JTAM | Jurnal Teori dan Aplikasi Matematika

Journal Information
ISSN / EISSN: 25977512 / 26141175
Total articles ≅ 124

Latest articles in this journal

Viona Prisyella Balqis, Diah Chaerani, Herlina Napitupulu
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 947-962; https://doi.org/10.31764/jtam.v6i4.9446

Graph Coloring Problem (GCP) is the assignment of colors to certain elements in a graph based on certain constraints. GCP is used by assigning a color label to each node with neighboring nodes assigned a different color and the minimum number of colors used. Based on this, GCP can be drawn into an optimization problem that is to minimize the colors used. Optimization problems in graph coloring can occur due to uncertainty in the use of colors to be used, so it can be assumed that there is an uncertainty in the number of colored vertices. One of the mathematical optimization methods in the presence of uncertainty is Robust Optimization (RO). RO is a modeling methodology combined with computational tools to process optimization problems with uncertain data and only some data for which certainty is known. This paper will review research on Robust GCP with model validation to be applied to electrical circuit problems using a systematic review of the literature. A systematic literature review was carried out using the Preferred Reporting Items for Systematic reviews and Meta Analysis (PRISMA) method. The keywords used in this study were used to search for articles related to this research using a database. Based on the results of the search for articles obtained from PRISMA and Bibliometric R Software, it was found that there was a relationship between the keywords Robust Optimization and Graph Coloring, this means that at least there is at least one researcher who has studied the problem. However, the Electricity keyword has no relation to the other two keywords, so that a gap is obtained and it is possible if the research has not been studied and discussed by other researchers. Based on the results of this study, it is hoped that it can be used as a consideration and a better solution to solve optimization problems.
Ari Irawan, Wanti Rahayu, Rahnita Nuzulah
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 926-936; https://doi.org/10.31764/jtam.v6i4.9418

The problem-solving ability of students is still very low, so there is a need for media that can facilitate these abilities. Android-based learning media that is integrated with local wisdom of traditional games and mathematics in providing a new color for learning activities. This research aims to test whether the Kaulinan Barudak ethnomathematics android application that the researcher is making can improve students' problem-solving abilities. In addition, this research activity seeks to see how the user responds to the Kaulinan Barudak android application. The method used in this research is Research and Development (RnD) with the Borg and Gall model. There are 10 stages in this model, namely potential, data collection, product design, design validation, revision, product trial, revision, user experiment, revision, and mass production. Meanwhile, this research is already at the user trial stage. The experiment was conducted on 30 students of Junior High School/MTs Al Hidayah class VIII. Next, look to see if there are differences before and after treatment with applications using pre-test and post-test. The results of this research are (1) This research has provided an overview of the user's response to the Kaulinan Barudak ethnomathematics application which is not valid and feasible to be used as a medium for learning mathematics for seventh-grade students of junior high school; and (2) This research proves that with the use of the Kaulinan Barudak application, the student's understanding ability increases, this can be seen from the average pre-test and post-test and the results of the t-test that have been carried out.
Fandi Rezian Pratama Gultom, Solimun Solimun, Nurjannah Nurjannah
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 810-820; https://doi.org/10.31764/jtam.v6i4.8617

Soybean plants have limited growth with a planting period of 12 weeks, which causes the observed sample to be very small. A small sample of soybean plant growth observations can be bias causes in the conclusion of prediction results on soybean plant growth. The purpose this study is to apply the bootstrap resampling technique in Gompertz growth model which overcomes residual distribution with small samples, the research data was taken from soybean plant growth in four varieties with four spacing treatments, five replications and twelve weeks (long planting period). Gompertz growth model uses nonlinear least squares method in estimating parameters with Levenberg–Marquardt iteration. The value of the Gompertz model after resampling bootstrap has no significant difference. The adjusted R2 value of 0.96 is close to 1. This means that the total diversity of plant heights can be explained by the Gompertz model of 96 percent. Judging from the graph of predictions of soybean plant growth before resampling and after resampling coincide with each other it can also be seen in the initial growth values before resampling 14, 05 and 14.18, the maximum growth values are 55.13 and 55.60. Bootsrap resampling technique can overcome residual normality in the Gompertz growth model, but does not change the information in the initial data.
Septa Dwi Cahya, Bagus Sartono, Indahwati Indahwati, Evita Purnaningrum
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 844-856; https://doi.org/10.31764/jtam.v6i4.8968

In several research areas, it is common to have a dataset with more explanatory variables than the number of observations, called high-dimensional data. This condition can lead to multicollinearity problem. The least absolute shrinkage and selection operator (LASSO) solves the problem by shrinking the estimated coefficient to zero so that it can simultaneously carry on the variable selection and the parameter estimation. But LASSO performs poorly when the data contains some outliers in the response or explanatory variables. Robust methods have addressed this problem based on the least-absolute-deviation approach, such as LAD-LASSO and WLAD-LASSO. This current research aims to evaluate the performance of the LAD-LASSO and WLAD-LASSO methods on high-dimensional and low-dimensional data containing outliers. To evaluate the performance of these methods, the simulation study was conducted. The simulation study used three scenarios (without outliers, outliers on the response variable (5%, 10%, 15%), outliers both on the response and explanatory variables (5%, 10%, 15%)). We also used the Minimum Regularized Covariance Determinant (MRCD) estimator in calculating the weights on the WLAD-LASSO. The best method from this simulation then will be applied to sembung leaf extract data to identify antioxidant marker compounds in sembung leaf extract. The simulation results show that LAD-LASSO tends to be very tight in selecting, while LASSO tends to be too loose. Meanwhile, WLAD-LASSO is in the middle of those two techniques and performs the best in identifying the important variables correctly. Even the existence of weights cause WLAD-LASSO more robust against the presence of outliers in the response and explanatory variables compared to LAD-LASSO. Furthermore, performance of these methods on high-dimensional data decrease compared to low-dimensional data. The performance of these methods also tends to decrease when the rate of outlier increases. The WLAD-LASSO was then implemented in actual data to find the compound of antioxidant markers in the sembung leaf extract. The compounds/formulas obtained are Umbelliferone, 12-Hydroxyjasmonic Acid, C22H14N8O2, and Acetyleugenol (with a prediction error is 0.133050). These compounds/formulas can be developed as natural antioxidants and have the potential to be developed as medicinal ingredients.
Mutia Atika, Bib Paruhum Silalahi, Fahren Bukhari
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 991-1003; https://doi.org/10.31764/jtam.v6i4.9933

We consider the problem of three-dimensional cutting of a large block that is to be cut into some small block pieces, each with a specific size and request. Pattern generation is an algorithm that has been used to determine cutting patterns in one-dimensional and two-dimensional problems. The purpose of this study is to modify the pattern generation algorithm so that it can be used in three-dimensional problems, and can determine the cutting pattern with the minimum possible cutting residue. The large block will be cut based on the length, width, and height. The rest of the cuts will be cut back if possible to minimize the rest. For three-dimensional problems, we consider the variant in which orthogonal rotation is allowed. By allowing the remainder of the initial cut to be rotated, the dimensions will have six permutations. The result of the calculation using the pattern generation algorithm for three-dimensional problems is that all possible cutting patterns are obtained but there are repetitive patterns because they suggest the same number of cuts.
Muhammad Wiranadi Utama, I Wayan Mangku, Bib Paruhum Silalahi
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 1081-1095; https://doi.org/10.31764/jtam.v6i4.10213

In this paper, an asymptotic distribution of the estimator for the variance function of a compound periodic Poisson process with power function trend is discussed. The periodic component of this intensity function is not assumed to have a certain parametric form, except it is a periodic function with known period. The slope of power function trend is assumed to be positive, but its value is unknown. The objectives of this research are to modify the existing variance function estimator and to determine its asymptotic distribution. This research begins by modifying the formulation of the variance function estimator. After the variance function is obtained, the research is continued by determining the asymptotic distribution of the variance function estimator of the compound periodic Poisson process with a power function trend. The first result is modification of existing estimator so that its asymptotic distribution can be determined. The main result is asymptotic normality of the estimator of variance function of a compound periodic Poisson process with power function trend.
Ajeng Gelora Mastuti, Syafruddin Kaliky, Juanda Arman
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 963-975; https://doi.org/10.31764/jtam.v6i4.9772

Epistemological beliefs simultaneously affect mathematical communication skills. The higher the epistemological beliefs of a person's ability to formulate concepts, convey ideas, and hone ideas to convince others, the more mathematical communication skills will increase. This qualitative study uses three variables to describe mathematical communication and students' epistemological beliefs on linear system material. The subjects in this study were students who had epistemological beliefs from the test results, and students who were taken were students who were able to meet the indicators of epistemological confidence. Data collection techniques are tests, interviews and documentation. The results of this study indicate that students have beliefs that do not change or remain in solving test questions. The method used is more consistent with the way of solving, which according to students, is easy to do, able to solve problems by multiplying exercises and repeating what has been learned, solving problems by following the steps and methods of completion taught by the teacher, students can estimate answers or problem solving because of problems The subject obtained is obtained from experience and observations in everyday life.
Sumardi Sumardi, Anggit Cahyaning Tyas
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 905-914; https://doi.org/10.31764/jtam.v6i4.9376

The many Adversity Quotient kinds that each individual possesses will have an impact on how they respond to addressing difficulties. The person's efforts to tackle the current difficulties get more difficult as their degree of Adversity Quotient rises.This study's purpose is to describe students' reflective thinking profile in solving HOTS-type questions in terms of level adversity quotient. The subjects of this study, namely three students from class X of senior high school, were taken based on the Adversity Responses Profile (ARP) questionnaire results. The data collection techniques carried out by this study include analysis of test answer results and in-depth interviews. In addition, source triangulation is used for the validity of the data. Data analysis is carried out through five stages: data collection, data reduction, data presentation, data verification, and conclusions. The data table is obtained from the results of the analysis of the answers to the three questions presented in the form of tables based on the components of reflective thinking and problem-solving steps. The research results in this article are three, (1) the reflective thinking profile of students in solving HOTS-type questions can meet the components of reflective thinking and go through the steps of problem-solving Polya: analysis, plan, implement, and evaluation; (2) the reflective thinking profile of students in solving HOTS-type questions cannot meet all the components of reflective thinking, namely the comparing component and through the steps of problem-solving Polya: analysis, plan, implementation, and evaluation. However, at the step of the problem-solving plan, there is one plan that is not by mathematical concepts; and (3) the reflective thinking profile of quitter students in solving HOTS-type problems cannot meet all the components of reflective thinking, namely the contemplating component and not going through all the steps of problem-solving, namely the step of implementing the plan and evaluation. The three types of adversity questions have different reflective thinking profiles according to the criteria of each type.
Rinaldi Kurniawan, Eka N. Kencana, G. K. Gandhiadi
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 821-833; https://doi.org/10.31764/jtam.v6i4.8734

East Lombok is a regency that has tourism potential to be developed. In accelerating the pace of tourism development in East Lombok Regency, a decision support system is needed to make it easier to determine development priorities in the tourist sector. Analytical Hierarcy Process is a decision-making method that can solve the problem of multicriteria in the aspect of tourism in East Lombok. The data used are 50 data by prioritizing the opinions of experts and policy makers, namely the East Lombok Tourism Office, Head of tourism awareness groups and people involved in the tourism sector. The results showed that the value of index consistency was below 10% for each indicator and subindicator with infrastructure indicators as the highest priority with a value of 29.4545% and the highest subindicator was accessibility with a value of 17.8381%. The result of the calculation are expected to help policy makers in determining the strategy in the development of the tourism sector in Eaast Lombok district and in the future it can be developed by considering other factors.
Djihan Wahyuni, Eni Sumarminingsih, Suci Astutik
JTAM | Jurnal Teori dan Aplikasi Matematika, Volume 6, pp 937-946; https://doi.org/10.31764/jtam.v6i4.10096

This study aims to determine the implementation of Fuzzy Sugeno in classifying textual data obtained from Twitter so as to determine the polarity of public opinion regarding PPKM policies and Covid-19 vaccinations. This study uses primary data via Twitter related to COVID-19 vaccination and PPKM policies in Indonesia starting from February 9, 2021 to January 17, 2022. There are several stages carried out, namely data collection, data pre-processing, data labeling, data weighting. , identification of membership functions, determination of fuzzy sets, formation of classification systems, and evaluation of classification results. The results of this study explain that Fuzzy Sugeno's performance in classifying tweets is quite good with an average accuracy of 89.13%. Meanwhile, public opinion regarding PPKM policies and Covid-19 vaccinations tends to be balanced with 36.92% of tweets classified as positive sentiments, 22.85% negative sentiments, and another 40.23% classified as neutral sentiments. In addition, the fuzzy set that is formed based on the data observation method is very well done because it is able to adjust the frequency of the data in each category. This really helps improve the performance of the built classification system.
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