Interval max-plus systems of linear equations

In this paper, we shall deal with solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by circle plus and circle times, where a circle plus b = max{a, b}, a circle times b = a + b. The notation A circle times x = b represents an interval system of linear equations, where A = ((A) under bar, (A) over bar), b = ((b) under bar, (b) over bar) are given interval matrix and interval vector, respectively, and a solution is from a given interval vector x = ((x) under bar, (x) over bar). We can define several types of solvability of interval systems. In this paper, we define six types of solvability of interval max-plus systems of linear equations and give necessary and sufficient conditions for them. (C) 2012 Elsevier Inc. All rights reserved.