On the Approximation of Linear AE-Solution Sets
Alexandre Goldsztejn, Gilles Chabert · 2006
When considering systems of equations, it often happens that parameters are known with some uncertainties. This leads to continua of solutions that are usually approximated using the interval theory. A wider set of useful situations can be modeled if one allows furthermore different quan- tifications of the parameters in their domains. In particu- lar, quantified solution sets where universal quantifiers are constrained to precede existential quantifiers are called AE- solution sets. A state of the art on the approximation of linear AE- solution sets in the framework of generalized intervals (in- tervals whose bounds are not constrained to be ordered in- creasingly) is presented in a new and unifying way. Then two new generalized interval operators dedicated to the ap- proximation of quantified linear interval systems are pro- posed and investigated.