  We consider a fuzzy linear system with crisp coefficient matrix and with an
arbitrary fuzzy number in parametric form on the right-hand side. It is known
that the well-known existence and uniqueness theorem of a strong fuzzy solution
is equivalent to the following: The coefficient matrix is the product of a
permutation matrix and a diagonal matrix. This means that this theorem can be
applicable only for a special form of linear systems, namely, only when the
system consists of equations, each of which has exactly one variable. We prove
an existence and uniqueness theorem, which can be use on more general systems.
The necessary and sufficient conditions of the theorem are dependent on both
the coefficient matrix and the right-hand side. This theorem is a
generalization of the well-known existence and uniqueness theorem for the
strong solution.
