Interval strong solutions of interval systems of max-plus linear equations

This paper considers the existence and uniqueness of interval strong solutions of interval systems of max-plus linear equations. A necessary and sufficient condition for the existence of interval strong solutions is presented. The proof of the existence of interval strong solutions is constructive and results in a formula for computing such solutions. A necessary and sufficient condition for the uniqueness of interval strong solutions is established by testing the unique solvability of a finite number of subsystems rather than all subsystems. On this basis, a polynomial algorithm is developed to verify the uniqueness of interval strong solutions.