Solving arbitrary fully fuzzy Sylvester matrix equations and its theoretical foundation

Two-stage Algorithm for solving Arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations

“…Recently, authors in [11] considered the solution of TrFFSME by transforming the TrFFSME to a system of crisp linear equations where the positive and negative fuzzy solutions are obtained by applying Vec-operator and Kronecker product method. TFFSME with arbitrary coefficients has been studied by Daud et al, [9][10][11][12] using fuzzy Vec-operator and Kronecker products. However, these methods need further modifications as the Vec-operator and Kronecker product method is not applicable for arbitrary fuzzy systems with near-zero fuzzy numbers.…”

Solving Bipolar Fully Fuzzy Sylvester Matrix Equations With Negative Fuzzy Numbers

“…In a preliminary study, Daud et al (2016) utilized the method proposed by Malkawi et al (2015) to compare FSME to FFSME. Following that, Daud et al (2018) extended the method to solve FFSME with arbitrary coefficients by modifying the associated linear system described in Malkawi et al (2015), given that FFSME involves positive coefficients. Several years later, Elsayed et al (2020) and Elsayed et al (2022) applied a similar method as Malkawi et al (2015) and Daud et al (2018) to address FFSME with positive negative coefficients and extended it to handle arbitrary generalized FFSME for trapezoidal fuzzy numbers, respectively.…”

“…proach of the embedding technique, which ct and Vec-operator. Malkawi et al (2015) y equations such that Fully Fuzzy Sylvester e Kronecker product, Vec-operator and an l. ( 2016) utilized the method proposed by wing that, Daud et al (2018) extended the ying the associated linear system described e coefficients. Several years later, Elsayed od as Malkawi et al (2015) and Daud et al ients and extended it to handle arbitrary ely.…”

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

“…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).…”

“…Since the beginning of the 21 st century, several experts have discussed the problem of fuzzy equation systems with various methods to solve them. Some of them are Daud et al (2018), Elsayed et al (2022). Guo and Shang (2013), He et al (2018), Malkawi et al (2015b), Ramli et al (2010), and Jafarian and Jafari (2019).…”