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<![CDATA[MODEL LOGISTIK FUZZY DENGAN ADANYA PEMANENAN PROPORSIONAL ]]>
<![CDATA[Fitri Nor Annisa]]>;
<![CDATA[Muhammad Ahsar Karim]]>;
<![CDATA[Yuni Yulida]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 16(1), 2022 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v16i1.5552
<![CDATA[The logistic growth model with proportional harvesting is a population growth model that takes into account harvesting factors. In real life, not all conditions can be known with certainty, such as different growth rates in each population and harvest rates depending on the needs of the harvester. To overcome these conditions, there is a concept that accommodates the problem of uncertainty, namely the fuzzy concept. This concept can be induced into a logistic model with proportional harvesting which assumes the intrinsic growth rate and the harvest rate is expressed by fuzzy numbers. The purpose of this research is to form a logistic model with fuzzy proportional harvesting, analyze the stability of the model, and form a numerical simulation. This study uses the alpha-cut method to generalize the intrinsic growth rate and harvest rate from crisp numbers to fuzzy numbers, then the Graded Mean Integration Representation (GMIR) method to defuzzify the model, and the linearization method to analyze the stability of the model. The results of this study obtained a logistic model with proportional harvesting. Then the model was developed into a logistic model with fuzzy proportional harvesting by assuming the intrinsic growth rate and the harvest rate expressed by fuzzy numbers. From the model obtained 2 equilibrium points, namely the first equilibrium point is unstable and the second equilibrium point is asymptotically stable under certain conditions. Model simulation is given to show illustration of stability analysis. From the simulation, it can also be shown that the higher the graded mean value, the lower the population.]]>
<![CDATA[SOLUSI PERSAMAAN DIFERENSIAL FRAKSIONAL LINIER HOMOGEN DENGAN METODE MITTAG-LEFFLER ]]>
<![CDATA[Helfa Oktafia Afisha]]>;
<![CDATA[Yuni Yulida]]>;
<![CDATA[Nurul Huda]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 10, No 1 (2016): JURNAL EPSILON VOLUME 10 NOMOR 1 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v10i1.53
<![CDATA[The classical calculus only studies derivatives as well as differential equations of integers, whereas for non-integral integers and differential equations are not included. Thus the concept of fractional calculus, which studies the integral and non-integral order of abbreviated diferintegral including fractional differential equations (PDF). In this paper we present a method for obtaining a homogeneous linear PDF solution built in the Mittag-Leffler function in the form of a series ???????? (????????) = ????????αα (???????????? αα) = ???????????????????????????????????????? Γ (???????????????? + 1) ∞???????? = 0 This series converges for ???????? at ????-1????????, 1????????????. The derivative search of ???????? (????????), is done by deriving each term from ???????? (????????) using the definition of Caputo derivative followed by determining the coefficient ???????????????? to obtain the PDF solution.]]>
<![CDATA[MODULAR BLOK DI RUANG BARISAN TERJUMLAH CESARO ORLICZ ]]>
<![CDATA[Haryadi Haryadi]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 15(2), 2021 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v15i2.4330
<![CDATA[On the Cesaro summable of orde-p sequence space, if the fuction is replaced by Orlicz function, it is not always easy to define norm in the space. In this paper, we study some properties of the Cesaro Orlicz summable sequence space. First, on the space we define a modular and its the luxemburg norm, and then some topological properties is explored. The results show that the sequence spaces is modular complete and nom complete. In addition, the space is a BK-space but not an AK-space. ]]>
<![CDATA[PENERAPAN PROGRAM LINIER PADA PERMAINAN NON-KOOPERATIF ]]>
<![CDATA[Pardi Affandi]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 5, No 2 (2011): JURNAL EPSILON VOLUME 5 NOMOR 2 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v5i2.71
<![CDATA[This paper will examine the application of linear programming to the game non-cooperative. It starts with the application of a linear program on the game of point of view of player I. In the same way players II problems can be brought into the form of a linear program. The equation obtained is the form dual program, the same result will be obtained that is the maximum result gained player I equal to the minimum result that players sought II against player I. Furthermore the game will be solved by the pivot method, so that the strategy and results obtained from the game.]]>
<![CDATA[METODE TAGUCHI UNTUK PENINGKATAN KUALITAS MUTU PRODUK ]]>
<![CDATA[Akhriyandi Wijanarta]]>;
<![CDATA[Nur Salam]]>;
<![CDATA[Dewi Anggraini]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 8, No 1 (2014): JURNAL EPSILON VOLUME 8 NOMOR 1 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v8i1.103
<![CDATA[Costumers tend to choose a better product so that the quality improvement of a product is crucial. Quality control is a continuous process to ensure the quality of the products. The Taguchi method that was introduced by Dr. Genichi Taguchi in 1940 used to improve the quality of product and process as well as to reduce the production cost incurred by the company to minimize damage or defect in the products. The purpose of this research is to explain the procedures of Taguchi method to improve product quality. The results of the research show that the procedures using Taguchi method, are: the first step is counting the number of experiments and choosing the form of orthogonal arrays from the number of factors and levels that will be tested. The second step is conducting experiment and obtains data than calculating the mean value, and determining signal to noise rasio that is consistent to the quality characteristics of the experiment. The third step is analyzing experiment data using analysis of variance to determine factors that have a significant influence, then calculating the contribution value of each factor. If the contribution value of factor is smaller than the contribution value of error value then the factor will be pooling up. After getting the optimal alternative factors the fourth step is confirming experiment to examine the conclusion of the obtained data experiment. Furthermore, the five step is calculating the confidence intervals of response mean value betwen the prediction result of Taguchi method and the result of confirming experiment. After that, the sixth step is calculating Taguchi loss function to determine the amount of damage cost spent to improve the quality of product.]]>
<![CDATA[PENYELESAIAN MODEL TRANSPORTASI MENGGUNAKAN METODE ASM ]]>
<![CDATA[Nurul Iftitah]]>;
<![CDATA[Pardi Affandi]]>;
<![CDATA[Akhmad Yusuf]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 14, No 1 (2020): JURNAL EPSILON VOLUME 14 NOMOR 1 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v14i1.3197
<![CDATA[Transportation problem is related by goods shipments from sources (supplies) to destination(demand). the method that could be used for solving the transportation problem is to directly find theoptimal solution. The direct method that used in this study id the ASM method for solving the balancetransportation problem and revised ASM method for solving the unbalance transportation problem.This study aims to construct a transportation model using those methods and it solution. The methodon this study is to identify the transportation model, construct the transportation model matrixes,construct an algorithm table using ASM method and to determine the optimal solution of thetransportation problem. The obtained result from this study was the model ASM method coulddetermine the optimum value without using initial feasible solution. On solving the unbalancetransportation problem, there is an addition of dummy cell or column step. Then reducing the cost ofcell and column and change the dummy cost with the biggest cost of reduced cell or column.]]>
<![CDATA[APLIKASI EVOLUTIONARY DISCRETE FIREFLY ALGORITHM DALAM PENYELESAIAN TRAVELLING SALESMAN PROBLEM ]]>
<![CDATA[Cahya, Nila]]>;
<![CDATA[Soesanto, Oni]]>;
<![CDATA[Affandi, Pardi]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 13, No 1 (2019): JURNAL EPSILON VOLUME 13 NOMOR 1 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v13i1.3194
<![CDATA[Proses distribusi barang pada suatu industri memerlukan bentuk efisiensi dalam pemilihan jalur terpendek yang akan dilalui seorang salesman. Secara matematis, pemilihan jalur terpendek merupakan suatu permasalahan optimasi yang disebut Travelling Salesman Problem (TSP). Terdapat banyak metode yang dapat diterapkan untuk menemukan solusi dari TSP, salah satunya Evolutionary Discrete Firefly Algorithm (EDFA) yang merupakan metode metaheuristik terbaru yang ditemukan oleh Jati dan Suyanto (2011) sebagai perkembangan dari Firefly Algorithm (FA) yang hanya didesain untuk permasalahan kontinu. Penelitian ini bertujuan untuk menjelaskan penerapan EDFA dalam penyelesaian TSP. Data yang digunakan dalam penelitian ini merupakan data kasus TSP berupa koordinat titik kota yang diambil dari database TSP Libary (TSPLIB) dengan 7 jenis kasus berbeda yaitu Ulysses16, Ulysses22, Eil51, Berlin52, St70, Rat99, dan Gr202. Kasus-kasus tersebut diselesaikan dengan menerapkan EDFA untuk menemukan solusi optimalnya melalui beberapa langkah yang terdapat dalam algoritma ini. Penyelesaian kasus TSP melalui EDFA juga dilakukan menggunakan bantuan program simulasi untuk mempermudah pehitungan. Hasil penelitian menunjukkan bahwa EDFA sebagai perkembangan FA telah berhasil diterapkan untuk kasus TSP yang memiliki solusi dalam ruang diskrit. Simulasi program EDFA yang diterapkan pada kasus-kasus tersebut memberikan solusi lebih baik pada beberapa kasus dengan hasil jarak optimal yang lebih pendek dibandingkan jarak optimal yang telah ditemukan sebelumnya.]]>
<![CDATA[DETERMINAN MATRIKS DENGAN ELEMEN BILANGAN FIBONACCI ORDER-???????? YANG DIGENERALISASI ]]>
<![CDATA[Fadly Ramadhan]]>;
<![CDATA[Thresye Thresye]]>;
<![CDATA[Akhmad Yusuf]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 10, No 2 (2016): JURNAL EPSILON VOLUME 10 NOMOR 2 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v10i2.34
<![CDATA[Bilangan Fibonacci didefinisikan sebagai barisan bilangan yang suku-sukunya merupakan penjumlahan dua suku sebelumnya. Penelitian sebelumnya menjelaskan tentang bilangan Fibonacci yang digeneralisasi hingga order-????????. Selanjutnya bilangan Fibonacci tersebut dibentuk dalam matriks berukuran ????????×???????? yang akan ditentukan nilai determinannya. Tujuan dari penelitian ini adalah untuk mengetahui bentuk barisan Fibonacci order-???????? yang digeneralisasi, kemudian mengetahui bentuk matriks persegi yang elemennya berupa bilangan Fibonacci order-???????? yang digeneralisasi dan membuktikan teorema untuk menentukan determinan dari matriks persegi yang elemennya berupa bilangan Fibonacci order-???????? yang digeneralisasi. Hasil dari penelitian ini adalah diperoleh bentuk barisan dari bilangan Fibonacci order-???????? yang digeneralisasi, diperoleh bentuk matriks persegi yang elemennya berupa bilangan Fibonacci order-???????? yang digeneralisasi dan diperoleh determinan dengan 4 kondisi yang berbeda.Kata Kunci : Bilangan Fibonacci, bilangan Fibonacci order-???????? yang digeneralisasi, matriks.]]>
<![CDATA[MODIFIKASI MODEL SEIR PADA PENYAKIT CAMPAK ]]>
<![CDATA[Sofia Faridatun Nisa]]>;
<![CDATA[Yuni Yulida]]>;
<![CDATA[Faisal Faisal]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 16(1), 2022 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v16i1.4649
<![CDATA[The epidemic models Susceptible, Exposed, Infected and Recovered (SEIR) are used for the spread of diseases that have a latent period (incubation period) which one is measles disease. Latent periods are entered into the Exposed class. Measles itself after the incubation period will experience clinical symptoms consisting of three stages, which are prodromal stage, eruption stage and healing stage. Due to these clinical symptoms, the SEIR model can be modified by dividing the Infected class into two classes, which are Infected Prodromal class and Infected Eruption class. While the healing stage enters Recovered class. The spread of measles can be made into an epidemic model with five classes which are and . The purpose of this study is to explain the modification of the model, determine and analyze the model's local stability at the equilibrium point of the model and to interpret model simulations with multiple stability-eligible parameter values. The results obtained from this study are modification of model which is model. Based on model, two equilibrium points obtained which are disease-free equilibrium points and endemic equilibrium points, which are locally asymtotics stable with conditions. Model simulations are presented to support an explanation of model stability analysis based on stability-meeting parameters]]>
<![CDATA[HOMOMORFISMA PADA SEMIGRUP-Г ]]>
<![CDATA[Ismania Tanjung Sari]]>;
<![CDATA[Na'imah Hijriati]]>;
<![CDATA[Thresye Thresye]]>
<![CDATA[ EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 5, No 2 (2011): JURNAL EPSILON VOLUME 5 NOMOR 2 ]]>
Publisher : <![CDATA[Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat ]]>
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DOI: 10.20527/epsilon.v5i2.76
<![CDATA[Abstract algebra is a part of mathematics that studies the principles orrules which will then be used to demonstrate the truth of a statement (theorem).One part of abstract algebra is semigroup and one of it’s generalization is Г-semigroup. An nonempty sets S is called Г-semigroup if γ, μ Г and a, b, c S by aγb S and (aγb)μc = aγ(bμc). On Г-semigroup, there is theorem ofhomomorphism and called Γ-homomorphism. A mapping : S T , with S and Tis a Г-semigroup called Γ-homomorphism if x, y S dan γ Г, it’s exist (xγy) = (x)γ (y).]]>
