A quantitative treatment of multilevel specificity and certainty in variable precision reasoning

The authors develop a methodology for reasoning about the state of the environment based on evidence received from some source. It is assumed that the evidence is expressed as a probability mass function defined on a discrete set of mutually exclusive hypotheses about the state of the environment. Given that the quality of the evidence is variable, it follows that the precision of the reasoning process must also vary. That is, the level of specificity and the certainty associated with decisions made at that level depend directly on the quality of the evidence. An indistinguishability measure is used to generate a core set of aggregate focal elements, each of which may consist of logical disjunctions of the basic hypothesis set. The measure takes into account both the differences in support levels for the hypotheses and the degree to which they are similar. Partial dominance is then used to associate a basic probability assignment on the core set. This approach makes it possible to apply simple, quantitative methods to express the variations in the precision associated with decisions. The result is a set of aggregate hypotheses and their support levels which become input to the classification process. In most cases, multiple sets of aggregate hypotheses will be used in an evidential classification scheme to produce a composite characterization of the environment.<>