Interval max-plus matrix equations

This paper deals with the solvability of interval matrix equations in max-plus algebra. Max-plus algebra is the algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗, where a⊕b=max⁡{a,b}a⊕b=max⁡{a,b} and a⊗b=a+ba⊗b=a+b.The notation A⊗X⊗C=BA⊗X⊗C=B represents an interval max-plus matrix equation, where A, B, and C are given interval matrices. We define four types of solvability of interval max-plus matrix equations, i.e., the tolerance, weak tolerance, left-weak tolerance, and right-weak tolerance solvability. We derive the necessary and sufficient conditions for checking each of them, whereby all can be verified in polynomial time.