In this paper, we propose the least-squares method for computing the positive solution of a $mtimes n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of ...

Copyright © 2013 X. Guo and D. Shang.This is an open access article distributed under theCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The fuzzy matrix equations ?̃?⊗?̃?⊗?̃? = ?̃? in which ?̃?, ?̃?, and ?̃? arem×m, n×n, andm×n nonnegative LR fuzzy numbers matrices, respectively, are invest...

In this article, we introduce ST decomposition procedure to solve fully fuzzy linear systems. This paper mainly to discuss a decomposition of non singular fuzzy matrix, Symmetric times triangular(ST) decomposition. Every non singular fuzzy matrix can be represented as a product of symmetric matrix S and triangular matrix T in the form of trapezoidal fuzzy number matrices. By this method, we obt...

‎in this paper‎, ‎we propose two preconditioned aor iterative methods to solve systems of linear equations whose coefficient matrices are z-matrix‎. ‎these methods can be considered as improvements of two previously presented ones in the literature‎. ‎finally some numerical experiments are given to show the effectiveness of the proposed preconditioners‎.‎

different methods have been proposed for finding the non-negative solution of fully fuzzy linear system (ffls) i.e. fuzzy linear system with fuzzy coefficients involving fuzzy variables. to the best of our knowledge, there is no method in the literature for finding the non-negative solution of a ffls without any restriction on the coefficient matrix. in this paper a new computational method is ...

in this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. this paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (st) decomposition. by this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix s and a fuzzy triangular matrix t.

The main aim of this paper intends to discuss the solution of fuzzy Sylvester matrix equation AX +XB = C where A = (aij) ∈ Rn×n , B = (bij) ∈ Rm×m are crisp Mmatrices, C = (cij) ∈ Rn×m is fuzzy matrix and X ∈ Rn×m is unknown,by applying a special algorithm based on a class of ABS algorithms called Huang algorithm. At first, we transform this system to an (mn)×(mn) fuzzy system of linear equatio...

The fuzzy matrix equations AX̃ = Ỹ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the e...

Fuzzy systems of linear equations play a vital role in various applications of engineering, science and finance problems. This paper proposes a new method for solving Fully Fuzzy System of Linear Equations (FFSLE) using the linear programming problem approach. There is no restriction on the elements of coefficient matrix. The proposed method is able to solve the system, when the elements of the...