Jurnal Matematika, Statistika dan Komputasi

Pengelompokan Kabupaten/Kota di Provinsi Papua Barat Berdasarkan Indikator Kesejahteraan Rakyat Tahun 2023 Menggunakan Metode C-means dan Fuzzy C-means Clustering

2024-10-24T00:44:25+00:00

Kesejahteraan rakyat adalah suatu kondisi yang menampilkan tentang keadaan kehidupan masyarakat yang dapat dilihat dari standar kehidupan masyarakat. Di Indonesia bantuan terutama di Provinsi Papua Barat, tingkat sosial yang masih sangat rendah dan banyak masyarakat yang hidup di garis kemiskinan. Salah satu upaya menuju kesejahteraan rakyat adalah dengan meningkatkan kesejahteraan masyarakat dalam aspek ekonomi dan sosial. Untuk mencapai tujuan ini, penting untuk memahami kondisi awal kesejahteraan mayarakat. Kondisi awal dapat ditentukan dengan mengelompokkan suatu kabupaten/kota dan melakukan pemerataan kesejahteraan masyarakat di setiap daerah. Dalam statistika terdapat dua metode yaitu pengelompokan dan klasifikasi. Dalam penelitian ini, metode statistika yang digunakan yaitu pengelompokan. Pengelompokan (clustering) adalah teknik mengelompokan data, yang bertujuan untuk mengelompokkan objek berdasarkan kesamaan karakteristiknya. Terdapat dua pendekatan dalam clustering yaitu berhierarki dan non-berhierarki. Dalam penelitian ini,pendekatan non-berhierarki yang digunakan. Non-berhierarki terdiri dari dua metode yaitu c-means dan fuzzy c-means. Tujuan pada penelitian ini adalah untuk mengelompokkan indikator kesejahteraan rakyat dengan metode c-means dan fuzzy c-means menggunakan data indikator kesejahteraan rakyat dari tahun 2023. Metode c-means adalah metode clustering yang membagi data ke dalam satu cluster atau lebih sebanyak buah, sedangkan metode fuzzy c-means adalah metode pengelompokan objek yang memanfaatkan dasar pembobotan dengan teori himpunan fuzzy. Hasil penelitian ini adalah membandingkan kedua metode tersebut untuk mendapatkan hasil pengelompokan terbaik, hasil yang diperoleh yaitu fuzzy c-means clustering dengan jumlah cluster dengan pembagian cluster yaitu cluster 1 terdapat 2 kabupaten. Cluster 2 terdapat 1 kabupaten, cluster 3 terdapat 4 kabupaten, cluster 4 terdapat 2 kabupaten dan cluster 5 terdapat 4 kabupaten. Diperoleh nilai indeks siluet sebesar 0,3428 yang dapat dikategorikan baik dan nilai rasio sigma w/sigma b adalah 0,7613.

Examination of School Participation Rates with Nonparametric Geographically Weighted Regression-Truncated Spline Approach

2024-10-23T06:48:33+00:00

This study analyzes school participation rates (APS) in Indonesia using the Nonparametric Geographically Weighted Regression-Truncated Spline (NGWR-TS) method. The objective is to identify significant factors influencing APS across 34 provinces, considering geographic variations and nonlinear data patterns. Secondary data was obtained from the Central Bureau of Statistics (BPS), the Ministry of Education and Culture (Kemendikbud), and the Ministry of Women's Empowerment and Child Protection (KemenPPPA). The analysis results indicate that APS are influenced by accessibility to education, teaching quality, and socioeconomic conditions. Spatial mapping reveals that regions with high APS, such as Special Region of Yogyakarta, have good educational infrastructure support, while Papua exhibits low participation due to geographic and social challenges. This study emphasizes the need for more focused and locally responsive education policies to improve APS, especially in underdeveloped regions. The contribution of this research to achieving the Sustainable Development Goals (APS) in Indonesia is significant, particularly in enhancing educational participation in areas that require more attention. The aim of this approach is to develop policies that will substantially enhance educational outcomes and increase school attendance across Indonesia.

Global Stability and Sensitivity Analysis of a Mumps Transmission Model

2024-10-22T03:12:12+00:00

Mumps is a viral infection that targets the parotid glands, caused by a virus from the Rubulavirus genus within the Paramyxoviridae family. Early symptoms include fever, headache, muscle pain, and facial swelling. Transmission occurs through droplets, fomites, or direct contact. The best prevention is the MMR vaccine, although its effectiveness is limited due to high virus mutation rates. Children aged five to nine and vaccinated young adults are also at risk. Due to the decreased effectiveness of the vaccine, new management strategies such as quarantine have been introduced. This study builds on previous research by focusing on both global stability and sensitivity analysis, which had not been addressed before. It uses Lyapunov functions to analyze global stability at both equilibria and sensitivity analysis with respect to the basic reproduction number and the infected population size to identify factors contributing to high transmission rates. The findings show that global stability analysis indicates that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than or equal to 1, while the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than 1. Sensitivity analysis identifies that the most influential parameters on the infected population are those affecting the graph directly and inversely, namely the contact rate between susceptible and infected individuals, the natural death rate, and the birth rate. Increasing the contact rate between susceptible and infected individuals and the birth rate raises the number of infected individuals, whereas increasing the natural death rate reduces the number of infected individuals.

Bahasa Indonesia Hybrid Hierarchical Clustering Via Mutual Cluster pada Pengelompokan Kabupaten/Kota di Pulau Kalimantan Berdasarkan Indikator Kemiskinan

2024-10-21T15:39:31+00:00

Analisis cluster adalah salah satu teknik analisis data yang digunakan untuk mengelompokkan suatu objek dalam satu cluster berdasarkan kemiripan karakteristik antar objeknya. Hybrid hierarchical clustering via mutual cluster merupakan metode pengelompokan yang menggabungkan keunggulan dari dua pendekatan yang bersifat buttom up dan yang bersifat top down. Hierarchical clustering digunakan untuk membangun struktur hierarki dari data, sedangkan mutual cluster membantu dalam penentuan jumlah cluster optimal serta memastikan kestabilan hasil clustering. Tujuan penelitian ini adalah melakukan pengelompokan Kabupaten/Kota di Pulau Kalimantan berdasarkan indikator-indikator yang diduga berpengaruh terhadap kemiskinan Tahun 2022. Hasil penelitian, diperoleh cluster optimal sebanyak 4 cluster dari hasil validitas menggunakan Cluster Tightness Measure (CTM) dengan nilai terkecil yaitu sebesar 0,655. Karakteristik dari setiap cluster yang terbentuk dapat menjadi informasi untuk pemetaan daerah kemiskinan.

Kata kunci: Analisis Cluster, Buttom Up, Hybrid Hierarchical Clustering, Mutual Cluster,

Top Down, dan Cluster Tightness Measure (CTM)

A NOTE ON EQUIVALENCE RELATIONS ON TERNARY SEMIGROUPS

2024-10-18T12:16:05+00:00

The awareness of ideals affects obviously to the concern of certain equivalence relations over a ternary semi-group. These equivalence relations, early studied by J.A. Green (1951), have acted a basic role in the progress of semi-group theory. The majorapplication of this paper is to find the some results on Greens Relations and their conditions on ternary semigroups.

Average Temperature Prediction Using The Singular Spectrum Analysis Method

2024-10-17T03:19:56+00:00

Surabaya is one of the cities with the highest population density in Indonesia, which continues to grow and urbanize at an extraordinary speed. In addition to having a dense population, the capital of East Java Province has a complex infrastructure, so ma

2024-10-14T08:00:45+00:00

Surabaya is one of the cities with the highest population density in Indonesia, which continues to grow and urbanize at an extraordinary speed. In addition to having a dense population, the capital of East Java Province has a complex infrastructure, so many emergency events occur. According to the annual report of BPBD Surabaya City, as many as 13 thousand emergency events occurred in 2023. Therefore, with a large chance of emergency events occurring, it is necessary to reduce the risk of emergency events. Therefore, capacity building is important to increase community resilience during emergency events. This research aims to determine the level of capacity of an area. This calculation is carried out using the Principal Component Analysis (PCA) method based on the parameters that determine the capacity of an area. The calculation results found that there are 9 sub-districts with high capacity levels, 17 sub-districts with medium capacity levels, and 5 sub-districts with low capacity levels. So it can be concluded that Surabaya City still needs an increase in capacity.

Capacity Analysis of Emergency Events in Surabaya City Using Principal Component Analysis (PCA) Method

2024-10-14T07:51:34+00:00

The Generalized Riemann Integral

2024-10-12T23:07:55+00:00

Riemann integration theory integrates functions on a bounded interval as a Riemann sum approach (integral) where the fineness of the partitions is controlled by a number (norm) of the partition. In Generalized Riemann integral theory, the Riemann sum approach of functions is controlled by a gauge on tagged partition so that enabling integrating functions with much larger collections. Therefore, the theorems that apply to Generalized Riemann integral theory have differences in their hypotheses and conclusions. In this paper, theory of Generalized Riemann integral is studied by giving some examples of functions that are Generalized Riemann integrable such that they are not Riemann integrable; and proving some theorems that apply in this theory. The functions are integrable by constructing a gauge on the tagged partition of the interval such that the Riemann sum of the function is very close to some real number. Functions defined on a bounded interval that are Generalized Riemann integrable such that they are or not Riemann integrable have the general form of the function: a function f on [a,b] is continuous on [a,b]\Z and discontinuous on Z, where Z is a null set. Moreover, an unbounded function f on [a,b] is integrable, if the set Z where f is unbounded on Z is a countable set. Furthermore, these two criteria can be extended to infinite intervals, i.e. a function defined on an infinite interval can be Generalized Riemann integrable such that it is not Riemann integrable, if the set of discontinuous and unbounded points of the function is a null set. A sequence of integrable functions on an interval I that converges to a function on I, satisfies that this limit function is integrable if it satisfies that the existence of the dominating functions.

APPLICATION OF PATH ANALYSIS TO ANALYZE THE FACTORS THAT INFLUENCE THE QUALITY OF THE HUMAN DEVELOPMENT INDEX IN BUTON DISTRICT

2024-10-09T23:38:11+00:00

Indicators of the success of human development in a country can be measured through the human development index, which includes three basic dimensions of long and healthy life, knowledge, and a decent standard of living. This research aims to identify factors that directly and indirectly influence HDI in Buton Regency using the path analysis method. The results of the analysis show that there is a significant direct influence between the variables life expectancy, per capita expenditure and expected length of schooling on the human development index of 99.4%. The results of the indirect influence of life expectancy, per capita expenditure and expected years of schooling through the poverty level on the human development index provide results that are not statistically significant.