Stable embedding of ill-posed linear equality and inequality systems into fuzzified systems (Q1189904)

The classical linear problem of the form \[ \sum^ n_{j=1}\alpha_{ij}x_ j=\alpha_{i0},\quad i=1,2,\dots,m,\qquad\sum^ n_{j=1}\alpha_{ij}x_ j\leq\alpha_{i0},\quad i=m,2,\dots,s \] with the real parameters \(\alpha_{ij}\in{\mathbf R}\) is generalized by treating these parameters as fuzzy numbers. The paper shows that this generalization provides regularization capabilities to otherwise ill-posed problem. It is also shown that a suitable selection of the parameters and \(t\)-norms guarantees the well-posedness of the linear system generalized in this manner.