A QUANTITATIVE TREATMENT OF MULTILEVEL SPECIFICITY AND UNCERTAINTY INVARIABLE PRECISION REASONING

Decision making under uncertainty requires that we mason about the tru e nature of the environment using perceived information that is usuall y incomplete and often ambiguous. Consequently, the reasoning process varies with the quality of the evidence the decision maker receives. I f the evidence can be represented as a probability mass function defin ed on the discrete set of hypotheses about the environment, then its q uality is dependent upon its ability to suggest clear choices among th e hypotheses. This is measured by the use of an indistinguishability m easure that focuses on the degree to which the hypotheses are similar to each other and the closeness of their probability support levels. T he two aspects of variable precision reasoning, specificity and certai nty, are addressed through the transformation of the basic probability mass function on the set of hypotheses into a belief function. The be lief function core set consists of aggregate disjunctive sets of hypot heses that reflect the degree of specificity present in the evidence. The set of basic probability assessments on the core establishes the d egree of certainty associated with the derived level of specificity. T he aggregation process is accomplished by applying the indistinguishab ility measure to the set of hypotheses. The core set is grown iterativ ely using binary set representations of the focal elements. The basic probability assessments are calculated using a fuzzy partial dominance measure that diffuses belief in a focal element in proportion to the number of basic hypotheses it is dose to.