Penyelesaian Sistem Persamaan Linier Fully Fuzzy Menggunakan Metode Dekomposisi Nilai Singular (SVD)

Abstract

Linear equation system can be arranged into the AX = B matrix equation. Constants in linear can also contain fuzzy numbers and all their parameters in fuzzy numbers known as fully fuzzy linear equation systems. singular value decomposition (SVD) is a method that decomposes an A matrix into three components of the USVH. The SVD method can be used to find a solution to the fully fuzzy fully linear equation system that is also an inconsistent fully fuzzy linear equation system. The solution obtained from a fully fuzzy linear equation system that is consistent using SVD is a single solution and many solutions. Whereas, the solution obtained from a fully fuzzy linear equation system that is inconsistent using SVD is the best approach solution.

Penyelesaian Sistem Persamaan Linier Fully Fuzzy Menggunakan Metode Dekomposisi Nilai Singular (SVD)

“…)) , 〉 = 〈 , 〉 − 〈 , 〉 = 0 Hal ini menunjukkan bahwa ( − ) adalah tegak lurus dengan setiap vektor di ( ) dan Persamaan (10) merupakan solusi pendekatan terbaik [8].…”

An Algebraic Solution of Dual Fuzzy Complex Linear Systems

“…Zadeh was the first to introduce and explore the concept of fuzzy numbers, along with the arithmetic operations associated with them [7]. The general form of a fuzzy linear equation system can be written as 𝐴𝑋 ̃= 𝑌 ̃ where 𝑋 ̃ and 𝑌 ̃ are parameters within a certain interval [8]. Various solution method of fuzzy linear systems can be observed in [9], [10], [11], [12] [13], [14], [15], [16], [17], [18].…”

Computational Mathematics: Solving Dual Fully Fuzzy Nonlinear Matrix Equations Numerically using Broyden’s Method

“…There are many authors have written about developing fuzzy analysis, significantly solving fully fuzzy linear and nonlinear systems. Different methods have been used to solve these two types of fully fuzzy systems, including a method for computing the positive solution of a fully fuzzy linear system (Ezzati et al, 2012); a method used to solve a fully fuzzy linear system via decomposing the symmetric coefficient matrix into two equations systems with the Cholesky method (Senthilkumar and Rajendran, 2011); the Jacobi iteration method for solving a fully fuzzy linear system with fuzzy arithmetic (Marzuki, 2015) and triangular fuzzy number (Megarani et al, 2022); a method for finding a positive solution for an arbitrary fully fuzzy linear system with a one-block matrix (Malkawi et al, 2015a); the singular value decomposition method for solving a fully fuzzy linear system (Marzuki et al, 2018); the Gauss-Seidel method for solving a fully fuzzy linear system via alternative multi-playing triangular fuzzy numbers (Deswita and Mashadi, 2019); the Jacobi, Gauss-Seidel, and SOR iterative methods for solving linear fuzzy systems (Inearat and Qatanani, 2018);a linear programming approach utilizing equality constraints to find non-negative fuzzy numbers (Otadi and Mosleh, 2012); combining interval arithmetic with trapezoidal fuzzy numbers to solve a fully fuzzy linear system (Siahlooei and Fazeli, 2018); using an ST decomposition with trapezoidal fuzzy numbers to solve dual fully fuzzy linear systems via alternative fuzzy algebra (Safitri and Mashadi, 2019), using LU factorizations of coefficient matrices for trapezoidal fuzzy numbers to solve dual fully fuzzy linear systems (Marni et al, 2018); combining QR decomposition with trapezoidal fuzzy numbers (Gemawati et al, 2018); and using an ST decomposition with trapezoidal fuzzy numbers to solve a dual fully fuzzy linear system (Jafarian, 2016). In the case of fully fuzzy linear matrix equations, several studies have identified methods for solving them, including a method that utilizes fully fuzzy Sylvester matrix equations (Daud et al, 2018;Elsayed et al, 2022;He et al, 2018;Malkawi et al, 2015b), and a method that finds fuzzy approximate solutions (Guo and Shang, 2013).…”