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Relevant bibliographies by topics / Fuzzy Elementary Row Operations Method

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Academic literature on the topic 'Fuzzy Elementary Row Operations Method'

Author: Grafiati

Published: 5 June 2025

Last updated: 16 July 2025

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Journal articles on the topic "Fuzzy Elementary Row Operations Method"

1

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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2

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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Conference papers on the topic "Fuzzy Elementary Row Operations Method"

1

Mashadi, Mashadi, Weni Gustiana, and Sri Gemawati. "Determining the General Inverse for Trapezoidal Fuzzy Numbers Matrix with Modification Elementary Row Operations." In Proceedings of the 3rd Sriwijaya International Conference on Basic and Applied Sciences, SICBAS 2023, November 3, 2023, Palembang, Indonesia. EAI, 2024. http://dx.doi.org/10.4108/eai.3-11-2023.2347906.

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