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Journal articles on the topic 'Fuzzy Elementary Row Operations Method'
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Ayu Puspita, Dian, and Mashadi Mashadi. "Modifikasi Aritmatika Aljabar pada Bilangan Fuzzy Hexagonal dan Penentuan Invers Matriks." Jurnal Axioma : Jurnal Matematika dan Pembelajaran 10, no. 1 (2025): 83–93. https://doi.org/10.56013/axi.v10i1.3545.
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Hexagonal fuzzy numbers are a development of trapezoidal fuzzy numbers. Just like algebra for trapezoidal fuzzy numbers. There are not many algebraic differences given by various authors for the many operations of addition, subtraction, and scalar multiplication. However, for multiplication, division, and inverse operations, there are many algebraic alternatives offered by various authors in parametric and ordinary forms. But the problems that arise do not always have an inverse for any hexagonal fuzzy number . In this paper, by changing hexagonal fuzzy numbers into another form and defining two midpoints and for any hexagonal fuzzy number . Thus, for the algebraic forms of multiplication, division, and inverse there is one that is produced using the elementary row method. At the end, an example of determining the inverse of a hexagonal fuzzy number matrix that has order . Keywords: Algebra arithmetic, hexagonal fuzzy number, inverse matrix
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Mashadi, Yuliana Safitri, Sukono, Igif Gimin Prihanto, Muhamad Deni Johansyah, and Moch Panji Agung Saputra. "The Inverse and General Inverse of Trapezoidal Fuzzy Numbers with Modified Elementary Row Operations." Mathematics 12, no. 7 (2024): 946. http://dx.doi.org/10.3390/math12070946.
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Trapezoidal positive/negative fuzzy numbers have no single definition; instead, various authors define them in relation to different concepts. This means that arithmetic operations for trapezoidal fuzzy numbers also differ. For the operations of addition, subtraction, and scalar multiplication, there are not many differences; for multiplication, however, there are many differences. In general, multiplication is divided into various cases. For the inverse operation, there is not much to define; in general, for any trapezoidal fuzzy number u~, u~⊗1u~=i~=(1,1,0,0) does not necessarily apply. As a result of the different arithmetic operations for multiplication and division employed by various authors, several researchers have tackled the same problem and reached different solutions, meaning that the application will also produce different results. To date, many authors have proposed various alternatives for the algebra of the trapezoidal fuzzy number. In this paper, using the parametric form approach to trapezoidal fuzzy numbers, an alternative to multiplication with only one formula is constructed for various cases. Furthermore, based on the definition of multiplication for any trapezoidal fuzzy number, u~ is constructed 1u~ so that u~⊗1u~=i~=(1,1,0,0). Based on these conditions, we show that various properties that apply to real numbers also apply to any trapezoidal fuzzy number. Furthermore, we modify the elementary row operational steps for the trapezoidal fuzzy number matrix, which can be used to determine the inverse of a trapezoidal fuzzy number matrix with the order m×m. We also give the steps and examples necessary to determine the general inverse for a trapezoidal fuzzy number matrix of the order m×n with m ≠n. This ability to easily determine the inverse and general inverse of a trapezoidal fuzzy number matrix has a number of applications, such as solving fully trapezoidal fuzzy number linear systems and fuzzy transportation problems, especially in applications in fields outside of mathematics; for example, the application of triangular fuzzy numbers in medical problems is a topic currently receiving a significant amount of attention.
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Özdemir, Mehmet Hakan. "Application of Change of Basis in the Simplex Method." European Journal of Social Sciences Education and Research 11, no. 1 (2017): 41. http://dx.doi.org/10.26417/ejser.v11i1.p41-49.
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The simplex method is a very useful method to solve linear programming problems. It gives us a systematic way of examining the vertices of the feasible region to determine the optimal value of the objective function. It is executed by performing elementary row operations on a matrix that we call the simplex tableau. It is an iterative method that by repeated use gives us the solution to any n variable linear programming model. In this paper, we apply the change of basis to construct following simplex tableaus without applying elementary row operations on the initial simplex tableau.
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MOHANA, N., and B. DHILSONA. "SOLVE THE TRANSPORTATION PROBLEM OF TRAPEZOIDAL FUZZY NUMBERS USING RUSSELL’S APPROXIMATION METHOD." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 08, no. 01 (2024): 1–11. http://dx.doi.org/10.55041/ijsrem28452.
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Fuzzy set theory has been applied in many fields such as management, engineering, theory of matrices and so on. In this paper, some elementary operations on proposed trapezoidal fuzzy numbers (TrFNs) are defined and also have been defined some operations on trapezoidal fuzzy matrices(TrFMs).Using Russell’s approximation method to solve the Fuzzy transportation problem of Trapezoidal Fuzzy numbers.
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Zhang, Xiaodan, and Xingping Sheng. "Two methods for computing the Drazin inverse through elementary row operations." Filomat 30, no. 14 (2016): 3759–70. http://dx.doi.org/10.2298/fil1614759z.
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In this paper, Let the matrix A ? Cnxn with Ind(A)=k, we first construct two bordered matrices based on [32], which gave a method for computing the null space of Ak by applying elementary row operations on the pair (A I). Then two new Algorithms to compute the Drazin inverse Ad are presented based on elementary row operations on two partitioned matrices. The computational complexities of the two Algorithms are detailed analyzed. When the index k = Ind(A) ? 5, the two Algorithms are all faster than the Algorithm by Anstreicher and Rothblum [32]. In the end, an example is presented to demonstrate the two new algorithms.
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P., Iswarya*1 &. Dr. A. Nagarajan2. "MATRIX SCRAMBLING TECHNIQUE BASED IMAGE ENCRYPTION." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 6, no. 5 (2019): 505–8. https://doi.org/10.5281/zenodo.3234976.
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Cryptography is the science of converting confidential information into unintelligible format. To provide security and authentication to the data, many algorithms and techniques were evolved, in which the cryptographic techniques remains best. For the encryption process, Images were considered as the best source to maintain security. The usage of image is good solution for providing better communication. Matrix operations are widely used in many cryptography algorithms to solve the complexity in means of speed and time. The proposed work of this research is a new image encryption method for matrix scrambling technique which is composite of multifaceted composition. The encryption for the images in this research work consists of the division of image into matrix and then, the elementary row and column operations are considered. The proposed method strength is analyzed by various parameters. The combination of basic matrix form and elementary row operations yields good results and better image encryption methods compared to existing works.
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Protacio, Judel Villas. "Computation of Matrix Determinants by Cross-Multiplication: A Rethinking of Dodgson’s Condensation and Reduction by Elementary Row Operations Methods." Symmetry 15, no. 7 (2023): 1456. http://dx.doi.org/10.3390/sym15071456.
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We formulate a more straightforward, symmetry-based technique for manually computing the determinant of any n×n matrix by revisiting Dodgson’s condensation method, as well as strategically applying elementary row (column) operations and the definition and properties of determinants. The result yields a more streamlined algorithm that is generalized through formulas and employs a smaller number of operations and succeeding matrices than the existing methods.
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Tatira, Benjamin. "Undergraduate students’ conceptualization of elementary row operations in solving systems of linear equations." Eurasia Journal of Mathematics, Science and Technology Education 19, no. 11 (2023): em2349. http://dx.doi.org/10.29333/ejmste/13679.
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The concept of systems of linear equations (SLEs) is fundamental and core in linear algebra, a subject, which has many applications in a number of disciplines. Gaussian elimination is a versatile method, which can be used to solve almost all types of SLEs by using row-reductions. This study focused on exploring undergraduate students’ conceptualizations of elementary row operations (EROs) as a means to solve SLEs. The purpose of this study was to explore undergraduate students’ conceptualizations of row reductions and their applications to the solutions of systems of equations. The perspectives of the action-process-object-schema theoretical framework were used in analyzing data and discussing the findings. To explore the students’ conceptualization of EROs, a descriptive research approach was followed. I considered a case study of 131 students registered for a mathematics for educators course, where linear algebra was one of the topics. The findings revealed that students attained the action conception of reducing a system with unique solutions but had challenges reducing and interpreting solutions to a system with non-unique solutions. The latter row-reduction implored process and object conceptions especially when variable elements in the augmented matrix were involved. As students find the learning of linear algebra difficult, this study contributes to the debate in literature on how to improve its teaching and make suggestions on the ways make more effective the learning of linear algebra.
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Kaczorek, Tadeusz. "Checking of the positivity of descriptor linear systems with singular pencils." Archives of Control Sciences 22, no. 1 (2012): 77–86. http://dx.doi.org/10.2478/v10170-011-0013-3.
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Checking of the positivity of descriptor linear systems with singular pencilsA method for checking of the positivity of descriptor continuous-time and discrete-time linear systems with singular pencil is proposed. The method is based on elementary row and column operations on the matrices of descriptor systems. Necessary and sufficient conditions for the positivity of the descriptor systems are established.
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Duan, Ban Xiang, Wen Ying Zeng, and Xiao Ping Zhu. "A Preconditioned Gauss-Seidel Iterative Method for Linear Complementarity Problem in Intelligent Materials System." Advanced Materials Research 340 (September 2011): 3–8. http://dx.doi.org/10.4028/www.scientific.net/amr.340.3.
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In this paper, the authors first set up new preconditioned Gauss-Seidel iterative method for solving the linear complementarity problem, whose preconditioned matrix is introduced. Then certain elementary operations row are performed on system matrix before applying the Gauss-Seidel iterative method. Moreover the sufficient conditions for guaranteeing the convergence of the new preconditioned Gauss-Seidel iterative method are presented. Lastly we report some computational results with the proposed method.
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SISWANDI, SISWANDI, SUGI GURITMAN, NUR ALIATININGTYAS, and TEDUH WULANDARI. "A COMPUTATION PERSPECTIVE FOR THE EIGENVALUES OF CIRCULANT MATRICES INVOLVING GEOMETRIC PROGRESSION." Jurnal Matematika UNAND 12, no. 1 (2023): 65. http://dx.doi.org/10.25077/jmua.12.1.65-77.2023.
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In this article, the eigenvalues and inverse of circulant matrices with entries in the first row having the form of a geometric sequence are formulated explicitly in a simple form in one theorem. The method for deriving the formulation of the determinant and inverse is simply using elementary row or column operations. For the eigenvalues, the known formulation of the previous results is simplified by considering the specialty of the sequence and using cyclic group properties of unit circles in the complex plane. Then, the algorithm of eigenvalues formulation is constructed, and it shows as a better computation method.
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Kaczorek, Tadeusz. "Analysis of the descriptor Roesser model with the use of the Drazin inverse." International Journal of Applied Mathematics and Computer Science 25, no. 3 (2015): 539–46. http://dx.doi.org/10.1515/amcs-2015-0040.
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AbstractA method of analysis for a class of descriptor 2D discrete-time linear systems described by the Roesser model with a regular pencil is proposed. The method is based on the transformation of the model to a special form with the use of elementary row and column operations and on the application of a Drazin inverse of matrices to handle the model. The method is illustrated with a numerical example
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Abbasi, Fazlollah, Saeid Abbasbandy, and Juan J. Nieto. "A new and efficient method for elementary fuzzy arithmetic operations on pseudo-geometric fuzzy numbers." Journal of Fuzzy Set Valued Analysis 2016, no. 2 (2016): 156–73. http://dx.doi.org/10.5899/2016/jfsva-00303.
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Kaczorek, Tadeusz. "Design of regular positive and stable descriptor systems via state-feedbacks for descriptor continuous-time linear systems with singular pencils." Archives of Control Sciences 24, no. 3 (2014): 289–97. http://dx.doi.org/10.2478/acsc-2014-0017.
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Abstract A new method is proposed of design of regular positive and asymptotically stable descriptor systems by the use of state-feedbacks for descriptor continuous-time linear systems with singular pencils. The method is based on the reduction of the descriptor system by elementary row and column operations to special form. A procedure for the design of the state-feedbacks gain matrix is presented and illustrated by a numerical example
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Chang, Ping-Teng, and Lung-Ting Hung. "Discussion on fuzzy decision making based on fuzzy number and compositional rule of inference." Yugoslav Journal of Operations Research 25, no. 2 (2015): 271–82. http://dx.doi.org/10.2298/yjor130402008c.
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This paper provides an improved decision making approach based on fuzzy numbers and the compositional rule of inference by Yao and Yao (2001). They claimed to have created a new method that combines statistical methods and fuzzy theory for medical diagnosis. Currently, numerous papers have cited that work. In this study, we show that if we follow their matrix multiplication operation approach, we will obtain the same result as the original method proposed by Klir and Yuan (1995). Owing to a wellknown property of (row) stochastic matrices, if the multiplication is closed, the fuzzy and defuzzy procedure of Yao and Yao (2001) is redundant. Therefore, we advise researchers to think twice before applying this approach to medical diagnosis.
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Kaczorek, T. "Positive fractional continuous-time linear systems with singular pencils." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 1 (2012): 9–12. http://dx.doi.org/10.2478/v10175-012-0002-0.
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Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.
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Homaeinezhad, Mohammad Reza, and Sadeq Yaqubi. "Two-sided linear matrix inequality solution of affine input matrix for feasible discrete finite-time sliding mode control of uncertain nonlinear mechanical machines." Journal of Vibration and Control 26, no. 23-24 (2020): 2243–60. http://dx.doi.org/10.1177/1077546320916637.
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In this article, a new control method is proposed based on finite-time discrete sliding mode control for uncertain multi-input multi-output systems which are affine to their inputs considering uncertain input multipliers in the case where signs of input gains remain constant over uncertainty spaces. In addition, a method for solving a set of convex control inequalities is introduced. The proposed control strategy is based on merging data obtained from investigation of common candidate Lyapunov functions assigned to various subsystems and their subsequent decoupling based on matrix elementary row operations. Initially, separate sliding functions corresponding to a single degree of freedom are assigned to each subsystem in the overall multi-input multi-output system, which results in obtaining a convex inequality corresponding to input bounds. Stacking the data obtained from various subsystems, the product of the uncertain input gain matrix in input vector is obtained as the middle term in a set of convex inequalities. Subsequently, the convex inequality is solved according to a set of matrix elementary row operations transforming the corresponding input matrix to row echelon form such that the bounds of each input are clearly expressed. Then, based on assigning input bounds proximity factors to each lower bound–upper bound duo, appropriate control inputs are generated. Chattering effects are eliminated as no switching term is included in construction of the control model. Effectiveness of the proposed method is demonstrated using numerical simulations. The implementation of control algorithm using microprocessors is also illustrated, indicating the feasibility of digital application.
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Sheng, Xingping. "Execute Elementary Row and Column Operations on the Partitioned Matrix to Compute M-P InverseA†." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/596049.
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We first study the complexity of the algorithm presented in Guo and Huang (2010). After that, a new explicit formula for computational of the Moore-Penrose inverseA†of a singular or rectangular matrixA. This new approach is based on a modified Gauss-Jordan elimination process. The complexity of the new method is analyzed and presented and is found to be less computationally demanding than the one presented in Guo and Huang (2010). In the end, an illustrative example is demonstrated to explain the corresponding improvements of the algorithm.
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Siahaan, Meiva Marthaulina Lestari, Fitriani Fitriani, and Prudensius Manek. "Hypothetical Learning Trajectory: To Determine The Solution of Linear Equation System in Elementary Row Operation." Mathline : Jurnal Matematika dan Pendidikan Matematika 8, no. 1 (2021): 246–55. http://dx.doi.org/10.31943/mathline.v8i1.379.
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The background of this research is the learning obstacles that arise on the topic of determining the solution of a system of linear equations (SLE) in applying elementary row operations (ERO). From these findings, it is necessary to formulate a hypothetical learning trajectory (HLT) that can guide the flow of thinking in designing didactic situations in the learning process. HLT expect to anticipate learning obstacles (LO) that arise. This research is a preliminary design of a series of didactical design research. The steps taken in compiling the HLT are 1) reviewing the lesson plan, the methods used to convey the material to determine SST solutions, and the textbooks used; 2) reviewing students' thinking processes conceptually and procedurally regarding theoretically determining SLE solutions; 3) reviewing design plans didactic. HLT is formulated into five types of student responses. It integrates into didactic situations by explaining the relevance of the elimination method in high school with three operations on ERO and then by explaining matrix material before SPL material. From this didactic situation, it can be formulated in teaching material that can accommodate emerging LO.
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Batlajery, Hardy, and Venn Ilwaru. "Penugasan Tutor Sebaya dengan Metode Pinalti." Contemporary Mathematics and Applications (ConMathA) 4, no. 2 (2022): 105–12. http://dx.doi.org/10.20473/conmatha.v4i2.39524.
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This research focuses on the assignment of peer tutors in the Mathematics Study Program, Mathematics Department, FMIPA Unpatti. The purpose of this study was to obtain the completion of peer tutor assignments with the penalty method. The penalty method is a method used to solve the problem of unbalanced assignments. The processed two parts, namely finding the initial solution and finding the optimal solution. The column penalty method or the row penalty method is used to get the initial solution. In this study, the row penalty method is used because the number of rows is less than the number of columns, and the optimal solution is sought. The data used are student names, courses, and final grades. The results obtained using the Penalty method are that David becomes a tutor in the Statistical Method course, Alfito becomes a tutor in the Operations Research course, Christin becomes a tutor in the Linear Program course, Gabriella becomes a tutor in the Analytical Geometry course and Navila becomes a tutor in the course Elementary Statistics.
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Guritman, Sugi, Jaharuddin, Teduh Wulandari, and Siswandi. "An Efficient Method for Computing the Inverse and Eigenvalues of Circulant Matrices with Lucas Numbers." Journal of Advances in Mathematics and Computer Science 39, no. 4 (2024): 10–23. http://dx.doi.org/10.9734/jamcs/2024/v39i41879.
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In this article, the inverse including the determinant, and the eigenvalues of circulant matrices with entry Lucas numbers are formulated explicitly in a simple way so that their computations can be constructed efficiently. The formulation method of the determinant and inverse is simply applying the theory of elementary row or column operations and can be unified in one theorem. Meanwhile, for the eigenvalues formulation, the recently known formulation in the case of general circulant matrices is simplified by observing the specialty of the Lucas sequence and applying cyclic group properties of unit circles in the complex plane. Then, an algorithm of those formulations is constructed efficiently. From some implementation facts also showed that the algorithms performed very fast and was able to calculate large size of circulant matrices.
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Jurnal, Redaksi Tim. "RANCANG BANGUN APLIKASI PENGHITUNGAN INVERS MATRIKS ORDO 3X3 DAN 4X4 DENGAN METODE INCREMENTAL PROCESS BERBASIS MULTIMEDIA." PETIR 10, no. 2 (2018): 82–88. http://dx.doi.org/10.33322/petir.v10i2.27.
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Matrix inverse method consists of a method of partitioning a matrix, adjoint matrix, and elementary row operations. In the matrix inverse learning application that was created earlier, it was contains only one method of inverse matrix in each application. Existing application still separated for each method cause made by different people. When lecture used the application in courses of Linear Algebra, actualy the application can only run on a particular computer device. This was motivated writers to created applications that can run on all devices komputer and combines of all methods in a single application. Application form is accompanied by material simulations, exercises and games to enable students to understand the material of the inverse matrix given in class. Software development methods or SDCL (System Development Life Cycle) is the method Incremental Process Model, interface design and coding using Microsoft Visual Studio 2010 Ultimate.
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Arifin, Samsul, Indra Bayu Muktyas, Puguh Wahyu Prasetyo, and Abdul Azis Abdillah. "Unimodular matrix and bernoulli map on text encryption algorithm using python." Al-Jabar : Jurnal Pendidikan Matematika 12, no. 2 (2021): 447–55. http://dx.doi.org/10.24042/ajpm.v12i2.10469.
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One of the encryption algorithms is the Hill Cipher. The square key matrix in the Hill Cipher method must have an inverse modulo. The unimodular matrix is one of the few matrices that must have an inverse. A unimodular matrix can be utilized as a key in the encryption process. This research aims to demonstrate that there is another approach to protect text message data. Symmetric cryptography is the sort of encryption utilized. A Bernoulli Map is used to create a unimodular matrix. To begin, the researchers use an identity matrix to generate a unimodular matrix. The Bernoulli Map series of real values in (0,1) is translated to integers between 0 and 255. The numbers are then inserted into the unimodular matrix's top triangular entries. To acquire the full matrix as the key, the researchers utilize Elementary Row Operations. The data is then encrypted using modulo matrix multiplication.
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Siahaan, Meiva Marthaulina Lestari, Fitriani, and Angelika Rosa Da Lima Leli. "A Study of Learning Obstacles: Determining Solutions of a System of Linear Equation Using Gauss-Jordan Method." Mosharafa: Jurnal Pendidikan Matematika 12, no. 1 (2023): 25–34. http://dx.doi.org/10.31980/mosharafa.v12i1.748.
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Salah satu metode pencarian solusi SPL yang dipelajari di pendidikan tinggi adalah metode Gauss-Jordan. Berdasarkan data penelitian, mahasiswa melakukan kesalahan dalam melakukan operasi baris elementer (OBE), membentuk ke dalam matriks yang diperbesar, dan bahkan pemahaman mendasar mengenai reduksi baris dan ini berpengaruh dalam menentukan solusi suatu SPL. Untuk itu perlu dianalisis hambatan belajar yang terjadi dalam menentukan solusi SPL menggunakan metode Gauss-Jordan. Peneitian ini merupakan penelitian kualitatif dan merupakan bagian dari Didactical Design Research (DDR). Penelitian ini dilaksanakan di salah satu universitas di Nusa Tenggara Timur (NTT) dengan subjek penelitian merupakan 20 mahasiswa calon guru matematika. Teknik penelitian ini adalah tes diagnostik dan wawancara. Hasil penelitian menunjukkan beberapa hambatan yang dialami mahasiswa adalah keterbatasan pemahaman pada OBE, pengklasifikasian MEBT, dan merepresentasikan MEBT ke dalam solusi SPL. Rekomendasi dari penelitian ini adalah pengajar hendaknya membuat suatu bahan ajar yang dapat meminimalisir hambatan belajar yang dialami mahasiswa. One of many methods of finding solution of a system of linear equations (SLE) studied in higher education is the Gauss-Jordan method. Based on the research, students made mistakes in performing elementary row operations (ERO), forming into augmented matrices, and even basic understanding of row subtraction and this has an effect on determining the solution of an SLE. For this reason, it is necessary to analyze the learning obstacles that occur in determining the solution of LES using the Gauss-Jordan method. This qualitative research is part of the Didactical Design Research (DDR). This research was conducted at a university in East Nusa Tenggara (NTT) involving 20 students as preservice mathematics teacher. The technique of this research is diagnostic test and interview. The results show that some of the obstacles faced by students are insufficient understanding of ERO, classifying reduced row-echelon form (RREF), and representing MEBT into SPL solutions. This study recommends that teachers create teaching materials that minimizes learning obstacles experienced by students.
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Siahaan, Meiva Marthaulina Lestari, Fitriani Fitriani, and Angelika Rosa Da Lima Leli. "A Study of Learning Obstacles: Determining Solutions of a System of Linear Equation Using Gauss-Jordan Method." Mosharafa: Jurnal Pendidikan Matematika 12, no. 1 (2023): 25–34. http://dx.doi.org/10.31980/mosharafa.v12i1.1921.
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AbstrakSalah satu metode pencarian solusi SPL yang dipelajari di pendidikan tinggi adalah metode Gauss-Jordan. Berdasarkan data penelitian, mahasiswa melakukan kesalahan dalam melakukan operasi baris elementer (OBE), membentuk ke dalam matriks yang diperbesar, dan bahkan pemahaman mendasar mengenai reduksi baris dan ini berpengaruh dalam menentukan solusi suatu SPL. Untuk itu perlu dianalisis hambatan belajar yang terjadi dalam menentukan solusi SPL menggunakan metode Gauss-Jordan. Peneitian ini merupakan penelitian kualitatif dan merupakan bagian dari Didactical Design Research (DDR). Penelitian ini dilaksanakan di salah satu universitas di Nusa Tenggara Timur (NTT) dengan subjek penelitian merupakan 20 mahasiswa calon guru matematika. Teknik penelitian ini adalah tes diagnostik dan wawancara. Hasil penelitian menunjukkan beberapa hambatan yang dialami mahasiswa adalah keterbatasan pemahaman pada OBE, pengklasifikasian MEBT, dan merepresentasikan MEBT ke dalam solusi SPL. Rekomendasi dari penelitian ini adalah pengajar hendaknya membuat suatu bahan ajar yang dapat meminimalisir hambatan belajar yang dialami mahasiswa. AbstractOne of many methods of finding solution of a system of linear equations (SLE) studied in higher education is the Gauss-Jordan method. Based on the research, students made mistakes in performing elementary row operations (ERO), forming into augmented matrices, and even basic understanding of row subtraction and this has an effect on determining the solution of an SLE. For this reason, it is necessary to analyze the learning obstacles that occur in determining the solution of LES using the Gauss-Jordan method. This qualitative research is part of the Didactical Design Research (DDR). This research was conducted at a university in East Nusa Tenggara (NTT) involving 20 students as preservice mathematics teacher. The technique of this research is diagnostic test and interview. The results show that some of the obstacles faced by students are insufficient understanding of ERO, classifying reduced row-echelon form (RREF), and representing MEBT into SPL solutions. This study recommends that teachers create teaching materials that minimizes learning obstacles experienced by students.
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Attaullah, Shahzaib Ashraf, Noor Rehman, Asghar Khan, Muhammad Naeem, and Choonkil Park. "Improved VIKOR methodology based on $ q $-rung orthopair hesitant fuzzy rough aggregation information: application in multi expert decision making." AIMS Mathematics 7, no. 5 (2022): 9524–48. http://dx.doi.org/10.3934/math.2022530.
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<abstract><p>The main objective of this article is to introduce the idea of a q-rung orthopair hesitant fuzzy rough set (q-ROHFRS) as a robust fusion of the q-rung orthopair fuzzy set, hesitant fuzzy set, and rough set. A q-ROHFRS is a novel approach to uncertainty modelling in multi-criteria decision making (MCDM). Various key properties of q-ROHFRS and some elementary operations on q-ROHFRSs are proposed. Based on the q-ROHFRS operational laws, novel q-rung orthopair hesitant fuzzy rough weighted averaging operators have been developed. Some interesting properties of the proposed operators are also demonstrated. Furthermore, by using the proposed aggregation operator, we develop a modified VIKOR method in the context of q-ROHFRS. The outcome of this research is to rank and select the best alternative with the help of the modified VIKOR method based on aggregation operators for q-ROHFRS. A decision-making algorithm based on aggregation operators and extended VIKOR methodology has been developed to deal with the uncertainty and incompleteness of real-world decision-making. Finally, a numerical illustration of agriculture farming is considered to demonstrate the applicability of the proposed methodology. Also, a comparative study is presented to demonstrate the validity and effectiveness of the proposed approach. The results show that the proposed decision-making methodology is feasible, applicable, and effective to address uncertainty in decision making problems.</p></abstract>
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Mahmood, Tahir, Ahmad Idrees, Khizar Hayat, Muhammad Ashiq, and Ubaid ur Rehman. "Selection of AI Architecture for Autonomous Vehicles Using Complex Intuitionistic Fuzzy Rough Decision Making." World Electric Vehicle Journal 15, no. 9 (2024): 402. http://dx.doi.org/10.3390/wevj15090402.
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The advancement of artificial intelligence (AI) has become a crucial element in autonomous cars. A well-designed AI architecture will be necessary to attain the full potential of autonomous vehicles and will significantly accelerate the development and deployment of autonomous cars in the transportation sector. Promising autonomous cars for innovating modern transportation systems are anticipated to address many long-standing transporting challenges related to congestion, safety, parking, and energy conservation. Choosing the optimal AI architecture for autonomous vehicles is a multi-attribute decision-making (MADM) dilemma, as it requires making a complicated decision while considering a number of attributes, and these attributes can have two-dimensional uncertainty as well as indiscernibility. Thus, in this framework, we developed a novel mathematical framework “complex intuitionistic fuzzy rough set” for tackling both two-dimensional uncertainties and indiscernibility. We also developed the elementary operations of the deduced complex intuitionistic fuzzy rough set. Moreover, we developed complex intuitionistic fuzzy rough (weighted averaging, ordered weighted averaging, weighted geometric, and ordered weighted geometric) aggregation operators. Afterward, we developed a method of MADM by employing the devised operators and investigated the case study “Selection of optimal AI architecture for autonomous vehicles” to reveal the practicability of the devised method of MADM. Finally, to reveal the dominance and supremacy of our proposed work, a benchmark dilemma was used for comparison with various prevailing techniques.
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Attaullah, Shahzaib Ashraf, Noor Rehman, Asghar Khan, and Choonkil Park. "A decision making algorithm for wind power plant based on q-rung orthopair hesitant fuzzy rough aggregation information and TOPSIS." AIMS Mathematics 7, no. 4 (2022): 5241–74. http://dx.doi.org/10.3934/math.2022292.
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<abstract><p>Wind energy is one of the most significant renewable energy sources due to its widespread availability, low environmental impact, and great cost-effectiveness. The effective design of ideal wind energy extraction areas to generate electricity is one of the most critical issues in the exploitation of wind energy. The appropriate site selection for wind power plants is based on the concepts and criteria of sustainable environmental advancement, resulting in a low-cost and renewable energy source, as well as cost-effectiveness and job creation. The aim of this article is to introduce the idea of q-rung orthopair hesitant fuzzy rough set (q-ROHFRS) as a robust fusion of q-rung orthopair fuzzy set, hesitant fuzzy set, and rough set. A q-ROHFRS is a new approach towards modeling uncertainties in the multi-criteria decision making (MCDM). Various key properties of q-ROHFRS and some elementary operations on q-ROHFRSs are established. A list of novel q-rung orthopair hesitant fuzzy rough weighted geometric aggregation operators are developed on the basis of defined operational laws for q-ROHFRSs. Further, a decision making algorithm is developed to handle the uncertain and incomplete information in real word decision making problems. Then, a multi-attribute decision making method is established using q-rung orthopair hesitant fuzzy rough aggregation operators. Afterwards, a practical case study on evaluating the location of wind power plants is presented to validate the potential of the proposed technique. Further, comparative analysis based on the novel extended TOPSIS method is presented to demonstrate the capability of the proposed technique.</p></abstract>
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Perfilieva, Irina, Tam Pham, and Petr Ferbas. "Quadrature Rules for the Fm-Transform Polynomial Components." Axioms 11, no. 10 (2022): 501. http://dx.doi.org/10.3390/axioms11100501.
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The purpose of this paper is to reduce the complexity of computing the components of the integral Fm-transform, m≥0, whose analytic expressions include definite integrals. We propose to use nontrivial quadrature rules with nonuniformly distributed integration points instead of the widely used Newton–Cotes formulas. As the weight function that determines orthogonality, we choose the generating function of the fuzzy partition associated with the Fm-transform. Taking into account this fact and the fact of exact integration of orthogonal polynomials, we obtain exact analytic expressions for the denominators of the components of the Fm-transformation and their approximate analytic expressions, which include only elementary arithmetic operations. This allows us to effectively estimate the components of the Fm-transformation for 0≤m≤3. As a side result, we obtain a new method of numerical integration, which can be recommended not only for continuous functions, but also for strongly oscillating functions. The advantage of the proposed calculation method is shown by examples.
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Levchenko, O. "A METHOD FOR FORMALIZING THE DECISION-MAKING PROCESS FOR PREVENTING DANGEROUS SITUATIONS IN THE E-NAVIGATION SYSTEM." Shipping & Navigation 34, no. 1 (2023): 115–26. http://dx.doi.org/10.31653/2306-5761.34.2023.115-126.
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The study aims to improve the safety of ship traffic by improving the methods of formalizing the decision-making process for preventing dangerous situations in a single e-navigation concept. The goal is achieved by a clear statement of the problem and the choice of appropriate approaches to its solution. The main stages of the decision-making cycle performed by the navigator in collision prevention are analysed. Particular attention is paid to the operations performed at the decisionmaking stage on the further movement of the vessel. The ship's movement plan is described by models of elementary behaviour, each of which consists of elementary actions represented by a set of fuzzy logic rules for performing a certain subtask. The structure of a system that implements the behavioural approach to decision-making by a navigator is proposed. Emphasis is placed on the need to coordinate vessels when deciding to plan a route based on models of elementary behaviours, and a method for coordinating the planning of the vessel's trajectory is developed. The sequence of stages of the method for coordinating the planning of the ship's trajectory is performed cyclically until the target point of the route is reached. At each stage of the vessel's movement, the navigation obstacles and other vessels entering the area of interest of the navigator are monitored and potential hazards from them are identified. A method for tracing the vessel's movement and existing vessels in the navigator’s interest area has been developed, which allows for predicting the location at subsequent moments and identifying the coordinates of the conflict site where a situation of dangerous proximity occurs. To formalize the areas dangerous for vessel traffic, a method for generating a map of navigational hazards and conflict situations in the navigator’s interest area has been developed, based on a modified method of potential fields. To formally describe the space, only the concept of a potential function is used to represent the space as a matrix of values. The most significant scientific result is the proposed approach to solving the problem of supporting the decision-making of a navigator based on a combination of methods using fuzzy logic and allowed domains, which allows obtaining options for actions that ensure the safety of ship movement in a dangerous situation. Keywords: ship, navigator, collision, navigation situation, navigation systems, e-navigation, tracing method, navigation hazard, navigation hazard map
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Wang, Sheng, Yanhong Sun, Chen Yang, and Yongchang Yu. "Advanced design and tests of a new electrical control seeding system with genetic algorithm fuzzy control strategy." Journal of Computational Methods in Sciences and Engineering 21, no. 3 (2021): 703–12. http://dx.doi.org/10.3233/jcm-215126.
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In the existing soybean breeding and planting machinery, the power source of the metering device adopts the ground wheel transmission method mostly. However, this power transmission method is likely to cause slippage during the planting operation, which will cause problems such as the increase of the missed seeding index and the increase of the coefficient of plant spacing. It is not conducive for scientific researchers to carry out breeding operations. Aiming at this problem, an electronically controlled soybean seeding system is designed, and the power of the seed metering device is derived from the motor. In order to improve the control accuracy of the electronically controlled seeding system, the precise control of the soybean seeding rate is finally realized. The electric drive soybean seeding system adopts closed-loop control, the motor model of the electric drive seeding system is established, and the transfer function of the motor is obtained. PID control based on a genetic algorithm is adopted, and the corresponding parameters are substituted into the control system simulation model established in MATLAB/SIMULINK. Field verification tests have been carried out on the conventional fuzzy PID control system and the electric drive soybean planter of the fuzzy PID control system based on a genetic algorithm. The result showed that the average of the repeat-seeding parameter is 1.30% better than the average of conventional seeding system (1.40%), the average of the miss-seeding parameter is 1.08% better than the average of conventional seeding system (2.09%) and the average of row-spacing variation parameter is 2.79% better than the average of conventional seeding system (2.34%). In conclusion, the new seeding system is robust obviously. Field trial results show that seeding with Genetic Algorithm Fuzzy control is better.
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Zhang, Shuo, Chengyang Guo, Zening Gao, Adilet Sugirbay, Jun Chen, and Yu Chen. "Research on 2D Laser Automatic Navigation Control for Standardized Orchard." Applied Sciences 10, no. 8 (2020): 2763. http://dx.doi.org/10.3390/app10082763.
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With the increase of labor cost and the development of agricultural mechanization, standardized orchards suitable for autonomous operations of agricultural machinery will be a future development trend of the fruit-planting industry. For field-planting processes of standardized orchards, autonomous navigation of orchard vehicles in complex environments is the foundation of mechanized and intelligent field operations. In order to realize autonomous driving and path-tracking of vehicles in complex standardized orchards that involve much noise and interference between rows of fruit trees, an automatic navigation system was designed for orchard vehicles, based on 2D lasers. First, considering the agronomic requirements for orchard planting such as plant spacing, row spacing and trunk diameter, different filtering thresholds were established to eliminate discrete points of 2D laser point cloud data effectively. Euclidean clustering algorithm and the important geometric theorems of three points collinearity was used to extract the central feature points of the trunk, as the same time, navigation path was fitted based on the least square method. Secondly, an automatic navigation control algorithm was designed, and the fuzzy control was used to realize the dynamic adjustment of the apparent distance of the pure pursuit model. Finally, the reliability of the proposed approach was verified by simulation using MATLAB/Simulink, and field tests were carried out based on electric agricultural vehicle. Experimental results show that the method proposed in this study can effectively improve the precision of automatic navigation in complex orchard environment and realize the autonomous operation of orchard vehicles.
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Keikha, Abazar, and Tabasam Rashid. "Non-linear averaging-based operators of pseudo-hesitant fuzzy elements and an application." Croatian operational research review 14, no. 2 (2023): 179–92. http://dx.doi.org/10.17535/crorr.2023.0015.
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Data modeling/aggregating, in many uncertain real-world' problems such as decision-making processes, has gotten more attention in recent years. Due to a variety of uncertainty sources, various types of fuzzy sets, and various types of averaging-based aggregation functions have been proposed. The power average operator (PAO), as a nonlinear operator, is more appropriate than other averaging-based functions for situations where different values are given on a single subject. In this paper, PAO will be extended to be used in the aggregation process of given pseudo-hesitant fuzzy elements (pseudo-HFEs), and some needed properties have been discussed, too. Then, four kinds of PAO with pseudo-HFEs, i.e., power average operator of pseudo-HFEs, power weighted average operator of pseudo-HFEs, power ordered weighted average operator of pseudo-HFEs and power hybrid average operator of pseudo-HFEs, will be defined. To solve a multi-attribute group decision-making (MAGDM) problem, the evaluation step done by both decision-makers and self-assessment will be quantified by pseudo-HFEs. Then the PAO will be applied to aggregate the row elements of the resulting decision matrix. The ranking orders of obtained pseudo-HFEs, show the options' orders. Finally, the proposed method will be used to solve a multi-attribute group decision-making problem, illustrated numerically, analyzed, and validated.
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Setyawati, Dian, Imam Santoso, and Mas’ud Effendi. "Value Chain Analysis on the Logistics Management as the Basis for Strategy Formulation to Increase Customer Satisfaction (Case Study in PT.Coca-Cola Amatil Indonesia - Plant East Java)." Agroindustrial Journal 1, no. 1 (2017): 28. http://dx.doi.org/10.22146/aij.v1i1.24991.
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PT. Coca-Cola Amatil Indonesia (PT. CCAI) - Plant East Java as a carbonated soft drinks manufacturer isexperiencing a mismatch between planning and realization of product shipments shown by fullfilment anddelivery mismatch among the company target at difotai (delivery infull ontime accurately invoice). This thingwas d ue to an incompatibility among logistics management activities, so it is necessary to do value chainanalysis to find out which activity is the cause of nonconformities in order to do strategy formulationimprovement to enhance customer satisfaction. The purpose of this study was to determine the advantagesand disadvantages of logistics management in PT.CCAI - Plant East Java and make it as one of the basis forstrategy formulation to improve customer satisfaction with value chain analysis approach. This researchused descriptive analytical method. The data was obtained by distributing questionnaires to the Warehouseand Transportation in PT. CCAI - Plant East Java and analysed using fuzzy AHP method. The resultsshowed that the overall weight of the main activities in a row from the top was the activity of supplymanagement, information flow and order processing, demand planning and operations, and transportation.Some things on the transportation activities that needed to be improved as the basis for the strategyformulation, among others, operational procedure, the carrying capacity of the facility, as well as thesocialization and communication of problems and changes handling.
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Chen, Zhijian, Jianjun Yin, Jiaxin Yang, Maile Zhou, Xinzhong Wang, and Sheikh Muhammad Farhan. "Development and Experiment of an Innovative Row-Controlled Device for Residual Film Collector to Drive Autonomously along the Ridge." Sensors 23, no. 20 (2023): 8484. http://dx.doi.org/10.3390/s23208484.
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The field harvesting process of harvesting machinery is often affected by high workload and environmental factors that can impede/delay manual rowing, thereby leading to lower efficiency and quality in the residual film collector. To address this challenge, an automatic rowing control system using the 4mz-220d self-propelled residual film collector as the experimental carrier was proposed in this study. Cotton stalks in the ridges were chosen as the research object, and a comprehensive application of key technologies, machinery, and electronic control was used, thereby incorporating a pure tracking model as the path-tracking control method. To achieve the automatic rowing function during the field traveling process, the fuzzy control principle was implemented to adjust the forward distance within the pure tracking model dynamically, and the expected steering angle of the steering wheel was determined based on the kinematic model of the recovery machine. The MATLAB/Simulink software was utilized to simulate and analyze the proposed model, thus achieving significant improvements in the automation level of the residual film collector. The field harvesting tests showed that the average deviation of the manual rowing was 0.144 m, while the average deviation of the automatic rowing was 0.066 m. Moreover, the average lateral deviation of the automatic rowing was reduced by 0.078 m with a probability of deviation within 0.1 m of 95.71%. The research study demonstrated that the designed automatic rowing system exhibited high stability and robustness, thereby meeting the requirements of the autonomous rowing operations of residual film collectors. The results of this study can serve as a reference for future research on autonomous navigation technology in agriculture.
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Weni, Gustiana, Mashadi, and Gemawati Sri. "Modification Elementary Row Operations to Determine the Inverse of Trapezoidal Fuzzy Numbers Matrix." September 30, 2023. https://doi.org/10.5281/zenodo.8394435.
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There are several algebraic solutions written by various authors for trapezoidal fuzzy numbers ~ u u v where u and v are the midpoint, is the left width, and is the right width. Furthermore, trapezoidal fuzzy numbers are used in various arithmetic of trapezoidal fuzzy numbers. There are not many differences made by writers, especially for addition, subtraction, and scalar multiplication operations. However, there are many options made for multiplication and division operations. With many options for multiplication and division operations, it still does not produce , ~ ~ 1 ~ u u therefore the author makes multiplication and division operations that can produce . ~ ~ 1 ~ u u Before making multiplication and division operations, the middle value of the trapezoidal fuzzy number u ~ is first determined, which is symbolized by m u q ~ . The middle value is used for constructing arithmetic multiplication, inverse, and divisibility of trapezoidal fuzzy numbers that can solve . ~ ~ 1 ~ u u Furthermore, the arithmetic of trapezoidal fuzzy numbers that have been constructed is used for are used to determine the inverse of the trapezoidal fuzzy number matrix using the modified fuzzy elementary row operations method. Until now, there is no single article that provides an alternative to the elementary row operations process of a matrix. So in this article in addition to modifying the multiplication, inverse, and division operations for trapezoidal fuzzy numbers. There will also be a modification of elementary row operations in calculating the inverse of a trapezoidal fuzzy number matrix.
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Solaiman, Edwin Julius. "Modifikasi Metode Gauss atau Operasi Baris Elementer pada Solusi Sistim Persamaan Linier 3 Variabel dan 3 Persamaan." TeIKa 6, no. 1 (2016). http://dx.doi.org/10.36342/teika.v6i1.271.
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AbstrakGauss menguraikan tiga teori untuk menyelesaikan persamaan linier. Dimana teori tersebut diturunkan dari metode eleminasi penjumlahan, pengurangan dan subsitusi. Kendala yang ditemukan dikelas adalah mahasiswa lambat memahaminya, sehingga diperlukan modifikasi metode Gauss yang dapat menerangkan dan menjembatani peralihan dari metode eliminasi ke metode Gauss.Peralihan yang dapat dilakukan adalah dengan menggabungkan dua teori Gauss/Operasi Baris Elementer yaitu dengan menggabungkan mengalikan sebuah baris dengan bilangan k ≠0 dari matrik A yang disebut Operasi Tipe II dan dengan menambahkan sebuah baris i dengan mengalikan k ≠0 pada baris yang lain dimana i ≠j dari matrik A disebut Operasi tipe III menjadi satu yaitu dengan menambahkan k1 ≠0 kali baris ke i dengan k2 ≠0 kali baris ke j dimana i ≠j dari matrik A yang disebut sebagai Modifikasi Operasi Tipe III.Modification of Gauss Method or the Elementary Row Operations System Solutions of Linear Equations of 3 Variables and 3 EquationsAbstractGauss outlines three theories to solve linear equations. The theory derived from the Elimination Method such that addition, reduction and aubstitution. Problems were found in class is a slow student to understand it, so that the necessary modifications Gauss method that can explain and bridge the transition from Elimination Method to Gaussian Method.Transition to do is to combine the two rule of Gaussian Method / Elemantary Row Operations by the incorporation multiplying a row with number k ≠0 of matix A so-called Operation Type II and by adding a row i by multiplying k ≠0 on the other row where i ≠j of matrix A is called Operation Type III into one by adding k1 ≠0 times row i with k2 ≠0 times row j where i ≠j of matrix A is referred to as Modification Operation Type III.
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Nurjannah, Nurjannah, Mutmainnah Muchtar, Sarimuddin Sarimuddin, Kharis Sya'ban, Rahmat Karim, and Muhammad Na'im Al Jum'ah. "PERANCANGAN SMART TRASH BIN MENGGUNAKAN LOGIKA FUZZY BERBASIS ARDUINO DI SDN 5 MAWASANGKA, BUTON TENGAH." Jurnal Informatika dan Teknik Elektro Terapan 12, no. 3 (2024). http://dx.doi.org/10.23960/jitet.v12i3.4358.
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Smart Trash Bin is a technological innovation that integrates sensors and automation systems to enhance waste management efficiency. This study aims to design and implement a Smart Trash Bin using fuzzy logic based on Arduino at SDN 5 Mawasangka, Buton Tengah. In this research, the system utilizes ultrasonic sensors to detect the trash level inside the bin, servo motors to control the automatic lid of the trash bin, and DFPlayer Mini along with a speaker to provide audio notifications to users. Fuzzy logic method is employed to regulate the system's decisions in managing the trash bin operations based on environmental conditions. The study involves the stages of design, fabrication, and system testing in the elementary school environment. The test results indicate that the designed Smart Trash Bin can effectively manage waste with adequate accuracy. It is expected that the implementation of this Smart Trash Bin can help raise awareness of environmental cleanliness within the school and surrounding community
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Oladigbolu, Jamiu Omotayo, and Ali Muhammad Ali Rushdi. "Investigation of the Corona Discharge Problem Based on Different Computational Approaches of Dimensional Analysis." Journal of Engineering Research and Reports, August 10, 2020, 17–36. http://dx.doi.org/10.9734/jerr/2020/v15i317146.
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Although corona discharge is notorious for its detrimental effects, it is also used in many beneficial practical applications. Despite the existence of a variety of sophisticated theoretical and experimental methods for investigating corona discharge, we explore yet a much simpler method that relies on the use of Dimensional Analysis (DA). The DA method does not demand profound knowledge of the underlying phenomenon or its governing equations, as it only needs the correct identification of the variables influencing the phenomenon, and the specification of their physical dimensions. The classical and well-known Gauss-Jordan elimination method is compared with other matrix-oriented computational approaches in analyzing the pertinent dimensional system. This method relies upon solution-preserving elementary row operations, i.e., operations that one can use on a matrix without spoiling the solution set for an associated matrix equation. A distinct advantage of this method is that it does not pre-suppose a particular value of the matrix rank but tackles the task of determining this rank while proceeding towards its ultimate result. Moreover, this method can also be used to find the inverse of a regular (invertible) matrix or to determine the solution (if any) of a system of linear equations. As a bonus, novel results of numerical investigations of bases, regimes, and dimensionless products are extensively presented in this paper. A remarkable observation made herein is that the set of variables pertinent for a particular phenomenon cannot be arbitrarily partitioned into basis (input) variables and regime (output or isolated) variables. The paper running example deals with expressing a specific variable, viz. ozone generation rate per unit length of wire (r0) through dimensionless products in terms of a set of determining or influencing variables.
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Alamdari, A. M., Y. Jabarzadeh, B. Adams, D. Samson, and S. Khanmohammadi. "An analytic network process model to prioritize supply chain risks in green residential megaprojects." Operations Management Research, June 22, 2022. http://dx.doi.org/10.1007/s12063-022-00288-2.
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AbstractMegaprojects and specifically ‘green’ construction of residential megaprojects can contain significant risks of failure. To design proper risk mitigation strategies, after identifying key risk factors, the next step is to conduct assessments that would facilitate the process of risk element prioritization. Risk assessment comprises the establishment of factor interrelation and discerning the indicators of importance. This research proposes a novel version of an integrated prioritization method and analyzes twelve all-inclusive key supply chain oriented risk factors identified in a previous study. Through a comprehensive literature review three criteria, impact, probability, and manageability are selected. Also, a fourth criterion namely influence rate is included in the model, based on the driving powers that can also be derived from the Interpretive Structural Modeling’s (ISM) assessment. Fundamentally, the calculations hinge on the Analytic Network Process (ANP) method which provides an assessment of the alternatives’ weights based on pairwise comparisons concerning the criteria specified. To enhance the accuracy of the perceptive judgments of the expert panelists, a bell-shaped fuzzy function is used to convert the verbal statements to crisp values. In addition, Row Sensitivity Analysis is administered to check the stability of the results and provide predictive scenarios. To validate the model, a case study, located in Iran, was conducted, where an expert panel consisting of four individuals made the pair-wise comparisons through an ANP questionnaire. Results indicate priority and sensitivity of the alternatives concerning criteria, for the case under study.
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Stikanov, Valerii, Bogdan Kyriusha, Viktoriia Hiorhizova-Hai, Vitalii Artuhov, and Oleksii Brytov. "ANALYSIS OF DIGITAL NETWORKS OF ARBITRARY STRUCTURE." European Academic Science and Research, No. XXV (2022) (February 28, 2022). https://doi.org/10.5281/zenodo.6354706.
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Digital signal processing systems play an important role in modern technology. They can be implemented in a number of structures. The structure of a digital system determines the number and order of execution of some elementary functions, such as arithmetic operations, storage, and others. This order is often critical to implement a signal processing algorithm with the required efficiency. Signal processing algorithms can often be implemented in a number of structures. The selection of an appropriate digital system structure is carried out as part of the design process. Typically, a comparison of structures from an appropriate set is based on a simulation of the system. To this end, it is necessary to develop a model of the system. For more efficient development of a number of models, it is desirable to use some unified method of system description and modeling. The described model is based on the representation of the system as a signal graph. Nodes of the graph represent internal signals while ribs represent signal transfers. There can be distinguished two types of ribs: with one cycle delays and without delays. This graph is described by the matrix equation linking current node signals to the node signals at the previous time. The signals transformations are described by a matrix of ribs without delays and a matrix of ribs with one cycle delays. The first one contains transfer coefficients of the ribs the second contains symbols z-1 representing one cycle delay. Input signal connection to the system is described by a column vector containing only one non-zero element corresponding to the node to which the input is connected. An additional row vector is used to identify the node from which output signal is read. The matrix equation can be solved in time domain to obtain time domain response to a specified input signal. To allow this the matrix of ribs without delays must be transformed to calculable form. That is it must be low triangular. In the Z domain solving the equation with respect to node signals we obtain transfer function and frequency response of the system.