An algorithm for solving two-sided interval system of max-plus linear equations

We study six types of solutions (weak, strong, tolerance, control, Left-localized, and Right-localized solutions) to a two-sided interval system of max-plus linear equations with the same vector of variables on both sides of the equations and obtain their corresponding solvability conditions. These conditions are in the form of two-sided systems of max-plus linear inequalities which can be derived as a union of a number of interval inclusion linear systems. Therefore, we could work on the interval inclusion linear systems, instead of directly solving these six types of solutions themselves. An optimization problem with the two-sided interval system of max-plus linear constraints may be solved using the convexity of each solution set of the interval inclusion linear systems.