Interval max-plus systems of linear equations

Abstract

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 ⊕ and ⊗, where a⊕b=max{a,b},a⊗b=a+b.The notation A⊗x=b represents an interval system of linear equations, where A=〈A̲,A¯〉, b=〈b̲,b¯〉 are given interval matrix and interval vector, respectively, and a solution is from a given interval vector x=〈x̲,x¯〉. 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.