An algorithm for testing T5 solvability of max-plus interval systems

Max-plus algebra is the algebraic structure in which classical addition and multiplication are replaced by a circle plus b = max{a, b} and a circle times b = a + b, respectively. Each system of linear equation in max-plus algebra we can write in the matrix form A circle times x = b, where A and b are matrix and vector of suitable size. If we replace the matrix elements with matrix interval A = [(A) under bar, (A) over bar] and vector elements by vector interval b = [(b) under bar, (b) over bar], we get an interval system of linear equations. We can define several types of solvability of interval systems in max-plus algebra. In this paper, we shall deal with one of them, the so called T5 solvability. We give the algorithm which answers the question whether the given interval system is T5 solvable or not.