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 = 〈 A , A ¯ 〉 , b = 〈 b , b ¯ 〉 are given interval matrix and interval vector, respectively, and a solution is from a given interval vector x = 〈 x , 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.