Selecting Uncertainty Calculi and Granularity: An Experiment in Trading-off Precision and Complexity

The management of uncertainty in expert systems has usually been left to ad hoc representations and rules of combina­ tions lacking either a sound theory or clear semantics. The objective of this paper is to establish a theoretical basis for defining the syntax and semantics of a small subset of calculi of uncertainty operating on a given term set of linguistic statements of likelihood. Each calculus will be defined by specifying a negation, a conjunction and a disjunction operator. Families of Triangular norms and conorms will provide the most general representations of conjunction and disjunction operators. These families provide us with a formalism for defining an infinite number of different calculi of uncertainty. The term set will define the uncertainty granularity, i.e. the finest level of distinction among different quantifications of uncertainty. This granularity will limit the ability to differentiate between two similar operators. Therefore, only a small finite subset of the infinite number of calculi will produce notably different results. This result is illustrated by an experi­ ment where nine different calculi of uncertainty are used with three term sets containing five, nine, and thirteen elements, respectively.