt double exponential smoothing method and the Cheng fuzzy time series. The model's performance is based on Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) indicators. Forecasting model based on Holt's double exponential smoothing method, the MSE value is 705967.4994 and the MAPE value is 7.91%. On the other hand, based on Cheng's fuzzy time series method, the performance of the forecasting model based on the MSE indicator is 566312.340 and based on the MAPE value of 6.75%. Based on these results, Cheng's fuzzy time series method is more accurate than Holt's double exponential smoothing method.ย Keywords: Double Exponential Smoothing Holt, Fuzzy Time Series Cheng, Rice Price, MAPE, MS
Fuzzy Metric Space and Its Topological Properties
Get PDFThe fuzzy set theory is mathematics that applies fuzziness characteristics, so that gives the truth value at interval [0,1]. It is different from the crisp set that gives a truth value of 0 if it is not a member and 1 if it is a member. The theory of fuzzy sets has been developed continuously by scientists. One of the developments of the fuzzy set is the fuzzy metric space which the definition was introduced by George and Veeramani. Based on the analysis results, it is found that every metric space X if and only if X is fuzzy metric space. As a result, the topological properties of the metric space still apply to the fuzzy metric spac
Application of the Greedy Algorithm for Graph Coloring of the Grobogan Regency Map: Application of the Greedy Algorithm for Graph Coloring of the Grobogan Regency Map
No full textThe district map in Grobogan Regency can be optimized using the Greedy algorithm. The point on the graph represents the district and the line represents two areas that are directly adjacent. Greedy Algorithm is one of the algorithms developed to solve the problem of graph coloring to be able to produce minimal colors that are used without having the same color in areas that are directly adjacent. Greedyโs algorithm uses a set of color candidates and solutions in its solution. Staining is done at the point with the greatest degree followed by an examination of the appropriateness of the color with the principle that no neighboring points have the same color. The resulting color is included in the solution set. The process is continued until all the dots have been colored. Regional coloring in Grobogan district produces four colors with a greedy algorithm as the minimum color solution obtainedPeta wilayah kecamatan pada Kabupaten Grobogan dalat dioptimalisasi dengan algoritma Greedy. Titik pada graf mewakili kecamatan dan garis mewakili dua wilayah yang berbatasan langsung. Algoritma Greedy adalah salah satu algoritma yang dikembangkan untuk menyelesaikan masalah pewarnaan graf untuk dapat menghasilkan warna minimal yang digunakan tanpa ada warna yang sama pada wilayahyang berbatasan langsung. Algoritma Greedy menggunakan himpunan kandidat warna dan solusi dalam penyelesaiannya. Pewarnaan dilakukan pada titik dengan derajat terbesar dilanjutkan dengan pemeriksaan kelayakan warna dengan prinsip tidak ada titik bertetangga memiliki warna yang sama. Warna yang dihasilkan masuk dalam himpunan solusi. Proses dilanjutkan sampai semua titik selesai diwarnai. Pewarnaan wilayah di kabupaten Grobogan menghasilkan empat warna dengan Algoritma greedy sebagai solusi minimal warna yang diperole
The Power Graph of a Dihedral Group
Get PDFGraph theory is one of the topics in mathematics that is quite interesting to study because it is applicable and can be combined with other mathematical topics such as group theory. The combination of graph theory and group theory is that graphs can be used to represent a group. An example of a graph is a power graph. A power graph of the group ย is defined as a graph whose vertex set is all elements of ย and two distinct vertices ย and ย are connected if and only if ย orย for a positive integer x and y. In this study, the author discusses the power graph of the dihedral group ย The results obtained from this study are the power graph of the dihedral group ย where ย with ย prime numbers and an ย natural number is a graph consisting of two non-disjoint subgraphs, namely complete subgraphs and star subgraphs. And we find that its radius and diameter are 1 and 2
Modeling the Number of Infant Mortality in East Lombok using Geographically Weighted Poisson Regression
Get PDFInfant mortality is death that occurs at the age of 0 to 1 year. According to the Provincial Health Office, East Lombok is the district with the largest infant mortality rate in NTB. Several factors influence infant mortality: childbirth with medical assistance, low birth weight, health facilities, health workers, and exclusive breastfeeding. These factors have a spatial influence because each region has different geographical, socio-cultural, and economic conditions. Therefore, the method that can be used is GWPR because it can model data with the response variable with a Poisson distribution and pay attention to location or spatial aspects. This study aims to determine the infant mortality model in East Lombok using Geographically Weighted Poisson Regression (GWPR) and to determine the factors that significantly influence the number of infant deaths in East Lombok. Based on the research conducted showed that low birth weight is the only factor that significantly affected infant mortality in 8 sub-districts, including Keruak, Sakra, West Sakra, East Sakra, Terara, Sukamulia, Selong, and Labuhan Haji. The model obtained gives a good estimator, with an R^2 value of 76,44%.Kematian bayi merupakan kematian yang terjadi pada usia 0 sampai menjelang 1 tahun. Menurut Dinas Kesehatan Provinsi, Lombok Timur merupakan kabupaten yang menyumbang kematian bayi terbesar di Nusa Tenggara Barat (NTB). Beberapa faktor yang mempengaruhi terjadinya kematian bayi yaitu persalinan yang dilakukan dengan bantuan medis, Berat Badan Lahir Rendah (BBLR), sarana kesehatan, tenaga kesehatan, dan ASI eksklusif. Faktor-faktor tersebut memiliki pengaruh spasial karena antara wilayah yang satu dengan lainnya memiliki kondisi geografis, sosial budaya, dan ekonomi yang berbeda. Oleh karena itu, metode yang dapat digunakan yaitu GWPR karena mampu memodelkan data dengan variabel respon berdistribusi Poisson dan memperhatikan aspek lokasi atau spasial. Adapun tujuan dari penelitian ini yaitu menentukan model kematian bayi di Kabupaten Lombok Timur dengan menggunakan Geographically Weighted Poisson Regression (GWPR) dan mengetahui faktor yang berpengaruh secara signifikan terhadap jumlah kematian bayi di Kabupaten Lombok Timur. Berdasarkan penelitian yang dilakukan, diperoleh bahwa hanya faktor BBLR yang signifikan mempengaruhi kematian bayi di 8 kecamatan di antaranya Kecamatan Keruak, Sakra, Sakra Barat, Sakra Timur, Terara, Sukamulia, Selong, dan Labuhan Haji. Model yang diperoleh memberikan hasil penduga yang baik, dengan nilai 2 sebesar 76,44%
Analisis Dampak COVID 19 terhadap PDRB Provinsi Bali dengan Model Intervensi
No full textCOVID 19 is a disease caused by SARS-CoV-2. This virus spread very quickly to almost all countries including Indonesia. Bali tourism has developed in such a way and contributed greatly to regional development directly or indirectly. Gross Regional Domestic Product or GRDP has an important role in increasing the economic growth of a region, where the higher the GRDP, it can be said that the economic growth is also high. This study aims to analyze the impact of COVID 19 on the GRDP of the Province of Bali using an intervention model. The data used in this study is secondary data from quarterly GRDP on the basis of current prices in the accommodation, food and drink sector. Data was collected from the first quarter of 2010 to the fourth quarter of 2021. Based on the modeling that has been carried out with the intervention model, the best model to predict the impact of COVID 19 on GRDP in Bali Province is ARIMA(0,1,0)(1,0,0)4 r=1 with SMAPE value of 8.327 and MdAPE of 0.067.
COVID 19 merupakan penyakit yang disebabkan oleh SARS-CoV-2. Virus COVID 19 tidak hanya berdampak pada aspek kesehatan, melainkan aspek kehidupan lainnya Pariwisata Bali telah tumbuh berkembang sedemikan rupa dan memberikan sumbangan yang besar terhadap pembangunan daerah langsung maupun tidak langsung. Produk Domestik Regional Bruto atau disingkat dengan PDRB memiliki peran penting dalam meningkatkan pertumbuhan ekonomi suatu daerah, dimana semakin tinggi PDRB maka dapat dikatakan bahwa pertumbuhan ekonominya juga tinggi. Berdasarkan hal tersebut, maka perlu dilakukannya suatu peramalan untuk mengetahui dampak COVID 19 terhadap PDRB Bali. Penelitian ini bertujuan untuk menganalisis dampak COVID 19 terhadap PDRB Provinsi Bali menggunakan model intervensi. Data yang digunakan dalam penelitian ini merupakan data sekunder dari PDRB triwulanan atas dasar harga berlaku sektor penyediaan akomodasi, makanan dan minum. Data dihimpun dari kuartal I 2010 sampai dengan kuartal IV 2021. Berdasarkan pemodelan yang telah dilakukan dengan model intervensi, model terbaik untuk meramalkan dampak COVID 19 terhadap PDRB di Provinsi Bali adalah ARIMA(0,1,0)(1,0,0)4 r=1 dengan nilai SMAPE 8,327 dan MdAPE sebesar 0,067.
 
Jaringan Syaraf Tiruan untuk Memprediksi Kadar Polutan Ozon di Kota Mataram
No full textOzone tropospher (O3) is one of the pollutants in the environment of Mataram City, Lombok, NTB, Indonesia. Based on the data obtained from the Agency of Environment and Forestry of West Nusa Tenggara Province, ozone pollutant concentrations in Mataram City have changed unpredictably. One time pollutant concentrations increase and then decrease, but then quickly increase again significantly. Therefore, the concentrations of ozone pollutant must be monitored because its presence at certain levels can cause various negative effects human health and the environment. Changes in ozone pollutant concentrations can be identified by carrying out a method of predicting ozone pollutant levels so that a decision can be taken to prevent the negative impact of the pollutant. In this research, a backpropagation artificial neural network is used to find the model prediction of the concentration of ozone in Mataram City. The input variables that are used in this network are air temperature (x_1 ), wind direction (x_2 ), wind speed (x_3 ), humidity (x_4 ), solar radiation (x_5 ), concentration of NO2 (x_6 ), the concentration of SO2 (x_7 ) and the concentration of O3 a day before (x_8 ) for the period of 6 July 2018 to 31 May 2019. The method in this study was to conduct trial and error on 60 different combinations of network architectures and parameters. Then all the network architectures performance will be compared based on the RMSE, MAPE and R2 indicators. Based on this research, the best neural network model to predict the concentration of ozone pollutant in Mataram City is the network with architecture 8-20-1, with logsig-purelin activation function and trainlm learning function. The performance of the training model is RMSE=0.011, MAPE = 1,043 % and R^2=0,9566. Meanwhile, the performance of the testing model is RMSE=0.001, MAPE = 0.749 % and R^2=0.497Jaringan syaraf tiruan telah digunakan dalam berbagai bidang. Salah satunya untuk memperoleh suatu model prediksi. Pada penelitian ini model prediksi kadar polutan ozon troposfer di Kota Mataram diperoleh menggunakan jaringan syaraf tiruan backpropagation. Prediksi kadar polutan ozon troposfer diperlukan agar diketahui kualitas udara di hari-hari berikutnya sehingga dapat diambil suatu keputusan untuk mencegah dampak negatif dari polutan yang lebih besar. Variabel-variabel yang dijadikan masukan (prediktor) pada jaringan ini adalah temperatur udara , arah angin , kecepatan angin , kelembaban udara , intensitas sinar matahari , kadar NO2 , kadar SO2 ย dan kadar O3 satu hari sebelumnya ย pada periode 6 Juli 2018 sampai dengan 31 Mei 2019. Data-data tersebut diperoleh dari Dinas Lingkungan Hidup dan Kehutanan Provinsi Nusa Tenggara Barat. Berdasarkan hasil penelitian ini, didapatkan model jaringan terbaik untuk memprediksi kadar polutan ozon di Kota Mataram adalah jaringan dengan arsitektur 8-20-1 dengan fungsi aktivasi logsig-purelin dan fungsi pembelajaran trainlm. Performa model pelatihan berdasarkan indikator RMSE, MAPE dan ย berturut-turut sebesar , , dan . Sedangkan, performa model pengujian berdasarkan indikator RMSE, MAPE dan ย berturut-turut sebesar , , dan . Dari delapan variabel prediktor kadar polutan ozon pada model, variabel yang memiliki pengaruh paling besar terhadap kadar polutan ozon berdasarkan metode Connection Weight Approach adalah variabel temperatur udara sedangkan berdasarkan metode Garsonโs Algorithm adalah variabel kadar polutan ozon satu hari sebelumnya
Klasifikasi Status Kemiskinan Menggunakan Algoritma Random Forest
No full textPoverty is a fundamental problem because it deals with the basic needs of society. In NTB Province, many households are living below the poverty line. One reason is that the government's efforts to reduce poverty are not optimal. Therefore, it is necessary to classify the factors that affect the poverty level so it can be used as a reference in making policies to reduce poverty. One of the classification methods is the Random Forest method. The Random Forest method with the optimal mtry and ntree scores, i.e., ย and , respectively, obtained an accuracy rate of 81.3%. This means that the accuracy of the Random Forest classification method for this data is very good. The income variable is the most influential factor in determining poverty status based on Random Forest analysis, with a Mean Decrease Accuracy score of 23.92%. It has the highest Mean Decrease Accuracy value among other attribute variables.Kemiskinan merupakan persoalan mendasar karena menyangkut pemenuhan kebutuhan dasar masyarakat. Di Provinsi NTB, tidak sedikit rumah tangga yang hidup di bawah garis kemiskinan. Salah satu penyebabnya adalah belum optimalnya upaya pemerintah dalam menurunkan tingkat kemiskinan. Oleh karena itu, perlu diklasifikasi faktor-faktor yang mempengaruhi tingkat kemiskinan sehingga dapat digunakan sebagai acuan dalam mengambil kebijakan untuk mengurangi tingkat kemiskinan. Salah satu metode untuk klasifikasi adalah metode Random Forest. Metode Random Forest dengan nilai mtry dan ntree optimal masing-masing yaitu ย dan ย menghasilkan tingkat akurasi sebesar 81,3%. Hal ini berarti ketepatan metode klasifikasi Random Forest untuk data ini sudah sangat baik. Adapun faktor yang paling berpengaruh dalam menentukan status kemiskinan berdasarkan analisis Random Forest adalah variabel penghasilan dengan dengan nilai Mean Decrease Accuracy sebesar 23,92%. Variabel ini yang memiliki paling nilai Mean Decrease Accuracy tinggi diantara variabel atribut yang lainnya.ย ย Keywords: Kemiskinan, Random Forest, Mean Decrease Accurac
Analysis of the Foreign Trade and Gross Domestic Product Effect on Foreign Direct Investment using Panel Data Regression Estimation
Get PDFInvestment is one of the components that determines a country's economic growth. Sources of investment funds can be seen through two approaches, domestic investment and foreign investment. One of the promising components of foreign investment is Foreign Direct Investment (FDI). FDI is considered more valuable for the country because it is more long-term in nature. This study aims to see the effect of Gross Domestic Product (GDP) and export-import as foreign trade activities on FDI, through estimation with panel data regression model. The data used is data from 20 countries with observation period from 2009 to 2018. With the Random Effect Model as the best model, which the estimators also qualify the BLUE estimator. it can be concluded that partially the GDP variable has no significant effect. Meanwhile, exports have a significant positive effect and imports have a significant negative effect on FDI