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.

In this paper, a new approach to determine the numerical solution of two-dimensional fuzzy Fredholm integral equation of the second kind (2DFFIE2) is proposed. This method is based on the fuzzy bivariate Bernstein polynomials. By using fuzzy bivariate Bernstein polynomials, a 2DFFIE2 can be transformed to a dual fuzzy linear system. The error estimate of this method is presented in terms of the...

in this paper, a novel hybrid method based on learning algorithmof fuzzy neural network and newton-cotesmethods with positive coefficient for the solution of linear fredholm integro-differential equation of the second kindwith fuzzy initial value is presented. here neural network isconsidered as a part of large field called neural computing orsoft computing. we propose alearning algorithm from ...

In this paper, we consider the fuzzy Sylvester matrix equation AX + XB = C, where A ∈ Rn×n and B ∈ Rm×m are crisp M-matrices, C is an n×m fuzzy matrix and X is unknown. We first transform this system to an (mn)× (mn) fuzzy system of linear equations. Then we investigate the existence and uniqueness of a fuzzy solution to this system. We use the accelerated overrelaxation method to compute an ap...

A new approach for pole placement of nonlinear systems using state feedback and fuzzy system is proposed. We use a new online fuzzy training method to identify and to obtain a fuzzy model for the unknown nonlinear system using only the system input and output. Then, we linearized this identified model at each sampling time to have an approximate linear time varying system. In order to stabilize...

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...

A‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. For this reason, many researchers have used various numerical methods to solve fuzzy linear systems. In this paper, we define the concepts of midpoint a...

In paper the fuzzy linear system d x C x A ~ ~ ~   where A and C are crisp matrices and n m  d~ is a LR fuzzy numbers vector, is investigated in detail. We generalize the definition and arithmetic operations of LR fuzzy numbers and convert the dual fuzzy linear system to two crisp systems of linear equations. Then the minimal fuzzy solution of the original fuzzy system is obtained by solving...

Systems of linear equations, with uncertainty on the parameters, play a major role in various problems in economics and finance. Fuzzy system of linear equations has been discussed in [1] using LU decomposition when the matrix A in Ax = b is a crisp matrix. Also the Adomian decomposition method and iterative methods have been studied in [2, 6] for fuzzy system of linear equations. In this paper...