  In this paper, linear systems with a crisp real coefficient matrix and with a
vector of fuzzy triangular numbers on the right-hand side are studied. A new
method, which is based on the geometric representations of linear
transformations, is proposed to find solutions. The method uses the fact that a
vector of fuzzy triangular numbers forms a rectangular prism in n-dimensional
space and that the image of a parallelepiped is also a parallelepiped under a
linear transformation. The suggested method clarifies why in general case
different approaches do not generate solutions as fuzzy numbers. It is
geometrically proved that if the coefficient matrix is a generalized
permutation matrix, then the solution of a fuzzy linear system (FLS) is a
vector of fuzzy numbers irrespective of the vector on the right-hand side. The
most important difference between this and previous papers on FLS is that the
solution is sought as a fuzzy set of vectors (with real components) rather than
a vector of fuzzy numbers. Each vector in the solution set solves the given FLS
with a certain possibility. The suggested method can also be applied in the
case when the right-hand side is a vector of fuzzy numbers in parametric form.
However, in this case, -cuts of the solution can not be determined by geometric
similarity and additional computations are needed.
