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Jurnal Matematika
Published by Universitas Diponegoro
ISSN : -     EISSN : -     DOI : -
Core Subject : Education,
Mathematics
Arjuna Subject : -
Articles 97 Documents
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METODE PENEGASAN BILANGAN TRAPEZOIDAL FUZZY PADA PROGRAM LINIER FUZZY TIDAK PENUH Muhammad ismail husein
Jurnal Matematika Vol 4, No 4 (2015): (OKTOBER2015)
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

ABSTRACT. Fuzzy linear programming is one of linier programming form which there is fuzzy number form on objective variable, objective variable coefficient, constraint coefficient or right hand constraint. Fuzzy linear programming solved by parameters changing which is in fuzzy number form into crisp number form. Crisp method used to averment  the trapezoidal fuzzy number and each method  is not always has same result. Fuzzy linear programming problem with objective function coefficient, constraint coefficient, or right hand as a fuzzy number is the form of not fully fuzzy linear programming. This paper will discuss three crisp method, they are Ranking Function, Yager Ranking Function, and Robust Ranking Function to solve fuzzy linear programming problem. The final solution can use simplex method, and then final result compared to determine crisp method which is optimal.
SUBGRUP -NORMAL DAN SUBRING -MAX Kristi Utomo Kristi Utomo
Jurnal Matematika JURNAL MATEMATIKA NO 2 2016
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

  ABSTRACT. For any group , subgroup  of  is called -normal subgroup if there exist a normal subgroup  of  such that  and  where  is maximal normal subgroup of  which is contained in . On the other side, for each ring , subring  of  is called -max subring if there exist an ideal  of  such that  and  where  is maximal ideal of  which is contained in . Subgroup normal  of  is -normal subgroup if and only if  is maximal normal subgroup and ideal  of  is -max subring if and only if  is maximal ideal. Every group and ring is -normal subgroup and -max subring of itself.  
Penerapan Metode Program Linear dan Analisis Sensitivitas Pada Optimalisasi Produksi Jenang Karomah (Studi Kasus Pada PJ.Karomah Kudus) Novita Hariyani; Bambang Irawanto
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

 ABSTRAK. Optimalisasi produksi Jenang Karomah PJ.Karomah Kudus menjadi sebuah hal yang penting untuk memaksimalkan laba dengan cara mengoptimalkan penggunaan bahan baku. Program linear dengan metode simpleks adalah metode yang tepat untuk mengetahui jenang varian manakah yang memberikan keuntungan yang paling maksimal. Analisis sensitivitas dilakukan untuk batas – batas perubahan nilai pada fungsi tujuan maupun fungsi kendala, dengan tetap diperoleh tujuan yang optimal. Metode enumerasi implisit digunakan untuk mencari solusi optimal pemilihan memasak jenang yang sesuai dengan keadaan nyata di lapangan. Pengoptimalan produksi Jenang Karomah dengan program linear menghasilkan Jenang Sirsak, Jenang Mellon Strawberry, dan Jenang Durian memberikan keuntungan yang paling optimal dalam 1 kali periode memasak jenang dengan 60,0005 kg Jenang Sirsak, 9,9995 kg Jenang Mellon Strawberry, 175 kg Jenang Durian. Setelah dihitung dengan integer programming didapatkan solusi bahwa jenang yang dimasak dalam satu periode memasak untuk menghasilkan yang paling optimal adalah Jenang Wijen, Jenang Sirsak, Jenang Ketan Hitam, Jenang Kacang Hijau, Jenang Coklat Susu, Jenang Mellon Strawberry dan Jenang Durian yang apabila jenang-jenang tersebut dimasak dalam 1 periode memasak akan menghasilkan laba sebesar Rp. 2.162.834,00.  
PENYELESAIAN MASALAH PROGRAM LINIER FUZZY DENGAN BILANGAN FUZZY MENGGUNAKAN METODE SABIHA LINEAR REAL Eky Pawestri Gita Asmara
Jurnal Matematika JURNAL MATEMATIKA NO 3 2016
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

 ABSTRACT. Fuzzy Linear Programming (FLP) is one form of a linear programming that includes fuzzy numbers. Several methods have been developed to solve the FLP problems, one of which Sabiha’s Methods. The method is modifying Two Phase Methods such that it can be used in the FLP. Modification is done by changing the general form to be adjusted with the "triplet matrix", such that the one matrix of the triplet matrix is divided into three single matrix. The method is using Linear Fuzzy Real Numbers (LFR). There are also Kumar’s Methods were also modify Two Phase Methods. The comparison of the Sabiha’s Methods with Kumar’s Methods is resulting the same optimal solution and value in the form of fuzzy but there is a different in the form of crisp. 
KONGRUENSI PADA SEMIALJABAR ATAS HEMIRING SaniMusyafa Hikam; Bambang Irawanto
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

A hemiringR is called S -semialgebra if R is a left and right semi module over S satisfying axb=a(xb) for all a,b ∈S and x∈R . On the S -semialgebra R can be defined a congruence. A congruence on the S -semialgebra R is any congruence on the hemiring R which is both a left and right compatible for any multiplication by element of S . Therefore, the properties of congruence on a hemiring can be  generalized to congruence on a semi algebra over a hemiring
PERBANDINGAN METODE TRUST-REGION DENGAN METODE NEWTON-RAPHSON PADA OPTIMASI FUNGSI NON LINIER TANPA KENDALA Yully Estiningsih; farikhin farikhin
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

Optimization is the best decision of  the objective functions for  produce a satisfactory solution. Optimization of multi variables unconstraints is to optimize the the objective functions which contains multi variable function freely without any specific requirements that restrict its function. Trust-Region methods methods is used to optimize multi variables unconstraint , Trust-Region methods quadratic approach of optimizing non linear the objective functions with a certain radius as the limit of the step size according to the quality of the approach. Newton-Raphson methods is a root search method with the the objective functions approaches a point, where the objective functions has a derivative. In this final will be talking about Trust-Region methods will compared with Newton-Raphson methods, and rendered example problem in which only be solved using Trust-Region methods.Keywords : Trust-Region Methods, Optimization, Newton-Raphson Methods 
KONSTRUKSI IMPLIKASI XOR DAN IMPLIKASI E PADA LOGIKA FUZZY Karunia TyasLukita
Jurnal Matematika JURNAL MATEMATIKA NO 4 2016
Publisher : MATEMATIKA FSM, UNDIP

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Penghubung Xor digunakan untuk menyelesaikan masalah aljabar boolean, tetapi penghubung xor juga bisa menyelesaikan masalah pada logika fuzzy. Diperlukan konsruksi baru agar penghubung Xor bisa dioperasikan dalam himpunan atau logika fuzzy. Konstruksi Xor diperoleh dari tiga fungsi dasar pada logika fuzzy yaitu t-norm, t-conorm dan negasi. Terdapat tiga konstruksi Xor yaitu penghubung Xor dengan komposisi utama t-norm (ET), penghubung Xor dengan komposisi utama t-conorm (ES),merupakan fungsi negasi dari penghubung Xor (NE). Didefinisikan       ET(x,y) = T(S(x,y), N(T(x,y))) , ES(x,y) = S(T(N(x), y), T(x, N(y)))dan NE(x)= E(1,x).Sedangkan untuk konstruksinya terdapat dua implikasi yaitu implikasi Xor(IE,S,N)dan implikasi E (IS,N,E). Didefinisikan  IE,S,N (x, y) = E(x, S(N(x),N(y))) danIS,N,E(x, y) = S(N(x), E(N(x), y)). Penghubung Xor  dan implikasinya dioperasikan pada himpunan fuzzy dan hasilnya berbeda-beda untuk setiap fungsi dasar yang digunakan. Penghubung Xor dan Implikasinya sangat bergantung pada konstruksi fungsi dasar yang digunakan dan tidak dapat berdirisendiri seperti pada operasi aljabar Boolean.    
ENERGI LAPLACIAN SKEW PADA DIGRAF Fitria Dewi Puspitasari; Bayu Surarso
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

Digraph G is a pairs of set (V,Γ) , with V(G) is set of vertices G , and Γ(G) is set of arc G . Graph G can be representated in to matrix adjacencyS(G) , from matrix S(G) be obtained eigenvalues of graph G . The sum of the absolute values of its eigenvalues is energy skew of digraph G . From digraph G be obtained DG=diag(d1,d2,d3,…,dn) the diagonal matrix with the vertex degrees d1,d2,d3,…,dn of v1,v2,v3,…,vn . Then LG=DG-S(G) is called the laplacian matrix of digraph G . The sum of the quadrate values of each eigenvalues is energy laplacian skew. In this final project will explain about the concept of the skew laplacian energy of a simple, conected digraph G . Also find the minimal value of this energy in the class of all connnected digraphs on n≥2 vertices.
PELABELAN DIVISOR CORDIAL PADA BEBERAPA GRAF Aptri Wijayanti; Lucia Ratnasari
Jurnal Matematika Vol 2, No 3 (2013): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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ABSTRAK. Diberikan pemetaan bijektif f dari himpunan titik V(G) ke {1,2,…,|V|}. Pelabelan sisi induced berlabel 1 apabila f(u) dapat membagi f(v) atau f(v) dapat membagi f(u) dan berlabel 0 untuk yang lainnya, dimana u dan v adalah titik yang incident dengan sisi uv. Pemetaan f disebut pelabelan divisor cordial bila harga mutlak dari selisih banyaknya sisi yang mempunyai label 0 dan banyaknya sisi yang mempunyai label 1 kurang dari atau sama dengan 1. Graf yang memenuhi syarat pelabelan divisor cordial disebut graf divisor cordial. Pada jurnal ini dikaji bahwa graf path, graf cycle, graf wheel, graf star, graf bipartit lengkap K_(2,n), graf bistar dan graf subdivisi dari graf star (S(K_(1,n) )) merupakan graf divisor cordial.
HUBUNGAN ANTARA KONGRUENSI GRUP PADA SUATU SEMIGRUP DENGAN HIMPUNAN BAGIAN DARI SEMIGRUP TERSEBUT YANG MEMENUHI SIFAT DENSE, FULL, TERTUTUP, E-KONJUGAT DAN KUAT-KONJUGAT Muhammad Alfian Toni
Jurnal Matematika Vol 4, No 4 (2015): (OKTOBER2015)
Publisher : MATEMATIKA FSM, UNDIP

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 ABSTRAK. A congruence on a semigrup which classes form a group and the group hereinafter referred congruence. Semigrup subset of properties that meet dense, full, closed, E- conjugate and strong-conjugate. Given semigrup and  nonempty subsets of is said to be full if , H is said to be dense if for every  are  such that   is said to be closed if  with ,  is said to be strong-conjugate if  with  then for each ,  is said to be E-conjugate if  with  then  for each. In this thesis studied the relationship between the group on semigrup congruence with the semigrup subsets that meet the nature of dense, full, closed, E-conjugate and strong-conjugate. For each congruence group form a subset semigrup that meets the dense, full, closed, E-conjugate and strong-conjugate. And vice versa for each subset semigrup that meets the dense, full, closed, E-conjugate and strong-conjugate formed a group congruence.Kata Kunci : congruence group, dense, full, closed, E-conjugate and strong-conjugate

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