This paper is dealing with solvability of interval systems of linear equations in max-min algebra. Max-min algebra is the algebraic structure in which classical addition and multiplication are replaced by ⊕ and \kr, where a⊕b=max{a,b},a\krb=min{a,b}. The notation \mbfA\krx=\mbfb represents an interval system of linear equations, where \mbfA=[\pA,\nA] and \mbfb=[\pb,\nb] are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 and T5 solvability and give necessary and sufficient conditions for them.
Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by ⊕ and \kr, where a⊕b=max{a,b},a\krb=min{a,b}. The notation \mbfA\kr\mbfx=\mbfb represents an interval system of linear equations, where \mbfA=[\pA,\nA], \mbfb=[\pb,\nb] are given interval matrix and interval vector, respectively, and a solution is from a given interval vector \mbfx=[\px,\nx]. We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them.
In this paper, we shall deal with the 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 \kr, where a⊕b=max{a,b}, a\krb=a+b. The notation \mbfA\krx=\mbfb represents an interval system of linear equations, where \mbfA=[\pA,\nA] and \mbfb=[\pb,\nb] are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and give an algorithm for checking the T4 solvability.