Pub Date : 2022-01-23DOI: 10.24198/jmi.v17.n2.35025.127-135
Sagita Charolina Sihombing, Dina Agnesia Sihombing
Grouping the level of community welfare in North Sumatra Province needs to be done to make it easier for the government to focus on development in cities / districts whose welfare levels are still low. In this study, the level of welfare of the people of North Sumatra was grouped based on several variables. The grouping is done using the K-means clustering method. K-means clustering is one of the clustering methods used to classify large amounts of data. This method produces groups of data based on the number of groups desired. In this study, to determine the best number of groups, the Elbow method was used. The first step in this study was to divide the data into groups of data for the number of groups (k) starting from k = 2 to k = 8. Next, calculate the SSE (Sum of Square Error) from cluster k = 2 to k = 8. After that, create an Elbow graph from the resulting SSE values to determine the most optimal amount of k. Data processing to obtain groups based on the number of clusters (k) was carried out using Matlab 2013b software. Group data from the software is stored in Ms.excel. Meanwhile, the resulting Elbow graphic display is created in the Matlab GUI. From the resulting elbow graph, it can be seen that the SSE value has decreased drastically when k = 2 to k = 5, while from k = 5 to k = 8, the decrease in the graph is not significant. From this we know that the optimal number of clusters is k = 5. So, from the elbow graph, the results show that the North Sumatran people are optimally grouped into five clusters. Cluster 1 is only filled by the city of Medan, cluster 2 consists of North Tapanuli Regency, Toba Regency, Simalungun Regency, Dairi Regency, Karo Regency, Langkat Regency, Humbang Hasundutan Regency, West Pakpak Regency, Samosir Regency, Serdang Bedagai Regency, Padangsidimpuan City, Kota Gunungsitoli, cluster 3 consists of Deli Serdang Regency, Pematangsiantar City, Tebingtinggi City, Binjai City, cluster 4 consists of Labuhanbatu Regency, Asahan Regency, Batu Bara Regency, South Labuhanbatu Regency, North Labuhanbatu Regency, Sibolga City, Tanjungbalai City, and cluster 5 consisting of Nias Regency, Mandailing Natal Regency, South Tapanuli Regency, Central Tapanuli Regency, South Nias Regency, North Padang Lawas Regency, Padang Lawas Regency, North Nias Regency, West Nias Regency.
{"title":"Pengelompokan Tingkat Kesejahteraan Masyarakat di Sumatera Utara dengan Metode K-Means Clustering","authors":"Sagita Charolina Sihombing, Dina Agnesia Sihombing","doi":"10.24198/jmi.v17.n2.35025.127-135","DOIUrl":"https://doi.org/10.24198/jmi.v17.n2.35025.127-135","url":null,"abstract":"Grouping the level of community welfare in North Sumatra Province needs to be done to make it easier for the government to focus on development in cities / districts whose welfare levels are still low. In this study, the level of welfare of the people of North Sumatra was grouped based on several variables. The grouping is done using the K-means clustering method. K-means clustering is one of the clustering methods used to classify large amounts of data. This method produces groups of data based on the number of groups desired. In this study, to determine the best number of groups, the Elbow method was used. The first step in this study was to divide the data into groups of data for the number of groups (k) starting from k = 2 to k = 8. Next, calculate the SSE (Sum of Square Error) from cluster k = 2 to k = 8. After that, create an Elbow graph from the resulting SSE values to determine the most optimal amount of k. Data processing to obtain groups based on the number of clusters (k) was carried out using Matlab 2013b software. Group data from the software is stored in Ms.excel. Meanwhile, the resulting Elbow graphic display is created in the Matlab GUI. From the resulting elbow graph, it can be seen that the SSE value has decreased drastically when k = 2 to k = 5, while from k = 5 to k = 8, the decrease in the graph is not significant. From this we know that the optimal number of clusters is k = 5. So, from the elbow graph, the results show that the North Sumatran people are optimally grouped into five clusters. Cluster 1 is only filled by the city of Medan, cluster 2 consists of North Tapanuli Regency, Toba Regency, Simalungun Regency, Dairi Regency, Karo Regency, Langkat Regency, Humbang Hasundutan Regency, West Pakpak Regency, Samosir Regency, Serdang Bedagai Regency, Padangsidimpuan City, Kota Gunungsitoli, cluster 3 consists of Deli Serdang Regency, Pematangsiantar City, Tebingtinggi City, Binjai City, cluster 4 consists of Labuhanbatu Regency, Asahan Regency, Batu Bara Regency, South Labuhanbatu Regency, North Labuhanbatu Regency, Sibolga City, Tanjungbalai City, and cluster 5 consisting of Nias Regency, Mandailing Natal Regency, South Tapanuli Regency, Central Tapanuli Regency, South Nias Regency, North Padang Lawas Regency, Padang Lawas Regency, North Nias Regency, West Nias Regency.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42214584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-23DOI: 10.24198/jmi.v17.n2.35522.147-153
Athia Nurindah Sari, Azmi Nazra, Dan Harimpyu
{"title":"Suatu Kasus Dispensable Set pada Fuzzy N-Soft Set","authors":"Athia Nurindah Sari, Azmi Nazra, Dan Harimpyu","doi":"10.24198/jmi.v17.n2.35522.147-153","DOIUrl":"https://doi.org/10.24198/jmi.v17.n2.35522.147-153","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45823284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-23DOI: 10.24198/jmi.v17.n2.35549.137-145
Jeane R. M. D. P Chantique, Herlina Napitupulu, Betty Subartini
{"title":"Perbandingan Algortime Dijkstra dan Node Combination Dalam Perhitungan Betweenness Centrality Pada Graf Jaringan Listrik Universitas Padjadjaran Jatinangor","authors":"Jeane R. M. D. P Chantique, Herlina Napitupulu, Betty Subartini","doi":"10.24198/jmi.v17.n2.35549.137-145","DOIUrl":"https://doi.org/10.24198/jmi.v17.n2.35549.137-145","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49056664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-23DOI: 10.24198/jmi.v17.n2.34360.97-108
David Eurico, Sandra Kezia, L. Noviyanti, Achmad Zanbar Soleh
Determination of life insurance reserves involving expenses in premiums is important to be calculated correctly so that insurance companies can manage benefit reserves properly. This study will calculate the reserve value of the single life double decrement endowment life insurance product (death and total disability) using the Gross Premium Valuation (GPV) method with a prospective approach. The reserve value obtained from the prospective GPV approach is zero at the beginning of the first year’s reserves. This shows that all incoming premium in the first year are used to cover expenses that must be incurred by the company. Furthermore, the value of GPV reserve will continue to increase so that at the end of the policy year it will be the same as the endowment benefits promised to the policyholder. In this study, administrative expenses, policy expenses, and loyalty bonuses are also involved. The result given is the amount of gross premium that must be paid from the insured woman aged 30 years, with a protection period of 20 years and a premium payment period of 20 years paid at the beginning of each year, which is Rp6.680.206,00 for an interest rate of 7% and Rp6.126.428,00 for an interest rate of 8%. Reserves that must be prepared by the insurance company at the end of the first year are Rp2.581.881,00 for an interest rate of 7% and Rp2.309.611,00 for an interest rate of 8% and will increase until the end of the 20th year of Rp200.000.000,00. The result is that gross premium and reserves will have a smaller value for a higher interest rate. The results of this study can be used by insurance companies as a reference for calculating reserves and interest rate sensitivity used in the GPV method.
{"title":"Cadangan Prospektif Produk Asuransi Jiwa Endowment dengan Metode Gross Premium Valuation","authors":"David Eurico, Sandra Kezia, L. Noviyanti, Achmad Zanbar Soleh","doi":"10.24198/jmi.v17.n2.34360.97-108","DOIUrl":"https://doi.org/10.24198/jmi.v17.n2.34360.97-108","url":null,"abstract":"Determination of life insurance reserves involving expenses in premiums is important to be calculated correctly so that insurance companies can manage benefit reserves properly. This study will calculate the reserve value of the single life double decrement endowment life insurance product (death and total disability) using the Gross Premium Valuation (GPV) method with a prospective approach. The reserve value obtained from the prospective GPV approach is zero at the beginning of the first year’s reserves. This shows that all incoming premium in the first year are used to cover expenses that must be incurred by the company. Furthermore, the value of GPV reserve will continue to increase so that at the end of the policy year it will be the same as the endowment benefits promised to the policyholder. In this study, administrative expenses, policy expenses, and loyalty bonuses are also involved. The result given is the amount of gross premium that must be paid from the insured woman aged 30 years, with a protection period of 20 years and a premium payment period of 20 years paid at the beginning of each year, which is Rp6.680.206,00 for an interest rate of 7% and Rp6.126.428,00 for an interest rate of 8%. Reserves that must be prepared by the insurance company at the end of the first year are Rp2.581.881,00 for an interest rate of 7% and Rp2.309.611,00 for an interest rate of 8% and will increase until the end of the 20th year of Rp200.000.000,00. The result is that gross premium and reserves will have a smaller value for a higher interest rate. The results of this study can be used by insurance companies as a reference for calculating reserves and interest rate sensitivity used in the GPV method.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43788178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-23DOI: 10.24198/jmi.v17.n2.34441.109-118
Dewinta Mamula, N. Achmad, Resmawan Resmawan
This article identifies the general form of matrix power and trace of an integer power of Special Form of the 3 × 3 Complex Circulant matrix. The research begins to determine the general form of an integer power of Special Form of the 3 × 3 Complex Circulant matrix, followed by determining the general form trace of an integer power of Special Form of the 3 × 3 Complex Circulant matrix. The proof is done by using mathematical induction. The final result of this article is to obtain the general form of the matrix A^n and tr(A^n) for n integers in special form of the 3 × 3 complex Circulant matrix.
{"title":"Matriks Circulant Kompleks Bentuk Khusus 3 × 3 Berpangkat Bilangan Bulat","authors":"Dewinta Mamula, N. Achmad, Resmawan Resmawan","doi":"10.24198/jmi.v17.n2.34441.109-118","DOIUrl":"https://doi.org/10.24198/jmi.v17.n2.34441.109-118","url":null,"abstract":"This article identifies the general form of matrix power and trace of an integer power of Special Form of the 3 × 3 Complex Circulant matrix. The research begins to determine the general form of an integer power of Special Form of the 3 × 3 Complex Circulant matrix, followed by determining the general form trace of an integer power of Special Form of the 3 × 3 Complex Circulant matrix. The proof is done by using mathematical induction. The final result of this article is to obtain the general form of the matrix A^n and tr(A^n) for n integers in special form of the 3 × 3 complex Circulant matrix.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41621775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-23DOI: 10.24198/jmi.v17.n2.35488.85-96
Dian Ariesta Yuwaningsih, Rusmining Rusmining
Given R and S are commutative rings, respectively, and (R,S)-module M with the property S = S and for each a ∈ M satisfy a ∈ RaS. A proper (R,S)-submodule P of M is called jontly α-prime (R,S)submodules if for each r ∈ R and m ∈M with r(m+m)S ⊆ P implies r + r ∈ (P :R M) or m + m ∈ P . If M has a jontly α-prime (R,S)submodules then the jointly α-prime radical of M is M or is the intersection of all jontly α-prime (R,S)-submodule of M . In this article, we present some properties of jointly α-prime radicals of an (R,S)module. Furthermore, at the end of this article, the jointly α-prime radical properties of a left multiplication (R,S)-module are presented.
{"title":"Radikal Prima-α Gabungan pada (R,S)-Modul","authors":"Dian Ariesta Yuwaningsih, Rusmining Rusmining","doi":"10.24198/jmi.v17.n2.35488.85-96","DOIUrl":"https://doi.org/10.24198/jmi.v17.n2.35488.85-96","url":null,"abstract":"Given R and S are commutative rings, respectively, and (R,S)-module M with the property S = S and for each a ∈ M satisfy a ∈ RaS. A proper (R,S)-submodule P of M is called jontly α-prime (R,S)submodules if for each r ∈ R and m ∈M with r(m+m)S ⊆ P implies r + r ∈ (P :R M) or m + m ∈ P . If M has a jontly α-prime (R,S)submodules then the jointly α-prime radical of M is M or is the intersection of all jontly α-prime (R,S)-submodule of M . In this article, we present some properties of jointly α-prime radicals of an (R,S)module. Furthermore, at the end of this article, the jointly α-prime radical properties of a left multiplication (R,S)-module are presented.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43947568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-05DOI: 10.24198/jmi.v17.n1.32682.5-13
Nurul Gusriani, Firdaniza Firdaniza
{"title":"Model Kasus Demam Berdarah Dengue (DBB) di Kabupaten Majalengka Tahun 2016 Berdasarkan Regresi TELBS","authors":"Nurul Gusriani, Firdaniza Firdaniza","doi":"10.24198/jmi.v17.n1.32682.5-13","DOIUrl":"https://doi.org/10.24198/jmi.v17.n1.32682.5-13","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48898208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-05DOI: 10.24198/jmi.v17.n1.32037.15-21
Yulianus - Brahmantyo, Riaman Riaman, F. Sukono
The high risk of losing fishermen's life while at sea is inversely proportional to their low welfare. Fishermen are also unable to meet their daily needs when they are not going to sea. Fishermen welfare insurance can be a solution for them to meet their daily needs. Willingness to Pay (WTP) of fishermen to participate in fishermen welfare insurance can be analyzed using Logistic Regression with Newton Raphson and Genetic Algorithm approximations. Some of the main factors that can support their WTP to participate in fishermen welfare insurance, are fishermen education, membership in the fishing community, membership in fisherman business cards, and knowledge about the existence of fishermen insurance. From these four factors, Logistic Regression Model is generated which is expected to help the increase of fishermen’s WTP on fishermen insurance in Indonesia.
{"title":"Willingness to Pay of Fishermen Insurance Using Logistic Regression with Parameter Estimated by Maximum Likelihood Estimation Based on Newton Raphson Iteration","authors":"Yulianus - Brahmantyo, Riaman Riaman, F. Sukono","doi":"10.24198/jmi.v17.n1.32037.15-21","DOIUrl":"https://doi.org/10.24198/jmi.v17.n1.32037.15-21","url":null,"abstract":"The high risk of losing fishermen's life while at sea is inversely proportional to their low welfare. Fishermen are also unable to meet their daily needs when they are not going to sea. Fishermen welfare insurance can be a solution for them to meet their daily needs. Willingness to Pay (WTP) of fishermen to participate in fishermen welfare insurance can be analyzed using Logistic Regression with Newton Raphson and Genetic Algorithm approximations. Some of the main factors that can support their WTP to participate in fishermen welfare insurance, are fishermen education, membership in the fishing community, membership in fisherman business cards, and knowledge about the existence of fishermen insurance. From these four factors, Logistic Regression Model is generated which is expected to help the increase of fishermen’s WTP on fishermen insurance in Indonesia.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44357453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-05DOI: 10.24198/jmi.v17.n1.30288.63-72
D. Chaerani, Naufal Badruzzaman, E. Hertini, E. Rusyaman
Maximum flow problem is one of optimization problems which aims to find the maximum flow value that is traversed in a network system. This problem can be solved using existing algorithms and linear programming. In the case of maximum flow, often the parameters used vary due to certain factors. [1] designed the Robust Counterpart Optimization Model for Maximum Flow Problems by assuming side and flow capacities from an indefinite point to destination point to solve the maximum flow problem with uncertainty. To facilitate the search for solutions with large amounts of data, a Graphical User Interface (GUI) was made. GUI is a pictorial interface of a program that can facilitate its users in completing their work such as counting, making, and so on. In this study, the GUI was created using Maple software and used the Adjustable Robust Counterpart Optimization Model made by [1]. Thus, the search for solutions to maximum flow problems can be resolved quickly and efficiently only by entering the data needed for calculations in the GUI.
{"title":"Designing Graphical User Interface (GUI) for Adjustable Robust Maximum Flow Problem","authors":"D. Chaerani, Naufal Badruzzaman, E. Hertini, E. Rusyaman","doi":"10.24198/jmi.v17.n1.30288.63-72","DOIUrl":"https://doi.org/10.24198/jmi.v17.n1.30288.63-72","url":null,"abstract":"Maximum flow problem is one of optimization problems which aims to find the maximum flow value that is traversed in a network system. This problem can be solved using existing algorithms and linear programming. In the case of maximum flow, often the parameters used vary due to certain factors. [1] designed the Robust Counterpart Optimization Model for Maximum Flow Problems by assuming side and flow capacities from an indefinite point to destination point to solve the maximum flow problem with uncertainty. To facilitate the search for solutions with large amounts of data, a Graphical User Interface (GUI) was made. GUI is a pictorial interface of a program that can facilitate its users in completing their work such as counting, making, and so on. In this study, the GUI was created using Maple software and used the Adjustable Robust Counterpart Optimization Model made by [1]. Thus, the search for solutions to maximum flow problems can be resolved quickly and efficiently only by entering the data needed for calculations in the GUI.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69268782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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