We present theoretical foundations and computational procedures of a theory for analyzing decisions under risk, when the available information is vague and imprecise. The impreciseness is expressed by a set of global distributions T over a set of space S, where the latter represents the classes of all probability and utility measures over a set of discrete outcomes. We show how local distributions, i.e. distributions over projections of S on various subspaces of S, can be derived from T and introduce consistency measures expressing the extent into which user-asserted local distributions can be used for defining T. The evaluation model used is based on the expected utility, but this is not a necessary restriction. The approach allows a decision maker to be as deliberately imprecise as she feels natural, as well as provide her with the means for expressing varying degrees of imprecision in the input sentences.
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