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All Journal IPTEK The Journal for Technology and Science JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA BAREKENG: Jurnal Ilmu Matematika dan Terapan Griya Journal of Mathematics Education and Application MATHunesa: Jurnal Ilmiah Matematika Scientica: Jurnal Ilmiah Sains dan Teknologi JMT (Jurnal Matematika dan Terapan)
Zumrotus Sya’diyah
Mathematics Study Program, Faculty Of Mathematics And Natural Sciences, Universitas Billfath, Indonesia
Religion Agriculture, Biological Sciences & Forestry Humanities Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Lyapunov-Max-Plus-Algebra Stability in Predator-prey Systems Modeled with Timed Petri Net Subiono Subiono; Zumrotus Sya’diyah
IPTEK The Journal for Technology and Science Vol 22, No 3 (2011)
Publisher : IPTEK, LPPM, Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j20882033.v22i3.70

Abstract

In this paper, we discuss the notion of max-plus algebra and their properties. We also construct a model of predator-prey systems with timed Petri net and analyze the stabilization of the systems. Furthermore, we analyze the periodic behavior of the systems. Using the Lyapunov stability theory, we will obtain the sufficient condition for the stabilization problem and the periodic duration of the oscillation will be also determined.
ANALISIS KESTABILAN MODEL EPIDEMIK TIPE SIR (SUSCEPTIBLE, INFECTIOUS, RECOVERED) PADA DINAMIKA PENYEBARAN PENYAKIT MALARIA DI KOTA AMBON Thoifah, Susiatut; Sya’diyah , Zumrotus; Nasrulyati , Tri Siwi
Scientica: Jurnal Ilmiah Sains dan Teknologi Vol. 3 No. 2 (2024): Scientica: Jurnal Ilmiah Sains dan Teknologi
Publisher : Komunitas Menulis dan Meneliti (Kolibi)

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Berdasarkan Riskesdas Tahun 2013, bahwa Maluku merupakan salah satu daerah provinsi yang termasuk dalam 5 provinsi dengan insiden dan prevalensi malaria tertinggi di Indonesia yang hingga kini masih memiliki prevalensi malaria diatas angka nasional. Hal ini menjadi suatu masalah yang perlu dilakukan penanganan secara serius dan bijak agar penyebaran penyakit malaria tersebut dapat dikendalikan, diantaranya dengan memanfaatkan kajian ilmu matematika yang memiliki kapabilitas dalam bidang ini yaitu pemodelan matematika. Penelitian ini membahas perilaku penyebaran penyakit malaria dengan menggunakan model epidemik tipe SIR (Susceptible, Infectious, Recovered). Pada tugas akhir ini dianalisis kestabilan titik kesetimbangan pada model deterministik dan ditentukan pula Basic Reproduction Ratio (R0) serta nilai ambang batasnya, dimana kestabilan titik setimbang ditentukan melalui linearisasi model deterministiknya tersebut. Studi kasus dalam penelitian ini mengarah pada data jumlah penderita malaria di Kota Ambon tahun 2012-2013 yang diperoleh dari Dinas Kesehatan Provinsi Maluku. Dari hasil proses analisis diketahui bahwa model epidemik mempunyai dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan epidemik . Syarat eksistensi dan kestabilan titik kesetimbangan ditentukan oleh bilangan reproduksi dasar (R0), yaitu bilangan yang menentukan ada tidaknya penyebaran penyakit pada suatu populasi. Bilangan reproduksi dasar penyakit malaria di Kota Ambon sebesar , dengan nilai ambang batas 2,990251. Hasil ini menunjukkan bahwa tidak akan terjadi epidemi penyakit malaria, karena lambat laun penyakit malaria di Kota Ambon akan berkurang dan pada akhirnya akan menghilang.
Strategi Optimasi Pemasaran Air Mineral di Kecamatan Maduran dengan Menggunakan Teori Permainan Shahadah, Zaqiyatus; Aris Alfan; Zumrotus Sya'diyah
JMT (Jurnal Matematika dan Terapan) Vol. 6 No. 2 (2024): JMT (Jurnal Matematika dan Terapan)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/jmt.6.2.1

Abstract

Mineral water company must design an effective marketing strategy to find optimal marketing opportunities. The method for developing marketing strategies that need to be optimized is using game theory. This research aims to analyze the optimal marketing strategy for mineral water Aqua, Cleo, and local brands (Como, Aidrat, Ake, etc.). Alternative strategies implemented include: profit, demand and quality. In this study, the optimal strategy for Aqua is demand and quality, the optimal strategy for Cleo is profit and demand, and the optimal strategy for Local Brands (Como, Aidrat, Ake, etc.) is profit and demand.
PERAMALAN JUMLAH KENDARAAN DI DKI JAKARTA DENGAN JARINGAN BACKPROPAGATION Smith, Alwi; Sya’diyah, Zumrotus
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 10 No 2 (2016): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (609.905 KB) | DOI: 10.30598/barekengvol10iss2pp117-125

Abstract

Kemacetan di ibukota DKI Jakarta tidak dapat dihindari, terutama pada titik-titik persimpangan baik di jalan-jalan protokol hingga di jalan lingkungan. Semakin hari, kemacetan di Jakarta semakin parah. Menurut sebuah penelitian, kemacetan tersebut membuat masyarakat Jakarta mengalami kerugian hingga Rp 48 triliun per tahun [1]. Dalam makalah ini akan dibahas mengenai prediksi jumlah kendaraan pada tahun 2017. Prediksi ini akan dilakukan dengan menggunakan jaringan syaraf tiruan, yaitu metode backpropagation. Metode ini digunakan karena keunggulannya dalam learning rate. Learning rate sangat berguna dalam menentukan prediksi dengan eror yang kecil. Prediksi jumlah kendaraan ini akan dilakukan pada kendaraan bermotor, mobil pribadi dan kendaraan umum. Sehingga dari hasil prdiksi ini akan dapat ditentukan langkah-langkah yang tepat untuk menekan laju pertumbuhan jumlah kendaraan. Dalam pembahasannya nanti akan digunakan Matlab 2009a.
KESTABILAN MODEL PETRI NET DARI SISTEM PEMBAYARAN TAGIHAN LISTRIK PT. PLN (Persero) RAYON AMBON TIMUR Sya'diyah, Zumrotus
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 15 No 4 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (457.751 KB) | DOI: 10.30598/barekengvol15iss4pp601-606

Abstract

This research develops the previous one of the electricity bill payment system in PT. PLN (Persero) Rayon East Ambon modelled by Petri Net. The previous researcher had built the Petri Net model of this payment system. In this research, we determine whether the system modelled before is stable or not. This stability will be analysed using the Lyapunov stability theory related to the Petri Net. The result shows that the electricity bill payment system modelled by Petri Net before is not stable but can be stabilized. This can be caused there is a transition which is ‘always enable’ in the modelled which is built. This research also performs a stable model of Petri Net that represents the electricity bill payment system with deleting the ‘always enable’ transition
MAX PLUS ALGEBRA OF TIMED PETRI NET FOR MODELLING SINGLE SERVER QUEUING SYSTEMS Sya'diyah, Zumrotus
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 1 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (442.901 KB) | DOI: 10.30598/barekengvol17iss1pp0155-0164

Abstract

This research modified a single server queuing system using timed Petri net. We add two places, a transition and its appropriate arcs. This research also considered all the holding times in the timed Petri net. We found that the Petri net is not stable but stabilizable according to Lyapunov stability criteria. The standard autonomous equation of the system is also determined. Furthermore, this system also has the eigen value which related to its periodical behavior, it is . This means that the periodical behavior of the system only depends on the value of holding times of place W, R, B, and I.
Max Plus Algebra Application In Air Defence Systems Zumrotus Sya'diyah
Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika Vol. 12 No. 2 (2025): Jurnal Derivat (Agustus 2025)
Publisher : Pendidikan Matematika Universitas PGRI Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31316/j.derivat.v12i2.8357

Abstract

Air defence is one of the vital systems in national defence. This system generally includes several processes, namely detection by radar, object identification and decision making. The level of success really depends on the accuracy of decision-making. However, it is not yet known for certain which processes critical processes in decision-making. In this research, we will discuss the application of max plus algebra in determining which process of the workflow for air defence systems is the most critical one. Graphical interpretation of the system using graphs and Timed Petri Nets to make it easier to understand and analyse. The research results show that the success of the entire process depends on the readiness of the radar in carrying out surveillance of the coverage area. This can be seen from the critical circuit, which only depends on the place relating to the situation. Keywords: Max plus algebra, Timed Petri Net, air defence system.
Aplikasi Aljabar Max-Plus pada Penjadwalan Periodik Produksi Kaos Kaki Nur Salamah; Zumrotus Sya'diyah
JMT (Jurnal Matematika dan Terapan) Vol. 7 No. 2 (2025): JMT (Jurnal Matematika dan Terapan)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/jmt.7.2.3

Abstract

Penelitian ini memodelkan sistem produksi kaus kaki di UD. Tunas Muda Jaya menggunakan pendekatan Aljabar Max-Plus. Model yang dibangun merepresentasikan ketergantungan waktu antar proses dalam bentuk sistem linier tropis. Analisis nilai eigen menunjukkan throughput maksimum sebesar 7 unit waktu per produk, sedangkan vektor eigen mengungkap penjadwalan relatif dan jalur kritis produksi. Temuan ini menegaskan bahwa upaya peningkatan produksi sebaiknya difokuskan pada proses dalam jalur kritis, karena proses di luar jalur tersebut tidak memengaruhi efisiensi sistem. Model ini menyediakan landasan kuat bagi perencanaan penjadwalan dan optimasi produksi periodik.
Pemodelan Sistem Antrian Pasien RSJ Menur Menggunakan Timed Petri Net Zumrotus Sya'diyah; Ari Maulida Intahaya
Griya Journal of Mathematics Education and Application Vol. 6 No. 1 (2026): Maret 2026
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v6i1.1048

Abstract

Queueing systems play an important role in operational management, particularly in healthcare services. Inefficient queue management can reduce service quality and patient satisfaction. This study aims to model the outpatient queueing system at Menur Mental Hospital, Surabaya, using a Timed Petri Net approach combined with Max-Plus Algebra. The data were obtained through a literature review and an interview with one outpatient clinic nurse at Menur Mental Hospital conducted in June 2025, which provided information on the stages of service and the average duration of each service process for BPJS outpatient patients. The Petri Net model represents the service flow graphically, while the Max-Plus Algebra formulation expresses the system dynamics in a recursive form. The resulting Max-Plus matrix describes the time dependency structure among service stages. Based on the transition duration analysis, the critical path of the system is identified in the polyclinic and pharmacy services with a total service time of 56 minutes, indicating these stages as potential bottlenecks. The proposed model provides a mathematical framework to evaluate system performance and support decision-making in improving the operational efficiency of outpatient services.
ALGORITHM DESIGN OF ELGAMAL MAX-PLUS ALGEBRA FOR LETTER AND NUMBER CRYPTOGRAPHY WITH UNI-CUSTOM CIPHERTEXT Zumrotus Sya'diyah; Nur Salamah; Faradilla Alfiani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3185-3196

Abstract

This study focuses on the design and implementation of a prototype cryptographic algorithm using the integration of Uni-Custom ciphertext transformation and Max-Plus algebra in the ElGamal scheme. The integration is performed through a sequential process, where the Uni-Custom ciphertext transformation converts plaintext into a dynamic numeric form, and then we use the ElGamal max plus-based algorithm in the encryption process through a public-key mechanism. The primary objective of this research is to explore the feasibility and functional correctness of the proposed hybrid framework rather than to provide a complete cryptographic performance evaluation. The implementation results show that the system exhibits high computational and structural complexity. The security of the proposed system is associated with the hardness of the discrete logarithm problem in the ElGamal scheme, while additional transformation layers enhance variability and reduce pattern predictability. Experimental results show consistent reconstruction of the original message without data loss, indicating promising potential for the development of alternative cryptographic methods based on non-conventional mathematical structures.
Co-Authors Ari Maulida Intahaya Aris Alfan Dewi Putri Rohmawati Faradilla Alfiani Nasrulyati , Tri Siwi Nur Salamah Nur Salamah Pukky Tetralian Bintining Ngastiti Shahadah, Zaqiyatus Smith, Alwi Subiono Subiono Thoifah, Susiatut