Summary: First, we find the solution of the system \(A*X\leq b\), where \(A\), \(b\) are the known suitable matrices and \(X\) is the unknown matrix over a pseudo-Boolean lattice. Then its application to find the solution of some fuzzy linear systems as well as finding the solution of the optimization problem \(Z= \max\{C*X\mid A* X\leq b\}\) is discussed.