Linear interval tolerance problem and linear programming techniques (Q1597633)

Let \([A]x= [b]\) be an \(n\)-dimensional system of linear interval equations. Then \(\Sigma_{\forall\exists}\) denotes the set of all \(x\in\mathbb{R}^n\) such that to any \(A\in [A]\) there exists a \(b\in [b]\) with \(Ax= b\). Two different subsets, \(S_1\) and \(S_2\) of \(\Sigma_{\forall\exists}\) which were defined by \textit{J. Rohn} [Lect. Notes Comput. Sci. 212, 157-158 (1986; Zbl 0588.65024)] are rewritten. Then the simplex algorithm together with an appropriate cost function is applied to find optimal interval vectors which are contained in \(S_1\) or \(S_2\).