Methods for reasoning with imprecise probabilities in intelligent decision systems

An approach to developing an analytically based methodology for effectively automating and supporting reasoning in environments characterized by uncertainty, imprecision, and vagueness is presented. The approach is applied to three cases. For one of the cases the procedure provides a reasoning system capable of completely distinguishing among alternatives (a total order is generated on the space of alternatives). However, it does not provide confidence statements on the selection. For another case the procedure provides a user with complete confidence in the set of alternatives selected, but might only provide a partial order on the set of alternatives. Procedures for providing intermediate values of confidence and distinguishability are needed in both cases. For the third case, methods that would represent important advances to existing capabilities for managing imprecision are needed. Six extensions of the procedures are presented