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A set-based Bayesianism is an extension and a more general form of convex Bayesianism and intervalism. The method does not require the conditions of unique real-valued probability function in any decision-making context and of convexity for a set-based representation. Levi's E-admissibility decision criterion, applicable to the nonconvex case as well, is used. A set-based Bayesianism represents uncertainty by a set of classical probability functions.

An algebra is presented for a simple probabilistic data model that may be regarded as an extension of the standard relational model. The probabilistic algebra is developed in such a way that (restricted to [alpha]-acyclic database schemes) the relational algebra is a homomorphic image of it. Strictly probabilistic results are emphasized. Variations on the basic probabilistic data model are discussed. The algebra is used to explicate a commonly used statistical smoothing procedure and is shown to be potentially very useful for decision support with uncertain information.