The general algebraic solution of fuzzy linear systems based on a block representation of {1}-inverses

A new method for solving a fuzzy linear system (FLS), $A\tilde X=\tilde Y$, where the coefficient matrix $A$ is an arbitrary real matrix is obtained. A necessary and sufficient condition for the ${\cal R}$-consistency of the associated system of linear equations is obtained, related to itsrepresentative solutions.  Moreover, the general form of representative solutions of such linear systems is presented. The straightforward method for solving $m\times n$ FLS based on an arbitrary $\{1\}$-inverse of $A$ is introduced. This method is illustrated by interesting examples.