On Unbounded Tolerable Solution Sets

Abstract

We prove that the nonempty tolerable solution set of the interval linear system Ax = b is unbounded if and only if the interval matrix of the system has linearly dependent degenerate columns. Also, we prove that the tolerable solution set may be represented as a sum of the linear subspace {c e ℝn ∨ Ac = 0} and a bounded convex polyhedron and propose a way for suitable estimation of unbounded tolerable solution sets.