Linear systems have important applications to many branches of Science and Engineering. In many applications, atleast some of the parameters of the system are represented by fuzzy rather than crisp numbers. This paper, discusses fully fuzzy linear systems with triangular fuzzy numbers. A matrix inversion method is proposed for solving Fully Fuzzy Linear System (FFLS) of equations. Finally, the ...

As can be seen from the definition of extended operations on fuzzy numbers, subtraction and division of fuzzy numbers are not the inverse operations to addition and multiplication . Hence, to solve the fuzzy equations or a fuzzy system of linear equations analytically, we must use methods without using inverse operators. In this paper, a novel method to find the solutions in which 0 is not the ...

A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and GaussSeidel methods on approximating the solution of FFLS. Keywords—fully fuzzy line...

in this paper, we investigate the general fuzzy linear system of equations.  the  main aim of this paper is based on the embedding approach. we find the necessary and sufficient conditions for the existence of fuzzy solution of the mentioned systems.  finally, numerical examples are presented to more illustration of the proposed model.

In cite{beh}, the authors claimed by a counterexample that the cross product definition in cite{molo} is not correct and thus the proposed technique is false. In this note, we show that this assertion is ‎incorrect.

In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming (abbreviated to FFLP) problems. Also, we employ linear programming (LP) with equality constraints to find a non-negative fuzzy number vector x̃ which satisfies Ãx̃ = b̃, where à is a fuzzy number matrix. Then we investigate the existence of a positive solution of fully fuzzy linear system (...

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, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. numerical examples are presented to illustrate the proposed method.

In this paper, we propose a method to obtain fuzzy solutions of duality fully fuzzy linear system (DFFLS) of the form ÃX̃ = B̃X̃ + C̃, where Ã, B̃ are fuzzy matrices and C̃, X̃ are fuzzy number vectors. To this end, we solve the 1-cut of DFFLS (which is a crisp system here) ,then some unknown spreads are allocated to any row of a 1-cut of dual fully fuzzy linear system in 1-cut position. Also, by usin...

Several authors have proposed different methods to find the solution of fully fuzzy linear programming (FFLP) problems. But all the existing methods are based on the assumption that all the fuzzy coefficients and the fuzzy variables are non-negative fuzzy numbers. in this paper a new method is proposed to solve an FFLP problems with arbitrary fuzzy coefficients and arbitrary fuzzy variables, th...