A computer-implemented decision device and a family of methods and procedures are used for representing and analyzing imprecise, vague, and incomplete probabilistic decision and risk problems and/or when a criteria hierarchy is present. Decision makers can state the problems simply with the precision the decision-makers feel they have evidence for. Probabilities, values (utilities), criteria weights with belief distributions over them, and optimization procedures for fast evaluation of decision rules with respect to such statements are determined and analyzed.

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> Automated trading system in an electronic trading exchange

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