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All Journal MATEMATIKA Jurnal Natur Indonesia Jurnal Sains Dasar Journal of the Indonesian Mathematical Society Jurnal Matematika & Sains JMPM: Jurnal Matematika dan Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Majalah Ilmiah Matematika dan Statistika (MIMS)
ARI SUPARWANTO
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SYSTEMS OF FUZZY NUMBER MAX-PLUS LINEAR EQUATIONS Rudhito, M. Andy; Wahyuni, Sri; Suparwanto, Ari; Susilo, Frans
Journal of the Indonesian Mathematical Society Volume 17 Number 1 (April 2011)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.17.1.10.17-28

Abstract

This paper discusses the solution of systems of fuzzy number max-plus linear equations through the greatest fuzzy number subsolution of the system. We show that if entries of each column of the coecient matrix are not equal to infinite, the system has the greatest fuzzy number subsolution. The greatest fuzzy number subsolution of the system could be determined by first finding the greatest interval subsolution of the alpha-cuts of the system and then modifying it if needed, such that each its components is a family of alpha-cut of a fuzzy number. Then, based on the Decomposition Theorem on Fuzzy Set, we can determine the membership function of the elements of greatest subsolution of the system. If the greatest subsolution satisfies the system then it is a solution of the system.DOI : http://dx.doi.org/10.22342/jims.17.1.10.17-28
Semiring Pseudo-Ternary Maxrizal, Maxrizal; Suparwanto, Ari
Jurnal Matematika dan Sains Vol 19 No 2 (2014)
Publisher : Institut Teknologi Bandung

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Abstract

Dalam makalah ini akan diperkenalkan definisi dan sifat-sifat semiring pseudo-ternary. Selanjutnya, akan diperkenalkan subsemiring pseudo-ternary dan ideal pada semiring pseudo-ternary. Lebih lanjut, ideal-ideal yang terbentuk pada semiring pseudo-ternary akan digunakan untuk membentuk semiring pseudo-ternary faktor.Pseudo-Ternary Semiring Abstract In this paper we introduce the notion of pseudo-ternary semiring. Furthermore, we will introduce pseudo-ternary subsemiring and ideals in pseudo-ternary semiring. Finally, ideals in pseudo-ternary semiring will be used for constructing pseudo-ternary factor semiring. Keywords:  Pseudo-ternary semiring, Factor pseudo-ternary semiring.
Ruang Vektor Eigen Suatu Matriks Atas Aljabar Max-Plus Interval Siswanto, Siswanto; Suparwanto, Ari; Rudhito, M. Andy
Jurnal Matematika dan Sains Vol 19 No 1 (2014)
Publisher : Institut Teknologi Bandung

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Abstract

Misalkan  himpunan bilangan real. Aljabar Max-Plus adalah himpunan Âmax = Â È {‑¥} dilengkapi dengan operasi maksimum Å dan plus Ä. Dapat dibentuk himpunan matriks berukuran n ´ n yang elemen-elemennya merupakan anggota himpunan Âmax, ditulis . Dibentuk himpunan I(Â)max yaitu himpunan yang anggotanya merupakan interval-interval tertutup dalam Âmax. Himpunan I(Â)max dilengkapi dengan operasi  dan  disebut aljabar Max-Plus interval. Selanjutnya, dapat pula dibentuk himpunan matriks berukuran n ´ n yang elemen-elemennya merupakan anggota himpunan I(Â)max, ditulis . Misalkan  dan , dengan , matriks interval A dikatakan tak tereduksi jika untuk setiap matriks  tak tereduksi. Jika tidak demikian matriks interval A dikatakan tereduksi. Dalam penelitian ini akan dibahas tentang ruang vektor eigen suatu matriks atas aljabar Max-Plus interval. Kata kunci : Ruang vektor eigen, Aljabar Max-Plus interval.   Eigenvector Space of a Matrix of Interval Max-Plus Algebra Abstract Let  be the set of real numbers. Max-Plus Algebra is the set Âmax = Â È {‑¥} equipped with the maximum operation Å and plus Ä. The set  is a set of n ´ n matrix with entries belonging to Âmax. Set I(Â)max i.e the set whose members are closed intervals in Âmax.The set I(Â)max equipped with the maximum operation  and plus  called interval Max-Plus algebra. Furthermore, we can also form the set of size n ´ n matrices whose elements are members of the set I(Â)max written . Suppose  and  where , the interval matrices A is irreducible if for any matrix  irreducible. Otherwise the interval matrix A is said reducible. In this research we will discuss eigenvector space of interval Max-Plus algebra matrix. Keywords : Eigenvector space, Interval Max-Plus algebra.
THE BEST SOLUTION FOR INEQUALITIES OF A O CROSS X LOWER THAN X FROM B O DOT X USING HIGH MATRIX RESIDUATION OF IDEMPOTENT SEMIRING Susilowati, Eka; Suparwanto, Ari
Jurnal Sains Dasar Vol 5, No 1 (2016): April 2016
Publisher : Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1062.184 KB) | DOI: 10.21831/jsd.v5i1.12663

Abstract

Abstract A complete idempotent semiring has a structure which is called a complete lattice. Because of the same structure as the complete lattice then inequality of the complete idempotent semiring can be solved a solution by using residuation theory. One of the inequality which is explained is  where matrices A,X,B with entries in the complete idempotent semiring S. Furthermore, introduced dual product , i.e. binary operation endowed in a complete idempotent semirings S and not included in the standard definition of complete idempotent semirings. A solution of inequality  can be solved by using residuation theory. Because of the guarantee that for each isotone mapping in complete lattice always has a fixed point, then is also exist in a complete idempotent semirings. This of the characteristics is used in order to obtain the greatest solution of inequality . Keywords: complete lattice, complete idempotent semiring, dual Kleene Star, dual product, residuation theory
Matriks atas Aljabar Max-Plus Interval Rudhito, Marcellinus Andy; Wahyuni, Sri; Suparwanto, Ari; Susilo, Frans
Jurnal Natur Indonesia Vol 13, No 2 (2011)
Publisher : Lembaga Penelitian dan Pengabdian kepada Masyarakat Universitas Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (244.728 KB) | DOI: 10.31258/jnat.13.2.94-99

Abstract

This paper aims to discuss the matrix algebra over interval max-plus algebra (interval matrix) and a method tosimplify the computation of the operation of them. This matrix algebra is an extension of matrix algebra over max-plus algebra and can be used to discuss the matrix algebra over fuzzy number max-plus algebra via its alpha-cut.The finding shows that the set of all interval matrices together with the max-plus scalar multiplication operationand max-plus addition is a semimodule. The set of all square matrices over max-plus algebra together with aninterval of max-plus addition operation and max-plus multiplication operation is a semiring idempotent. As reasoningfor the interval matrix operations can be performed through the corresponding matrix interval, because thatsemimodule set of all interval matrices is isomorphic with semimodule the set of corresponding interval matrix,and the semiring set of all square interval matrices is isomorphic with semiring the set of the correspondingsquare interval matrix.
ANALISIS LINTASAN KRITIS JARINGAN PROYEK DENGAN PENDEKATAN ALJABAR MAX-PLUS Rudhito, Andi; wahyuni, sri; suparwanto, Ari; Susilo, F
MATEMATIKA Vol 12, No 3 (2009): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

This paper proposes a method to critical path analysis in the project network using max-plus algebra approach.  The project network would be represented as a matrix over max-plus algebra. The dynamic of the project would be modeled and analyzed using max-plus algebra approach. The critical path analysis consists of determining earliest start time, latest completion time and float time. The finding show that the dynamic of the project is could be modeled in a systems of max-plus linear equations. The earliest start times of every node in the project are the solution of the system. The latest completion times of every node in the project are the solution of the modified system. The float time of every activity in the project could be detemined by modify and do some matrices operation over earliest start time vector and latest completion time vector. An example for modeling and computing a project using MATLAB example show that the result was appropriated with the critical path method (CPM).
SIFAT PERIODIK JARINGAN ANTRIAN SERI TERTUTUP DENGAN PENDEKATAN ALJABAR MAX-PLUS Rudhito, M Andy; Wahyuni, Sri; Suparwanto, Ari; Susilo, Frans
MATEMATIKA Vol 14, No 2 (2011): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

  Abstract. This article discussed about the properties of  closed periodic queuing network series susing max-plus algebra. The result showed that the properties of  closed periodic dinamic queuing network series can be determined by using the concept of eigen values ​​and eigen vectors of max-plus matrix in the network model. Through the max-plus eigen vector fundamental, can be determined faster early time departure of customers of departure to the next customer periodically, with a large period of max-plus eigenvalue
Representasi Nilai Eigen Matriks atas Aljabar Maks-Plus Tersimetri dengan ELCP Ariyanti, Gregoria; Suparwanto, Ari; Surodjo, Budi
JMPM: Jurnal Matematika dan Pendidikan Matematika Vol 5, No 2 (2020): September 2020 - Februari 2021
Publisher : Universitas Pesantren Tinggi Darul Ulum Jombang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26594/jmpm.v5i2.1942

Abstract

Aljabar maks-plus tersimetri merupakan perluasan dari aljabar maks-plus. Karena matriks atas aljabar maks-plus tersimetri dapat didefinisikan determinan maka persamaan karakteristiknya dapat diformulasikan sebagai sistem persamaan polinomial multivariabel aljabar maks-plus. Diperlukan suatu langkah menentukan nilai eigen dengan menggunakan alat yang disebut Masalah Linear Komplementer Diperluas (Extended Linear Complementarity Problem atau ELCP). Dalam tulisan ini, dipaparkan penggunaan ELCP dalam menentukan nilai eigen matriks atas aljabar maks-plus tersimetri. Penggunaan ELCP dilakukan dengan langkah-langkah yaitu mengubah persamaan karakteristik yang diperoleh dari suatu matriks ke bentuk sistem kesetimbangan linear. Selanjutnya, akar persamaan karakteristik yang diperoleh  merupakan penyelesaian dari sistem kesetimbangan linear yang merupakan nilai eigen dari matriks tersebut. Akibatnya, diperoleh representasi nilai eigen matriks atas aljabar maks-plus tersimetri dengan ELCP.
SYSTEMS OF FUZZY NUMBER MAX-PLUS LINEAR EQUATIONS M. Andy Rudhito; Sri Wahyuni; Ari Suparwanto; Frans Susilo
Journal of the Indonesian Mathematical Society Volume 17 Number 1 (April 2011)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.17.1.10.17-28

Abstract

This paper discusses the solution of systems of fuzzy number max-plus linear equations through the greatest fuzzy number subsolution of the system. We show that if entries of each column of the coecient matrix are not equal to infinite, the system has the greatest fuzzy number subsolution. The greatest fuzzy number subsolution of the system could be determined by first finding the greatest interval subsolution of the alpha-cuts of the system and then modifying it if needed, such that each its components is a family of alpha-cut of a fuzzy number. Then, based on the Decomposition Theorem on Fuzzy Set, we can determine the membership function of the elements of greatest subsolution of the system. If the greatest subsolution satisfies the system then it is a solution of the system.DOI : http://dx.doi.org/10.22342/jims.17.1.10.17-28
Diagonalisasi matriks atas ring dengan metode pemfaktoran secara lengkap Nikita, Nikita; Suparwanto, Ari; Sutopo, Sutopo
Majalah Ilmiah Matematika dan Statistika Vol. 24 No. 2 (2024): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v24i2.35918

Abstract

Generally, discussion about diagonalization of matrices in linear algebra is a matrix over the field. This research presents the diagonalization of matrices over commutative rings. Previous studies have explained the diagonalization of the matrix over a commutative ring, but there are some shortcomings in it. Therefore, this paper will present a matrix diagonalization process that could overcome these shortcomings. This research proposes a method for diagonalization matrices where the characteristic polynomial splits completely over the image of a ring homomorphism. Furthermore, the diagonalization is done over ring localization, so that there are more commutative ring matrices which can be diagonalized in this way. Meanwhile, the sufficient condition for a matrix which can be diagonalized in this thesis is when the determinant of the matrix whose columns are the eigenvectors is regular. Furthermore, to show this diagonalization method applies in general, given a special matrix n × n which satisfies the sufficient condition. Keywords: Matrices, diagonalization, eigenvector, determinant, localizationMSC2020: 15A09, 15A18, 15A20,13B05,13B20
Co-Authors Andi Rudhito Budi Surodjo Darlena, Darlena Eka Susilowati F Susilo F. SUSILO Frans Susilo Gregoria Ariyanti M Andy Rudhito M. Andy Rudhito M. ANDY RUDHITO M. Andy Rudhito Maharani, Andika Ellena Saufika Hakim Marcellinus Andy Rudhito Maxrizal Nikita S Siswanto Sri Wahyuni Sri Wahyuni Sutopo Sutopo