Inherited LU factorization for solving fuzzy system of linear equations

Araghi, Mohammad Ali Fariborzi; Fallahzadeh, Amir

doi:10.1007/s00500-012-0908-3

Cited by 13 publications

(9 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…. + a nn x n = y n , (1.1) where the coefficient matrix A = (a ij ) is a crisp matrix and y i is a fuzzy number, 1 6 i, j 6 n. Many authors study numerical methods for solving FLS (1.1), such as Abbasbandy, Ezzati and Jafarian [1][2][3]9], Allahviranloo [4][5][6], Dehghan and Hashemi [8], Fariborzi Araghi and Fallahzadeh [10], Li, Li, and Kong [14], Miao, Wang, Zheng, and Yin [15,[18][19][20][21], Nasser, Matinfar, and Sohrabi [16], and Zhu, Joutsensalo, and Hämäläinen [22]. Some applications lead to the linear system (1.1) with an M -matrix A. Hashemi, Mirnia, and Shahmorad [12] solved the fuzzy linear system whose coefficient matrix is an M -matrix by using the Schur complement.…”

Section: Introductionmentioning

confidence: 99%

M-Preconditioner for Solving Fuzzy Linear Systems

Dai

Wang

2015

Comput Math Model

View full text Add to dashboard Cite

An M -preconditioner is provided for solving fuzzy linear systems whose coefficient matrices are crisp M -matrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the M -preconditioned conjugate gradient ( M PCG) method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

show abstract

Section: Introductionmentioning

confidence: 99%

M-Preconditioner for Solving Fuzzy Linear Systems

Dai

Wang

2015

Comput Math Model

View full text Add to dashboard Cite

show abstract

“…Amirfakhrian in [21] considered the FSLEs by fuzzy distance, in [22] he presented the numerical solution of the FSLEs in the polynomial parametric form, and in [23] he studied the fuzzy matrix equations. Fariborzi Araghi et al in [24] applied the inherited LU factorization, Mikaeilvand and Noeiaghdam in [25][26][27] discussed the fuzzy linear matrix equations, general solutions of m × n fuzzy linear systems, and least square solutions of inconsistent fuzzy linear matrix equations. Furthermore, Wang and Zheng illustrated the inconsistent and general fuzzy linear systems in [28,29].…”

Section: Introductionmentioning

confidence: 99%

A Novel Technique to Solve the Fuzzy System of Equations

Mikaeilvand

Noeiaghdam

et al. 2020

Mathematics

View full text Add to dashboard Cite

The aim of this research is to apply a novel technique based on the embedding method to solve the n × n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created n × n crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created n × n crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectors.

show abstract

“…Inherited basis functions was introduced by the authors in [16,17]. Also, the inherited LU factorization was applied for solving fuzzy system of linear equations in [18]. At first in section 2, we remind some preliminaries of fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%