Several modelsfor handlingvagueand impreciseinformation in decision situations havebeensuggested.In those contexts, various interval methodshaveprevailed, i.e. methodsbasedoninterval estimatesof probabilities and,in somecases, interval utility estimates. Evenif these approachesin generalare wellfounded,little has beendone for demonstratingwhetherthe approachesare comprehensible for a decisionmaker.In particular, it is far fromalways clear whatis actuallyexpressedbya set of intervals where linear dependenciesdooccur.Furthermore,it is difficult to find reasonabledecisionrules that select an alternativeout of a set of alternativesandcorrespondto the intuition of a decisionmaker.In this article, weinvestigatesomeproblems that are inherentin interval approachesandsuggesthowthe choiceof particular evaluationrules mightcompensatefor this.