Incoherence Correction and Decision Making Based on Generalized Credal Sets

While making decisions we meet different types of uncertainty. Recently the concept of generalized credal set has been proposed for modeling conflict, imprecision and contradiction in information. This concept allows us to generalize the theory of imprecise probabilities giving us possibilities to process information presented by contradictory (incoherent) lower previsions. In this paper we propose a new way of introducing generalized credal sets: we show that any contradictory lower prevision can be represented as a convex sum of non-contradictory and fully contradictory lower previsions. In this way we can introduce generalized credal sets and apply them to decision problems. Decision making is based on decision rules in the theory of imprecise probabilities and the contradiction-imprecision transformation that looks like incoherence correction.