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Unnes Journal of Mathematics
Published by Universitas Negeri Semarang
ISSN : 22526943     EISSN : 24605859     DOI : https://doi.org/10.15294/ujm
Core Subject : Education,
Mathematics
Unnes Journal of Mathematics (UJM) publishes research issues on mathematics and its apllication. The UJM processes manuscripts resulted from a research in mathematics and its application scope, which includes. The scopes include research in: 1. Algebra 2. Analysis 3. Discrete Mathematics and Graph Theory 3. Differential Equation 4. Geometry 5. Mathematics Computation, 6. Statistics.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 234 Documents
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Perbandingan Metode Weighted Fuzzy Time Series, Seasonal ARIMA, dan Holt-Winter's Exponential Smoothing untuk Meramalkan Data Musiman Assidiq, Addinul; Hendikawati, Putriaji; Dwidayati, Nurkaromah
Unnes Journal of Mathematics Vol 6 No 2 (2017)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v6i2.12288

Abstract

Perkembangan metode peramalan data time series berpola musiman memberikan banyak pilihan metode yang dapat digunakan untuk meramalkan data musiman, sehingga perlu dilakukan perbandingan metode peramalan untuk mendapatkan hasil ramalan dengan akurasi yang tinggi. Pada penelitian ini permasalahan yang dikaji adalah perbandingan metode Weighted Fuzzy Time Series, Seasonal ARIMA, dan Holt-Winter’s Exponential Smoothing untuk meramalkan data musiman. Perbandingan yang dilakukan adalah membandingkan nilai akurasi ramalan RMSE dan MAPE. Penelitian ini menggunakan data pengunjung pariwisata Bali periode Januari 2009 s.d Desember 2013. Analisis metode Holt-Winter’s Exponential Smoothing menggunakan trial and error dengan kriteria MAPE dan MSE terkecil untuk mencari model terbaik. Diperoleh model terbaik dengan nilai α adalah 0,6, β adalah 0,1, dan γ adalah 0,1 serta menghasilkan RMSE dan MAPE sebesar 23165,04 dan 6,32. Analisis metode Seasonal ARIMA menggunakan estimasi model dengan kriteria MSE terkecil dan signifikansi model untuk mencari model terbaik. Diperoleh model terbaik SARIMA serta menghasilkan nilai RMSE dan MAPE sebesar 20499,69 dan 5,27. Analisis metode Weighted Fuzzy Time Series dilakukan dengan membagi himpunan sampel menjadi tiga bagian dengan panjang interval yang berbeda yaitu panjang interval 5000, panjang interval 7500, dan panjang interval 15000. Pada panjang interval 5000 menghasilkan nilai RMSE dan MAPE sebesar 17953,55 dan 4,87, panjang interval 7500 menghasilkan nilai RMSE dan MAPE sebesar 18992,53 dan 5,61, serta panjang interval 15000 menghasilkan nilai RMSE dan MAPE sebesar 21026,11 dan 6,21. Berdasarkan hasil penelitian dapat disimpulkan bahwa metode Weighted Fuzzy Time Series merupakan metode terbaik untuk meramalkan data musiman karena memiliki nilai akurasi ramalan RMSE dan MAPE lebih kecil. The development of methods forecasting time series data provides seasonal pattern selection methods that can be used for seasonal forecast data, so it is necessary to do a comparison of forecasting methods for getting the forecast best accuracy. In this research the problem studied is the comparison of methods is Weighted Fuzzy Time Series, Seasonal ARIMA and Holt-Winter's Exponential Smoothing for seasonal forecast data. The comparison is forecast accuracy RMSE and MAPE. This research used Bali's tourism visitors data in period January 2009 to December 2013. Analysis methods Holt-Winter's Exponential Smoothing using trial and error with the smallest MSE and MAPE criteria to find the best model. The best model is obtained with a value of α is 0,6, β is 0,1, and γ is 0,1, and value of RMSE and MAPE is 23165,04 and 6,32. The analysis method Seasonal ARIMA used model estimation with the smallest MSE criteria and significance of the model to find the best model. Retrieved best model SARIMA and value of RMSE and MAPE is 20499,69 and 5,27. Analysis methods Weighted Fuzzy Time Series do sample set split into three sections with different length interval is the interval length 5000, interval length 7500 and interval length 15000. In the long interval of 5000 resulted in the value of RMSE and MAPE is 17953,55 and 4 ,87, interval lenght of 7500 resulted in the value of RMSE and MAPE is 18992,53 and 5,61, and interval lenght of 15000 resulted in the value of RMSE and MAPE is 21026,11 and 6,21. Based on the results of this research concluded that the method of Weighted Fuzzy Time Series is the best method used forecasting seasonal data because it has the accuracy of the forecast RMSE and MAPE are smaller.
ANALISIS SISTEM ANTRIAN DISIPLIN PRIORITAS PADA BENGKEL MOTOR AHASS 10293 (ASZA MOTOR 2) CABANG UNGARAN Saraswati, Andhina; Hendikawati, Putriaji
Unnes Journal of Mathematics Vol 7 No 1 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i1.12394

Abstract

Abstrak Disiplin antrian yang sering digunakan adalah disiplin pelayanan FCFS, namun ada disiplin antrian lainnya yaitu disiplin prioritas. Bengkel Motor AHASS 10293 menerapkan disiplin prioritas dalam sistem antriannya. Penelitian dilakukan selama 3 hari pada hari dan waktu sibuk yang dipilih secara acak yaitu 27 Maret, 28 Maret, dan 30 Maret 2015. Data yang diambil adalah waktu antar kedatangan dan waktu pelayanan, sehingga dari data tersebut diperoleh hasil ukuran kinerja antrian prioritas. Hasil rata-rata perhitungan ukuran kinerja antrian dalam tiga hari adalah = 0,0000466987, = 0,0000000084, = 2,6667133647, = 2,1201413512, = 0,0000056505, = 0,0000000003, = 0,3226723168, = 0,0749116611. Biaya fasilitas ketiga hari adalah Rp. 31.250,00 dan biaya menunggu hari pertama Rp. 4.100,00, hari kedua Rp. 2.700,00, hari ketiga Rp. 3.700,00. Sistem antrian yang diterapkan oleh Bengkel Motor AHASS 10293 sudah cukup baik karena antrian yang terjadi tidak terlalu parah meski pelanggan yang datang tiap harinya cukup banyak. Abstract Queuing discipline that often used is FCFS, but there are another queuing disciplines one of which is priority queuing discipline. AHASS 10293 Machine Shop using priority discipline for their system. This study was conducted for 3 days in a busy day and time that selected randomly on March 27, March 28, and March 30, 2015. The captured data are time arrivals and service time, so that from those data obtained the results of priority queuing performance measurements. The average results from three days are = 0,0000466987, = 0,0000000084, = 2,6667133647, = 2,1201413512, = 0,0000056505, = 0,0000000003, = 0,3226723168, = 0,0749116611. Customer service cost for three days is Rp. 31.250,00 and customer waiting cost for the first day is Rp. 4.100,00, the second day is Rp. 2.700,00, the third day is Rp. 3.700,00. Queuing system that applied by AHASS 10293 Machine Shop is good enough because the queues are not too severe even though the customers who come every day quite a lot.
Implementasi Fuzzy Inference System Metode Sugeno pada Penentuan Produksi Sarung (Studi Kasus: PT. Asaputex Jaya Tegal) Irfan, Mohammad Syarif; Muslim, Much Aziz; Arini, Florentina Yuni
Unnes Journal of Mathematics Vol 6 No 2 (2017)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v6i2.12455

Abstract

Penelitian ini bertujuan untuk memperkirakan jumlah produksi dengan mengaplikasikan fuzzy inference system metode Sugeno berdasarkan variabel jumlah permintaan, persediaan, dan produksi. Pengambilan data diperoleh di PT. Asaputex Jaya Tegal dengan berbagai jenis produk sarung mulai tahun 2013 sampai dengan 2014. Hasil penelitian pada bulan Juli 2014 dilihat dari jumlah permintaan 3850 dan persediaan 350 sarung, dengan menggunakan metode Sugeno didapatkan hasil jumlah produksi sarung rayon yang harus di produksi sebanyak 3539 sarung. Berbeda dengan data jumlah produksi PT. Asaputex Jaya Tegal pada bulan Juli 2014 yaitu 3900 sarung, sehingga berdampak banyaknya penumpukan sarung di gudang. Berdasarkan perhitungan tersebut, disimpulkan bahwa Metode Sugeno lebih efektif dalam penentuan produksi sarung. The aim of the research is to estimate the amount of the production by applying fuzzy inference system with Sugeno method based on the request, stock, and production variables. This research got the data from PT. Asaputex Jaya Tegal with its sarong production from the year of 2013 up to 2014. The result of this study shows that in July 2014, the number of the request was 3850 and the stock was 350 sarongs. By using Sugeno method, it is got the number of sarong that have to be produced was 3539 sarongs. It is so different with production data from PT. Asaputex Jaya Tegal in July 2014, that was 3900 sarongs, therefore, there were too many sarong accumulation. Based on the calculation above, it is concluded that Sugeno method is more effective being used to determine the number of sarong production.
Pemodelan Matematika Penyebaran Penyakit Ebola dengan Model Epidemi SIR pada Populasi Manusia Tak Konstan dengan Treatment Himawan, Adhitya; Waluya, Stevanus Budi; Supriyono, Supriyono
Unnes Journal of Mathematics Vol 6 No 2 (2017)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v6i2.12508

Abstract

Virus Ebola termasuk ke dalam keluarga Filovirus. Filovirus diklasifikasikan ke dalam orde Mononegavirales yang berisi virus RNA untai – negatif tak bersegmen family Paramyxoviridae, Rhabdoviridae, dan Bornaviridae. Termasuk dengan epidemik saat ini, telah ada kira – kira 20 penyebaran Ebola yang dikenali, semua terjadi di Afrika, dengan tingkat kematian 25% hingga 90%. Mengingat betapa bahayanya penyakit Ebola terhadap umat manusia, maka sangat perlu bagi manusia untuk mempelajari penyakit tersebut, salah satunya dengan pemodelan matematika penyebaran penyakit Ebola. Model matematika yang digunakan dalam penelitian ini adalah model epidemi SIR yang ditambah dengan kompartemen/kelas Treatment. Setelah terbangun model matematika penyebaran penyakit Ebola, selanjutnya dianalisis sehingga nantinya akan diperoleh titik kesetimbangan (ekuilibrium) nya. Selanjutnya menentukan bilangan reproduksi dasar (R0) . Setelah didapat titik kesetimbangan dan bilangan reproduksi dasar (R0) tersebut, selanjutnya dilakukan analisis lebih lanjut tentang kestabilan titik kesetimbangannya. Lebih lanjut juga untuk mensimulasikan penyebaran penyakit Ebola maka dapat dilakukan dengan menggunakan Maple.
PERBANDINGAN TINGKAT AKURASI METODE AUTOMATIC CLUSTERING, AVERAGE BASED, DAN MARKOV CHAIN FUZZY TIME SERIES PADA NILAI TUKAR (KURS) RUPIAH hengky tri ikhsanto, hengky tri ikhsanto; Sugiman, Sugiman; Hendikawati, Putriaji
Unnes Journal of Mathematics Vol 7 No 1 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i1.12574

Abstract

Penelitian ini membahas perbandingan keakurasian model peramalan fuzzy time series dengan automatic clustering dan average based untuk membentuk interval dan proses defuzzifikasi menggunakan konsep markov chain. Model tersebut digunakan untuk meramalkan data nilai tukar (KURS) mata uang Rupiah terhadap US Dolar dan Euro. Pemilihan metode terbaik dalam menentukan interval berpengaruh terhadap hasil peramalan, serta menggabungkan kelebihan dari rantai markov dapat meningkatkan keakurasian dari hasil ramalan. Tujuan dari penelitian ini adalah pemilihan metode terbaik dalam menentukan interval serta mengetahui pengaruh adanya penggabungan dengan rantai markov. Berdasarkan penerapan metode fuzzy time series pada data nilai tukar Rupiah terhadap US Dolar dan Euro periode Januari-Maret 2016 diperoleh kesimpulan Automatic Clustering lebih baik daripada Average Based dalam pembentukan interval, dengan nilai MSE 1.065 dan MAPE 0,15% pada data nilai tukar rupiah terhadap US Dolar dan pada nilai tukar rupiah terhadap Euro dengan nilai MSE 694 dan MAPE 0,09%. Adanya penggabungan rantai markov pada metode Automatic clustering memberikan peningkatan akurasi sebesar 60,65% pada data nilai tukar rupiah terhadap US Dolar dan pada nilai tukar rupiah terhadap Euro meningkat sebesar 14,99%.
STRUKTUR DAN SIFAT-SIFAT K-ALJABAR Nugroho, Deni; Veronica, Rahayu Budhiati; Mashuri, Mashuri
Unnes Journal of Mathematics Vol 6 No 1 (2017)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v6i1.13066

Abstract

K-aljabar merupakan struktur aljabar <G,*,⊙,e>, di mana G merupakan grup terhadap operasi biner * dengan elemen identitas e, operasi ⊙ didefinisikan oleh ∀x,y∈G,x⊙y=x*y-1, dan memenuhi kelima aksioma dari K-aljabar. Konsep yang diterapkan dalam K-aljabar hampir sama dengan konsep dalam grup. Jika dalam grup terdapat subgrup dan homomorfisma grup, maka dalam K-aljabar terdapat K-subaljabar dan K-homomorfisma. Penelitian ini membahas mengenai struktur dan sifat-sifat yang terkait dengan K-aljabar, K-subaljabar, dan K-homomorfisma. Tujuan penelitian ini adalah menjelaskan struktur dan sifat-sifat dari kajian K-aljabar, K-subaljabar, dan K-homomorfisma. Penelitian ini menggunakan metode kajian pustaka, dengan cara mengumpulkan berbagai sumber dan teorema-teorema yang mendukung pada kajian K-aljabar. Pada penelitian ini dapat disimpulkan: 1) Dalam K-aljabar berlaku sifat-sifat berikut; hukum kanselasi; Suatu K-aljabar <G,*,⊙,e> dikatakan komutatif jika ∀x,g∈G berlaku g⊙(e⊙x)=x⊙(e⊙g) 2) K-subaljabar memiliki sifat sebagai berikut; misalkan <G,*,⊙,e> K-aljabar dan g∈G. Jika H suatu subgrup dari G, maka Hg2={g⊙(g⊙x)│x∈H} adalah suatu K-subaljabar dari <G,*,⊙,e>. 3) Homomofisma K-aljabar φ:K1→K2 memiliki sifat-sifat sebagai berikut; ∀x1∈K1,x2∈K2 berlaku φ(e1)=e2; φ(e1⊙x1 )=e1⊙φ(x1 ); φ(x1⊙x2)=e1⇔φ(x1)=φ(x2); dan jika H1 adalah K-subaljabar dari K1 maka φ(K1) adalah K-subaljabar dari K2. K-algebra is an algebraic structure <G,*,⊙,e>, when G is a group of the binary operation * with identity element e, the operation ⊙ defined by ∀x,y∈G,x⊙y=x*y-1, and fulfill the five axioms of K-algebra. The concept is applied in the K-algebra is similar to the concept of the group. If in the group there is a subgroup and group homomorphism, then in K-algebra is K-subalgebra and K-homomorphism. This study discusses the structure and properties associated with the K-algebra, K-subalgebra, and K-homomorphism. The purpose of this study is to explain the structure and properties of the study of K-algebra, K-subalgebra, and K-homomorphism. This study used literature review, by collecting a variety of sources and theorems that support the study of K-algebra. In this study it can be concluded: 1) In K-algebra have following properties; applicable with cancelation law; K-algebra <G,*,⊙,e> is commutative if ∀x,g∈G apply g⊙(e⊙x)=x⊙(e⊙g). 2) K-subalgebra have the following properties; eg <G,*,⊙,e> K-algebra and g∈G. If H subgroup of G, then Hg2={g⊙(g⊙x)│x∈H} is K-subalgebra of <G,*,⊙,e>. 3) K-algebra homomorphism φ:K1→K2 has properties follows; ∀x1∈K1,x2∈K2 apply φ(e1)=e2; φ(e1⊙x1 )=e2⊙φ(x1); φ(x1⊙x2 )=e2⇔φ(x1)=φ(x2); and if H1 is K-subalgebra of K1 then φ(K1) is K-subalgebra of K2.
MODEL EPIDEMI SIRS STOKASTIK DENGANSTUDI KASUS INFLUENZA Nurlazuardini, Novia Nilam; Kharis, Muhammad; Hendikawati, Putriaji
Unnes Journal of Mathematics Vol 5 No 1 (2016)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v5i1.13101

Abstract

Epidemic SIRS model is an epidemic model which illustrate the spread of disease from suscept to infected, and then become a recovered and become suscept again depend of the immunity. In this article, we dicussed epidemic stochastics SIRS model with embedding epidemic deterministic model, analysis of the model and the behavior of this disease in the future. To obtain the result of basic reproduction ration, Crump-Mode-Jagers process with embedding BGW branching process in some process. From the analysis and the simulation of the model were obtained , if 𝑅0 < 1 then the epidemic is extinct and if 𝑅0 ≥ 1 the epidemic is occurred. To illustrate the model simulation were carried out using Maple software. The model simulation give the same result with the analysis.
ANALISIS PERBANDINGAN MENGGUNAKAN ARIMA DAN BOOTSTRAP PADA PERAMALAN NILAI EKSPOR INDONESIA Cynthia, Ari; Sugiman, Sugiman; Zaenuri, Zaenuri
Unnes Journal of Mathematics Vol 5 No 1 (2016)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v5i1.13102

Abstract

In this research used the data export value of Indonesia as a case study. Indonesia's export would be predicted using ARIMA and bootstrap methods with the help of the program R 2.11.1. Bootstrap method used is bootstrap the ARIMA process. ARIMA method is one of the most common methods used in modeling of time series. However on certain data time series models can not guarantee the fulfillment of the assumptions in the classical statistical analysis. Bootstrap methods can be used in situations where standard assumptions are not met. The main objective of this study is to compare the methods ARIMA and bootstrap the Indonesian export data so as to obtain the best forecasting method that will be used to forecast the data export value of Indonesia for the next period. Based on the results of the two models forecasting, it would have been the result of forecasting that has the smallest value of standard error and approach the original data. Results forecasting export value of Indonesia on ARIMA (1,1,2) has the smallest value and the standard error tends to approach the original data when compared to bootstrap the process models ARIMA (1,1,2). Then ARIMA method is the best forecasting method. Next will be forecasting for the months of April to December 2015 using ARIMA method as the best method.
PEMODELAN GENERALIZED POISSON REGRESSION (GPR) UNTUK MENGATASI PELANGGARAN EQUIDISPERSI PADA REGRESI POISSON KASUS CAMPAK DI KOTA SEMARANG TAHUN 2013 Ruliana, Ruliana; Hendikawati, Putriaji; Agoestanto, Arief
Unnes Journal of Mathematics Vol 5 No 1 (2016)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v5i1.13103

Abstract

The measles the Semarang experience fluctuates every year, so that the City Health Agency (DKK) Semarang put special attention to reducing many cases measles.In the case of smallpox semarang 2013 was data discrete Poisson. Regression Poisson is nonlinear regression used to analyze data count variable response Poisson and meet the equidispersi. In practice often occurs in violation of discrete overdispersi analysis of data in regression poisson underdispersi and models or improper use.To anticipate such violation used Generalized Poisson Regression in modeling (GPR) data. In this research are variable response used in the case of smallpox Semarang 2013 and variable prediktor used is many medicines measles, community health centers, the poverty and overcrowding every subdistrict across Semarang town. The best model Generalized Poisson Regression (GPR) was gotten.
METODE LEAST TRIMMED SQUARE (LTS) DAN MM-ESTIMATION UNTUK MENGESTIMASI PARAMETER REGRESI KETIKA TERDAPAT OUTLIER Dewi, Elok Tri Kusuma; Agoestanto, Arief; Sunarmi, Sunarmi
Unnes Journal of Mathematics Vol 5 No 1 (2016)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v5i1.13104

Abstract

This article discusses the theoretical study and use excel and SPSS 19 application of Least Trimmed Square (LTS) methods and MM-estimation methods. Theoretical study focused on the elaboration of the concept of outlier, least trimmed square methods and MM-estimation methods and selection best model use the criteria R2 and resid value. Outlier is data on who did not attend a pattern common regression on the model produced, or not follow as a pattern data as a whole. The existence of outlier in the data can be disrupt the process of data analysis, that led to the data on residual and variance become larger. This research aims to know the effectiveness of robust regression method with Least Trimmed Square (LTS) and MM-estimation in multiple linear regression. This data consisting of age (X1) and body mass index (X2) as variable independent while systolik blood pressure (Y) as dependent variables. The model produced using Least Trimmed Square methods that is Y^=67.141+0.649X1+0.587X2. Regarding the resulting uses the method MM-estimation that is Y^=65.308+0.666X1+0.618X2. Because at Least Trimmed Square method (LTS) obtained the R2 value of is bigger and smaller than the residual method of MM-estimation then it can be concluded that the method of Least Square Trimmed (LTS) is more efficient in the estimate parameter of the regression compared the methods of MMestimation

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