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, respectively. Hence for solving equations or system of equations, we must use methods without using inverse operators. In this paper, we propose a novel method to find the nonzero solutions of fully fuzzy linear syst...

In this paper, we propose the least-squares method for computing the positive solution of a m × 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 the non...

Abstract: This paper proposes new matrix methods for solving positive solutions for a positive Fully Fuzzy Linear System (FFLS). All coefficients on the right hand side are collected in one block matrix, while the entries on the left hand side are collected in one vector. Therefore, the solution can be gained with a non-fuzzy common step. The necessary theorems are derived to obtain a necessary...

We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System (FFLS) of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an FFLS with a nonnegative coefficient matrix, we consider an equivalent FFLS by using an appropriate permutation to simplify fuzzy multiplications. To solv...

the sst decomposition method for solving system of linear equations make it possible to obtain the values of roots of the system with the specified accuracy as the limit of the sequence of some vectors. in this topic we are going to consider vectors as fuzzy vectors. we have considered a numerical example and tried to find out solution vector x in fuzzified form using method of sst decomposition.

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 SST decomposition method for solving system of linear equations make it possible to obtain the values of roots of the system with the specified accuracy as the limit of the sequence of some vectors. In this topic we are going to consider vectors as fuzzy vectors. We have considered a numerical example and tried to find out solution vector x in fuzzified form using method of SST decomposition.