Possibilistic approach to Bayes decisions

Abstract

The decision problems are considered when the prior probabilistic information about the state of nature and decision maker`s utility function are imprecisely defined. In such a case the risks (or the expected utility) of considered decisions are also imprecisely defined. We propose two-step procedure for finding the optimal decision. First, we order possible decisions using the lambda-average ranking method by Campos and Gonzalez. Then we use possibilistic possibility of dominance and necessity of strict dominance indices proposed by Dubois and Prade for the comparison of consequences of the most promising solutions.