Tolerance and Control Solutions of Two-Sided Interval Linear System and Their Applications

This work investigates tolerance and control solutions to a two-sided interval linear system. Their semantics are different, even though, we would be able to interchange the role of the interval information algebraically. We present necessary and sufficient conditions of their solvabilities as the inequalities depending on center and radius of coefficient interval matrices on both sides of the system. In a situation when the vector of variables is nonnegative, the conditions can simply be modified as the inequalities depending on boundaries of the interval matrices. This result helps to find out the feasible solutions of a quadratic programming problem with two-sided interval linear equation constraints.