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All Journal MATEMATIKA Wahana Matematika dan Sains CAUCHY: Jurnal Matematika Murni dan Aplikasi Al-Jabar : Jurnal Pendidikan Matematika Science and Technology Indonesia Jurnal Matematika: MANTIK Desimal: Jurnal Matematika Limits: Journal of Mathematics and Its Applications J Statistika: Jurnal Ilmiah Teori dan Aplikasi Statistika Jambura Journal of Mathematics Jurnal Matematika UNAND Jurnal Pengabdian Kepada Masyarakat (JPKM) Tabikpun Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Jurnal Siger Matematika Journal of Fundamental Mathematics and Applications (JFMA) Jurnal Matematika Integratif
Ahmad Faisol
Jurusan Matematika FMIPA, Universitas Lampung
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Engineering Environmental Science Health Professions Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Social Sciences Transportation

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Forecasting Seasonal Time Series Data Using The Holt-Winters Exponential Smoothing Method of Additive Models Nurhamidah Nurhamidah; Nusyirwan Nusyirwan; Ahmad Faisol
Jurnal Matematika Integratif Vol 16, No 2: Oktober 2020
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v16.n2.29293.151-157

Abstract

The purpose of this study was to predict seasonal time series data using the Holt-Winters exponential smoothing additive model.  The data used in this study is data on the number of passengers departing at Hasanudin Airport in 2009-2019, the source of the data obtained from the official website of the Central Statistics Agency.  The results showed that the Holt-Winters exponential smoothing method on the passenger's number at Hasanudin Airport in 2009 to 2019 contained trend patterns and seasonal patterns, by first determining the initial values and smoothing parameters that could minimize forecasting errors.
The Properties of Rough Submodule over Rough Ring Rahmawati, Rara Gusti; Fitriani, Fitriani; Faisol, Ahmad
Jurnal Matematika Integratif Vol 20, No 2: Oktober 2024
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v20.n2.55570.185-196

Abstract

A pair of non-empty set $U$ and equivalence relation $R$ on $U$, denoted as $(U,R)$, is called approximation space. Furthermore, equivalence classes form the construction of lower approximation and upper approximation. Let $X\subseteq U$, the lower approximation of $X$ denoted by $\underline{X}$ and the upper approximation of $X$ denoted by $\overline{X}$. A pair $Apr(X)=(\underline{X},\overline{X})$ is a rough set if $\underline{X}\neq \overline{X}$. $Apr(X)$ is rough module if $Apr(X)$ satisfies some conditions. In this research, we investigate some characteristics of the rough module and rough submodule over rough ring. Furthermore, we construct examples of the rough module and the rough submodule on approximation space $(U,R)$.
Construction of the Rough Quotient Modules over the Rough Ring by Using Coset Concepts Rahma, Aira; Fitriani, Fitriani; Faisol, Ahmad
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i1.23564

Abstract

Given an ordered pair $(U, \theta)$ where $U$ is the set universe and $\theta$ is an equivalence relation on the set $U$ is called an approximation space. The equivalence relation $\theta$ is a relation that is reflexive, symmetric, and transitive. If the set $X \subseteq U$, then we can determine the upper approximation of the set $X$, denoted by $\overline{Apr}(X)$, and the lower approximation of the set $X$, denoted by $\underline{Apr}(X)$. The set $X$ is said to be a rough set on $(U, \theta)$ if and only if $\overline{Apr}(X)-\underline{Apr}(X) \neq \emptyset$. A rough set $X$ is a rough module if it satisfies certain axioms. This paper discusses the construction of a rough quotient module over a rough ring using the coset concept to determine its equivalence classes and discusses the properties of a rough quotient module over a rough ring related to a rough torsion module.
(σ,τ)-derivasi pada Ring Grup Waluyo, Ridho; Faisol, Ahmad; Fitriani, Fitriani
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 13 Issue 2 August 2025
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v13i2.31564

Abstract

Derivations play a fundamental role in ring theory and have been extensively studied and generalized, including to (σ, τ)-derivations, which involve endomorphisms σ and τ. While many studies have focused on (σ, τ)-derivations in prime, semiprime, or commutative rings, explicit constructions and investigations of such derivations in group rings remain limited. This paper constructs several concrete examples of (σ, τ)-derivations on group rings and explores their algebraic properties. The approach provides systematic illustrations and characterizations of derivations in noncommutative ring structures based on groups, thereby contributing to the development of derivation theory in group ring contexts.
Commuting and Centralizing Maps on Modules Fitriani, Fitriani; Wijayanti, Indah Emilia; Faisol, Ahmad; Ali, Shakir
Science and Technology Indonesia Vol. 10 No. 3 (2025): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2025.10.3.690-697

Abstract

A ring is a mathematical structure composed of a set with two binary operations that follow certain axioms. One important function within a ring is the centralizing and commuting mapping, which has been extensively studied in recent decades. Commuting mappings are a special case of centralizing mappings. A module is a generalization of a ring. In this paper, we extend the concept of commuting mappings from ring to module structures. However, defining commuting mappings in modules presents a challenge, as multiplication is required for their definition, yet modules do not have this operation. Additionally, constructing nonzero centralizing and commuting mappings on modules is a nontrivial task. To address these challenges, we employ the concept of idealization as a framework for defining commuting mappings in modules. We also propose a method for constructing nonzero commuting mappings on modules by leveraging existing commuting mappings in rings. Specifically, if α is a commuting mapping on a ring T, then a corresponding commuting mapping α’ can be defined on the module by utilizing α. Moreover, we establish that the finite sum of commuting mappings is also a commuting mapping and that a linear combination of  commuting mappings is also a commuting mapping under certain conditions.
The Sufficient Conditions for M[[S,w]] to be T[[S,w]]-Noetherian R[[S,w]]-module Faisol, Ahmad; Fitriani, Fitriani
Al-Jabar: Jurnal Pendidikan Matematika Vol 10 No 2 (2019): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v10i2.5042

Abstract

In this paper, we investigate the sufficient conditions for T[[S,w]] to be a multiplicative subset of skew generalized power series ring R[[S,w]], where R is a ring, T Í R a multiplicative set, (S,≤) a strictly ordered monoid, and w : S®End(R) a monoid homomorphism. Furthermore, we obtain sufficient conditions for skew generalized power series module M[[S,w]] to be a T[[S,w]]-Noetherian R[[S,w]]-module, where M is an R-module.
The X[[S]]-Sub-Exact Sequence of Generalized Power Series Rings Pardede, Wesly Agustinus; Faisol, Ahmad; Fitriani, Fitriani
Al-Jabar: Jurnal Pendidikan Matematika Vol 11 No 2 (2020): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v11i2.6760

Abstract

Let  be a ring,  a strictly ordered monoid, and K, L, M are R-modules. Then, we can construct the Generalized Power Series Modules (GPSM) K[[S]], L[[S]], and M[[S]], which are the module over the Generalized Power Series Rings (GPSR) R[[S]]. In this paper, we investigate the property of X[[S]]-sub-exact sequence on GPSM L[[S]] over GPSR R[[S]].  
Sub-exact sequence of rough groups Setyaningsih, Nevi; Fitriani, Fitriani; Faisol, Ahmad
Al-Jabar: Jurnal Pendidikan Matematika Vol 12 No 2 (2021): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v12i2.8917

Abstract

Rough Set Theory (RST) is an essential mathematical tool to deal with imprecise, inconsistent, incomplete information and knowledge Rough Some algebra structures, such as groups, rings, and modules, have been presented on rough set theory. The sub-exact sequence is a generalization of the exact sequence. In this paper, we introduce the notion of a sub-exact sequence of groups. Furthermore, we give some properties of the rough group and rough sub-exact sequence of groups. 
The Annual Premium of Life Insurance on The Joint-Life Status based on The 2011 Indonesian Mortality Table Suryani, Stacia Litha; Ruswandi, Rudi; Faisol, Ahmad
Desimal: Jurnal Matematika Vol. 3 No. 3 (2020): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v3i3.6761

Abstract

Life insurance is insurance that protects against risks to someone's life. Joint Life Insurance is insurance where the life and death rules are a combination of two or more factors, such as husband-wife or parent-child, and if the first death occurs, then the premium payment process is stopped. The annual premium is the premium paid annually. In this study, the annual premium is calculated continuously with the equivalence principle based on the 2011 Indonesian Mortality Table.  The calculation shows that the amount of annual premiums for 2 (two) and 3 (three) people is not much different. The factors that influence the annual premium amount are the duration insurance period, age at signing the policy, interest rates, life chances, force of mortality, and the number of benefits.
Analysis of the annual vehicle tax payment service system using Petri net model Andriani, Jessica; Fitriani, Fitriani; Faisol, Ahmad
Desimal: Jurnal Matematika Vol. 4 No. 3 (2021): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v4i3.10379

Abstract

Service is the process of meeting needs through the activities of others directly. Service is usually synonymous with queues, and queues are what many people complain about. Most of the taxpayers complained about the queues, indirectly they would blame the poor service because of the queues that had piled up. Queues can be reduced by improving services, while one way to improve services is to analyze services using the Petri Net model. Petri Net is mathematical modeling for discrete event systems. Petri Net can be used to model and analyze algebraic problems of transportation networks, manufacturing systems, telecommunications networks, parallel process systems, and so on. In this study, a Petri Net Model of the annual vehicle tax payment service system was created as many as 16 places, 14 transitions, 2 operators, and 30 arcs using WOPED 3.2.0 software. The length of time for tax payment services for taxpayers who have completed the file is faster with a total time of 27 minutes compared to those who have not completed the file with a total time of 35 minutes. The Petri Net model of the annual type of vehicle tax payment service system can be presented in the form of a backward incidence and forward incidence matrix which is used to see the queuing pattern at Samsat Oku Timur 1 with a mathematical model. Columns in the backward incidence matrix can be used to determine which transitions are enabled.
Co-Authors . Wamiliana Aang Nuryaman Ahmad Rizki Wiranto Akmal Junaidi Ananto Adi Nugraha Andriani, Jessica Citra Puspa Tria Dian Kurniasari Dina Eka Nurvazly Eri Setiawan Eri Setiawan Fathudin Fathudin Fitri Ayuni Fitriani Indah Emilia Wijayanti Jessica Andriani Khoirin Nisa Listiana Listiana Lucia Ratnasari Muslim Ansori Nabilla Yolanda Paramitha Nevi Setyaningsih Nikken Prima Puspita Notiragayu Notiragayu Notiragayu Nurhamidah Nurhamidah Nurlela Nurlela Nusyirwan Nusyirwan Pardede, Wesly Agustinus Rahma, Aira Rahmawati, Rara Gusti Rizki Agung Wibowo Rudi Ruswandi Rudi Ruswandi Saidi, Subian Sam Wibowo Setyaningsih, Nevi SHAKIR ALI Silvi Fitriani Siti Khabibah Siti Laelatul Chasanah Stacia Litha Suryani Suryani, Stacia Litha Waluyo, Ridho Wesly Agustinus Pardede Wibowo, Sam