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<![CDATA[Simetrisasi Aljabar Min-Plus ]]>
<![CDATA[Suroto Suroto]]>
<![CDATA[ Vygotsky : Jurnal Pendidikan Matematika dan Matematika Vol 4, No 1 (2022): Vygotsky: Jurnal Pendidikan Matematika dan Matematika ]]>
Publisher : <![CDATA[Universitas Islam Lamongan ]]>
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DOI: 10.30736/voj.v4i1.444
<![CDATA[Pada makalah ini dibahas simetrasasi pada aljabar min-plus. Tujuan dari penelitian ini adalah mengonstruksi bentuk negatif dan setimbang dari setiap elemen pada aljabar min-plus. Metode penelitian mengadopsi dari cara perluasan aljabar max-plus menjadi aljabar max-plus tersimetri. Hasil penelitian adalah bentuk negatif dan setimbang dari elemen-elemen pada aljabar min-plus, yang dapat dianalogikan sebagai bentuk negatif dan nol pada aljabar konvesional. Hasil ini berpotensi dapat digunakan untuk mengatasi masalah invers penjumlahan pada aljabar min-plus.]]>
<![CDATA[Eigen Value of Fuzzy Matrices ]]>
<![CDATA[Suroto Suroto]]>;
<![CDATA[Ari Wardayanti]]>
<![CDATA[ Journal of Natural Sciences and Mathematics Research Vol 2, No 2 (2016): December ]]>
Publisher : <![CDATA[Faculty of Science and Technology, Universitas Islam Negeri Walisongo Semarang ]]>
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DOI: 10.21580/jnsmr.2016.1.2.1669
<![CDATA[In this paper we discuss about eigen value of fuzzy matrices by adopted the substract operation of fuzzy matrices in Sidky and Emam (1992). By applying this substraction, it’s yields that some properties eigen value of fuzzy matrices in Joe Anand and Edal Anand is not satisfied.©2016 JNSMR UIN Walisongo. All rights reserved.]]>
<![CDATA[Eigenvalue decomposition of a symmetric matrix over the symmetrized max-plus algebra ]]>
<![CDATA[Suroto Suroto]]>
<![CDATA[ Desimal: Jurnal Matematika Vol 4, No 3 (2021): Desimal: Jurnal Matematika ]]>
Publisher : <![CDATA[Universitas Islam Negeri Raden Intan Lampung ]]>
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DOI: 10.24042/djm.v4i3.9959
<![CDATA[This paper discusses topics in the symmetrized max-plus algebra. In this study, it will be shown the existence of eigenvalue decomposition of a symmetric matrix over symmetrized max-plus algebra. Eigenvalue decomposition is shown by using a function that corresponds to the symmetrized max-plus algebra with conventional algebra. The result obtained is the existence of eigenvalue decomposition of a symmetric matrix over symmetrized max-plus algebra and its application to determine eigenvalues and eigenvectors.]]>
<![CDATA[INVERS MOORE-PENROSE PADA MATRIKS ATAS ALJABAR MAX-PLUS TERSIMETRI ]]>
<![CDATA[Suroto Suroto]]>
<![CDATA[ Teorema: Teori dan Riset Matematika Vol 6, No 2 (2021): September ]]>
Publisher : <![CDATA[Universitas Galuh ]]>
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DOI: 10.25157/teorema.v6i2.5514
<![CDATA[Pada makalah ini dibahas tentang invers Moore-Penrose pada matriks atas aljabar max-plus tersimetri. Pendefinisian invers Moore-Penrose atas aljabar max-plus tersimetri dilakukan dengan mengadopsi invers Moore-Penrose pada aljabar konvensional. Relasi “sama dengan” pada aljabar konvensional diganti peranannya dengan relasi “setimbang” pada aljabar max-plus tersimetri. Eksistensi invers Moore-Penrose ditunjukkan dengan memanfaatkan suatu fungsi yang mengkorespondensikan aljabar max-plus tersimetri dengan aljabar konvensional. Hasil yang diperoleh adalah bentuk dan beberapa sifat invers Moore-Penrose pada matriks atas aljabar max-plus tersimetri. Hasil ini berpotensi dapat dimanfaatkan untuk menentukan solusi dari sistem kesetimbangan linier atas aljabar max-plus tersimetri yang memiliki kemiripan peranan dengan sistem persamaan linier pada aljabar konvensional.Kata kunci: Aljabar max-plus tersimetri, invers Moore-Penrose, matriks]]>
<![CDATA[RING MATRIKS ATAS RING KOMUTATIF ]]>
<![CDATA[Achmad Abdurrazzaq]]>;
<![CDATA[Ari Wardayani]]>;
<![CDATA[Suroto Suroto]]>
<![CDATA[ Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 7 No 1 (2015): Jurnal Ilmiah Matematika dan Pendidikan Matematika ]]>
Publisher : <![CDATA[Jurusan Matematika FMIPA Universitas Jenderal Soedirman ]]>
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DOI: 10.20884/1.jmp.2015.7.1.2895
<![CDATA[This paper discusses a matrices over a commutative ring. A matrices over commutative rings is a matrices whose entries are the elements of the commutative ring. We investigates the structure of the set of the matrices over the commutative ring. We obtain that the set of the matrices over the commutative ring equipped with an addition and a multiplication operation of matrices is a ring with a unit element.]]>
<![CDATA[SUBGRUP FUZZY ATAS SUATU GRUP ]]>
<![CDATA[Fatkhur Rozi]]>;
<![CDATA[Ari Wardayani]]>;
<![CDATA[Suroto Suroto]]>
<![CDATA[ Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 6 No 1 (2014): Jurnal Ilmiah Matematika dan Pendidikan Matematika ]]>
Publisher : <![CDATA[Jurusan Matematika FMIPA Universitas Jenderal Soedirman ]]>
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DOI: 10.20884/1.jmp.2014.6.1.2901
<![CDATA[This paper discusses a fuzzy subgroup of a classical group. It’s constructed by defining fuzzy subsets and employing products and inverse notions on classical group. The result obtained is sufficient and necessary conditions for the fuzzy subset to be fuzzy subgroup.]]>
<![CDATA[SEMI RING POLINOM ATAS ALJABAR MAX-PLUS ]]>
<![CDATA[Suroto Suroto]]>
<![CDATA[ Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 4 No 2 (2012): Jurnal Ilmiah Matematika dan Pendidikan Matematika ]]>
Publisher : <![CDATA[Jurusan Matematika FMIPA Universitas Jenderal Soedirman ]]>
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DOI: 10.20884/1.jmp.2012.4.2.2965
<![CDATA[In this paper we define polynomials over a max plus algebra. Furthermore we prove that the set of such polynomials is a semi ring.]]>
<![CDATA[PELABELAN FUZZY PADA GRAF ]]>
<![CDATA[Siti Rahmah Nurshiami]]>;
<![CDATA[Suroto Suroto]]>;
<![CDATA[Fajar Hoeruddin]]>
<![CDATA[ Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 6 No 1 (2014): Jurnal Ilmiah Matematika dan Pendidikan Matematika ]]>
Publisher : <![CDATA[Jurusan Matematika FMIPA Universitas Jenderal Soedirman ]]>
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DOI: 10.20884/1.jmp.2014.6.1.2898
<![CDATA[This paper discusses fuzzy labeling graph and its properties. The properties discussed are fuzzy labeling subgraph, union graph, and fuzzy magic graph. The results showed that the strength of connectedness for pair of vertices in a graph with fuzzy labeling is always greater than or equal to the strength of connectedness for pair of vertices in its subgraph. In addition, union of two graph with fuzzy labeling will form a graph with fuzzy labeling. Meanwhile, on magic labeling there is always a fuzzy bridge on fuzzy magic graph.]]>
<![CDATA[SEMI MODUL POLINOMIAL FUZZY ATAS ALJABAR MAX-PLUS FUZZY ]]>
<![CDATA[Ari Wardayani]]>;
<![CDATA[Suroto Suroto]]>
<![CDATA[ Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 3 No 1 (2011): Jurnal Ilmiah Matematika dan Pendidikan Matematika ]]>
Publisher : <![CDATA[Jurusan Matematika FMIPA Universitas Jenderal Soedirman ]]>
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DOI: 10.20884/1.jmp.2011.3.1.2968
<![CDATA[In this paper, we discuss the extension of fuzzy max-plus algebra on polynomial with coefficient in fuzzy number. We also proof that fuzzy polynomial is semi modul over fuzzy max-plus algebra.]]>
<![CDATA[EKSISTENSI DEKOMPOSISI RANK PADA MATRIKS ATAS ALJABAR MAX-PLUS TERSIMETRI ]]>
<![CDATA[Suroto Suroto]]>;
<![CDATA[Najmah Istikaanah]]>;
<![CDATA[Sri Maryani]]>
<![CDATA[ UNEJ e-Proceeding 2022: E-Prosiding Seminar Nasional Matematika, Geometri, Statistika, dan Komputasi (SeNa-MaGeStiK) ]]>
Publisher : <![CDATA[UPT Penerbitan Universitas Jember ]]>
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<![CDATA[In this paper, we discuss the rank-decomposition in the symmetrized max-plus algebraic matrix. The existence of rank decomposition is shown using minor rank in the symmetrized max-plus algebra and a link among symmetrized max-plus algebra and conventional algebra. The result is a rank-decomposition in symmetrized max-plus algebraic matrix exists. Furthermore, the rank-decomposition is not unique. Keywords: Existence, link, rank decomposition, symmetrized max-plus algebra]]>
