On the Approximation of Linear AE-Solution Sets

Abstract

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 quantifications of the parameters in their domains. In particular, 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 (intervals whose bounds are not constrained to be ordered increasingly) is presented in a new and unifying way. Then two new generalized interval operators dedicated to the approximation of quantified linear interval systems are proposed and investigated.