Linear Interval Tolerance Problem and Linear Programming Techniques

In this paper, we consider the linear interval tolerance problem, which consists of finding the largest interval vector included in Σ∀,∃([A], [b]) = {x ∈R | ∀A ∈ [A], ∃b ∈ [b], Ax = b}. We describe two different polyhedrons that represent subsets of all possible interval vectors inΣ∀,∃([A], [b]), and we provide a new definition of the optimality of an interval vector included in Σ∀,∃([A], [b]). Finally, we show how the Simplex algorithm can be applied to find an optimal interval vector in Σ∀,∃([A], [b]).