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Eksistensi Solusi Persamaan Lyapunov pada Sistem Linear Waktu Diskrit Atas Ring Komutatif Inna Kuswandari; Fatmawati Fatmawati; Mohammad Imam Utoyo
Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Vol 1 No 1 (2017): Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai Islami )
Publisher : Mathematics Department

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (557.962 KB)

Misalkan diberikan sistem linear atas ring komutatif. Beberapa sifat penting dari sistem linear adalah stabil asimtotis, terkendali, dan terobservasi. Sistem dikatakan stabil asimtotis jika solusi sistem dalam rentang waktu tak terbatas akan menuju ke suatu titik tertentu, dalam hal ini titik kesetimbangan. Selain menggunakan kriteria nilai eigen, kestabilan sistem linear berkaitan erat dengan eksistensi solusi persamaan Lyapunov. Tujuan penelitian ini adalah menentukan syarat cukup eksistensi solusi persamaan Lyapunov pada sistem linear waktu diskrit atas ring komutatif terkait kestabilan, keterkendalian, dan keterobservasian sistem.

MCGDM with AHP based on Adaptive Interval Value Fuzzy Yeni Kustiyahningsih; Fatmawati Fatmawati; Herry Suprijanto
TELKOMNIKA (Telecommunication Computing Electronics and Control) Vol 16, No 1: February 2018
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/telkomnika.v16i1.7000

The purpose research is to develop the decision model of Multi-Criteria Group Decision Making (MCGDM) into Interval Value Fuzzy Multi-Criteria Group Decision Making (IV-FMCGDM), while the specific purpose is to construct decision-making model of Adaptive Interval Value Fuzzy Analytic Hierarchy Process (AIV- FAHP) uses Triangular Fuzzy Number (TFN) and group decision aggregation functions using Interval Value Geometric Means Aggregation (IV-GMA). The novelty research is to study the concept of group decision making by improving the middle point on the Interval Value Triangular Fuzzy Number (IV TFN). It provides more accurate modeling, and better rating performance, and more effective linguistic representation. This research produced a new decision-making model and algorithm based on AIV-FAHP used to measure the quality of e-learning.

Image Encryption Technique Based on Pixel Exchange and XOR Operation Kiswara A. Santoso; Fatmawati Fatmawati; Herry Suprajitno
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Recently the information system develops quickly, especially information system via internet. It’s happened because the Internet can be used by anyone, anywhere and anytime. The information on the Internet has various types of data such as text, video, audio, and image/photo. Although we can access the Internet easily, but the data which transfered through internet isn’t safe. It caused by hacker, someone who manipulate information so that data become diﬀerent with the original. Many eﬀorts have been done to make the data that transmitted over the Internet to be secure, for example make the coding, disguise or hide data into other media. In this paper we intend to present the results of research about image encryption techniques to increase the security of data (image) so that safe if the data is transfered via the internet. This encryption using symmetric-key. The key is 4 BIT or a real number between 0 15. This key will be processed by each pixel in the image using XOR operation. The next step the BIT of pixels are devided into two part, LSB (least signiﬁcant bit) and MSB (Most signiﬁcant bit). Both will be exchanged if the conditions have completed. We do that to get better results, that is ﬁle size of the image encryption is smaller than the original image. The results of this research are image encryption have signiﬁcant diﬀerences with the original image, it can be proved by correlation between both images. Another advantage of this coding technique is the image encryption ﬁle size smaller than the original image ﬁle size so it can speed up of image transfer. Decode result of this coding technique is good enough, it can be seen from the mean square error (MSE) between the image encryption that has been restored to its original form and the original image. All the manufacturing process of encoding techniques have been simulated and analyzed using software MATLAB 2012a.

Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Penyakit Ebola dengan Penanganan Medis Sofita Suherman; Fatmawati Fatmawati; Cicik Alfiniyah
Contemporary Mathematics and Applications (ConMathA) Vol. 1 No. 1 (2019)
Publisher : Universitas Airlangga

Ebola disease is one of an infectious disease caused by a virus. Ebola disease can be transmitted through direct contact with Ebola’s patient, infected medical equipment, and contact with the deceased individual. The purpose of this paper is to analyze the stability of equilibriums and to apply the optimal control of treatment on the mathematical model of the spread of Ebola with medical treatment. Model without control has two equilibria, namely non-endemic equilibrium (E0) and endemic equilibrium (E1) The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is locally asymptotically stable if R0 < 1 and endemic equilibrium tend to asymptotically stable if R0 >1 . The problem of optimal control is then solved by Pontryagin’s Maximum Principle. From the numerical simulation result, it is found that the control is effective to minimize the number of the infected human population and the number of the infected human with medical treatment population compare without control.

Analisis Kontrol Optimal Model Matematika Penyebaran Penyakit Mosaic pada Tanaman Jarak Pagar Adiluhung Setya Pambudi; Fatmawati Fatmawati; Windarto Windarto
Contemporary Mathematics and Applications (ConMathA) Vol. 1 No. 2 (2019)
Publisher : Universitas Airlangga

Mosaic disease is an infectious disease that attacks Jatropha curcas caused by Begomoviruses. Mosaic disease can be transmitted through the bite of a whitefly as a vector. In this paper, we studied a mathematical model of mosaic disease spreading of Jatropha curcas with awareness effect. We also studied the effect of prevention and extermination strategies as optimal control variables. Based on the results of the model analysis, we found two equilibriums namely the mosaic-free equilibrium and the endemic equilibrium. The stability of equilibriums and the existence of endemic equilibrium depend on basic reproduction number ( ). When , the spread of mosaic disease does not occur in the population, while when , the spread of mosaic disease occurs in the population. Furthermore, we determined existence of the optimal control variable by Pontryagin's Maximum Principle method. Simulation results show that prevention and extermination have a significant effect in eliminating mosaic disease.

Polinomial Pembangun dari Ideal dan Dimensi dari Kode Siklik Tuhfatul Janan; Tuhfatul Janan; Tuhfatul Janan; Tuhfatul Janan; Mohammad Imam Utoyo; Fatmawati Fatmawati
Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 2 (2021)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v3i2.29887

Dalam penelitian ini, diberikan hubungan antara ideal dan kode siklik serta sifat-sifat polinomial pembangun dari ideal dan dimensi dari kode siklik. Sifat-sifat tersebut antara lain hubungan antara polinomial pembangun dari ideal dengan polinomial monik dengan derajat terkecil di ideal, eksistensi dan ketunggalan dari polinomial pembangun dari ideal, hubungan antara polinomial pembangun dari ideal dengan pembagi monik dari , dan hubungan antara derajat dari polinomial pembangun dari ideal dan dimensi dari kode siklik.

Polinomial Pembangun dari Ideal dan Dimensi dari Kode Siklik Tuhfatul Janan; Tuhfatul Janan; Tuhfatul Janan; Tuhfatul Janan; Mohammad Imam Utoyo; Fatmawati Fatmawati
Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 2 (2021)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v3i2.29887

Dalam penelitian ini, diberikan hubungan antara ideal dan kode siklik serta sifat-sifat polinomial pembangun dari ideal dan dimensi dari kode siklik. Sifat-sifat tersebut antara lain hubungan antara polinomial pembangun dari ideal dengan polinomial monik dengan derajat terkecil di ideal, eksistensi dan ketunggalan dari polinomial pembangun dari ideal, hubungan antara polinomial pembangun dari ideal dengan pembagi monik dari , dan hubungan antara derajat dari polinomial pembangun dari ideal dan dimensi dari kode siklik.

Polinomial Pembangun dari Ideal dan Dimensi dari Kode Siklik Tuhfatul Janan; Tuhfatul Janan; Tuhfatul Janan; Tuhfatul Janan; Mohammad Imam Utoyo; Fatmawati Fatmawati
Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 2 (2021)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v3i2.29887

Dalam penelitian ini, diberikan hubungan antara ideal dan kode siklik serta sifat-sifat polinomial pembangun dari ideal dan dimensi dari kode siklik. Sifat-sifat tersebut antara lain hubungan antara polinomial pembangun dari ideal dengan polinomial monik dengan derajat terkecil di ideal, eksistensi dan ketunggalan dari polinomial pembangun dari ideal, hubungan antara polinomial pembangun dari ideal dengan pembagi monik dari , dan hubungan antara derajat dari polinomial pembangun dari ideal dan dimensi dari kode siklik.

The Formula Study in Determining the Best Number of Neurons in Neural Network Backpropagation Architecture with Three Hidden Layers Syaharuddin Syaharuddin; Fatmawati Fatmawati; Herry Suprajitno
Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) Vol 6 No 3 (2022): Juni 2022
Publisher : Ikatan Ahli Informatika Indonesia (IAII)

The researchers conducted data simulation experiments, but they did so unstructured in determining the number of neurons in the hidden layer in the Artificial Neural Network Back-Propagation architecture. The researchers also used a general architecture consisting of one hidden layer. Researchers are still producing minimal research that discusses how to determine the number of neurons when using hidden layers. This article examines the results of experiments by conducting training and testing data using seven recommended formulas including the Hecht-Nelson, Marchandani-Cao, Lawrence & Fredrickson, Berry-Linoff, Boger-Guterman, JingTao-Chew, and Lawrence & Fredrickson modifications. We use rainfall data and temperature data with a 10-day type for the last 10 years (2012-2021) sourced from Lombok International Airport Station, Indonesia. The training and testing data used showed the results that in determining the number of neurons on the hidden-1 screen, it was more appropriate to use the Hecht-Nelson formula and the Lawrence & Fredricson formula which is more suitable for use in the 2nd & 3rd hidden layer. The resulting research was able to provide an accuracy rate of up to 97.79% (temperature data) and 99.94% (rainfall data) with an architecture of 36-73-37-19-1.

Aplikasi Reduksi Model dengan Metode Linear Matrix Inequality pada Masalah Kualitas Air Kali Surabaya Nenik Estuningsih; Fatmawati Fatmawati
Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Vol 1 No 1 (2017): Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai Islami )
Publisher : Mathematics Department

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (419.16 KB)

Pada realita yang banyak terjadi, sebuah sistem yang diperoleh dari suatu model matematika merupakan sistem yang berorder tinggi. Order dari sistem yang dimaksud adalah order atau dimensi dari ruang keadaan yang terbentuk sebagai realisasi lain sebuah sistem. Salah satu contoh sistem berorder tinggi adalah masalah kualitas air Kali Surabaya. Sistem berorder tinggi tersebut dapat direduksi menjadi sistem sederhana dengan order yang lebih kecil dari sistem awal dengan mempertahankan sifat-sifat sistem awal. Penelitian ini bertujuan untuk mereduksi sistem pada masalah air Kali Surabaya yang berorder tinggi dengan menggunakan metode Linear Matrix Inequality. Sistem yang akan direduksi dalam keadaan stabil, bisa disetimbangkan, dan selanjutnya dilakukan reduksi, dan diperoleh bahwa sistem tereduksi yang diperoleh tetap stabil, terkendali, dan terobservasi. Diperoleh bahwa error yang terjadi akibat reduksi dengan menggunakan metode Linear Matrix Inequality adalah lebih kecil dibandingkan dengan error yang terjadi akibat reduksi dengan metode pemotongan setimbang.

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