An ambiguous decision tree model based on nonadditive probabilities

Decision tree method is a common approach in classic decision theory. Its major advantage resides in provides a powerful formalism for representing comprehensible decision problems often easy to interpret. However, the theoretic foundations of it are v-N-M utilities and Savage's subjective probabilities, which are uneasy to cope with data pervaded with uncertainty both at the construction and computation phase. This paper extends the standard decision tree technique to an ambiguous environment where the subjective probability about nature is represented by nonadditive probability, which we name as ambiguous decision tree model. First, we analyze the reason why we introduce nonadditive probabilities into traditional decision tree technique, then, introduce some preliminaries of nonadditive probabilities. Finally, we present the modeling procedure and the algorithm of it. By this model we can describe the ambiguous decision problems more rationally.